1

Energy

ManySlidesAre FromProfTomMurphy(withPermission)ThankYouProfMurphy

Course Preview the Big Picture

bull We use a heck of a lot of energyndash primitive society uses lt 100 W of power per personndash our modern society burns 10000 W per personndash surely not in our homes Where is this going on

bull Energy availability has enabled us to focus onhigher-level issues as a societyndash artndash sciencendash home shopping network

2

bull Long ago almost all of our energy came fromfood (delivering muscle power) and almost all ourenergy went into securing food for ourselves

bull Enter the work animal supplementing our musclepower and enabling larger-scale agriculture

bull Next burn wood to run boilers trainsbull 150 years ago muscular effort and firewood

provided most of our energymdashand today this isless than 1 of the story

bull Today much more energy goes intogrowingharvesting food than comes out of food

bull Today in US 86 of our energy comes from fossilfuels (oilnatural gas coal)

Fuzzy on the concept of energy

bull Donrsquot worrymdashwersquoll cover that

3

A note on graphs log vs linearbull Many graphs are on logarithmic scales watch for thisbull This condenses wide-ranging information into a compact

areabull Pay attention because you could warp your intuition if you

donrsquot appreciate the scalebull Log scales work in factors of tenbull A given vertical span represents a constant ratio (eg

factor of ten factor of two etc)bull An exponential increase looks like a straight line on a

logarithmic scale

4

Example Plots

Exponential plot is curved on linear scale and straight on a logarithmic scale

5

A brief history of fossil fuels

bull Here today gone tomorrowbull What will our future hold

ndash Will it be back to a simple lifendash Or will we find new ways to produce all the energy we wantndash Or will it be somewhere in the middle

GlobalEnergyWhereDoes itComeFrom

72287Hydroelectric

then radiatedaway2000000

Sun Abs byEarth

0008003Solar Direct003013Wind01305Geothermal0416

Biomass(burning)

6626Nuclear Energy

22589Natural Gas23292Coal400158Petroleum

Percent ofTotal

1018 Joulesyr(~QBtuyr)Source

Ultimately derivedfrom our sun

Courtesy DavidBodansky (UW)

Btu=1055kJ

6

7

Why do we use so much energy

8

9

We live in a special time and placehellipbull We use almost 100 times the amount used by the rest of the

world (by population)bull This phase has only lasted for the last century or sobull Most of our resources come from fossil fuels presently and

this has a short finite lifetimebull Fossil fuels formed from solar energy over 300 million

years will be used up in a few centuries

2000 2500 3000 3500 4000150010005000

year

ener

gy u

sage

10

Energy the capacity to do work

bull This notion makes sense even in acolloquial contextndash hard to get work done when yoursquore wiped out

(low on energy)ndash work makes you tired yoursquove used up energy

bull But we can make this definition of energymuch more precise by specifying exactlywhat we mean by work

Work =Energy more than justunpleasant tasks

bull In physics the definition of work is the application of aforce through a distance Energy is needed to do it

W = Fd

bull W is the work done = energy usedbull F is the force appliedbull d is the distance through which the force actsbull Only the force that acts in the direction of motion counts

towards work

11

Okay what is Force thenbull Force is a pushingpulling agentbull Examples

ndash gravity exerts a downward force on youndash the floor exerts an upward force on a ball during its bouncendash a car seat exerts a forward force on your body when you accelerate forward from

a stopndash the seat yoursquore sitting in now is exerting an upward force on you (can you feel it)ndash you exert a sideways force on a couch that you slide across the floorndash a string exerts a centrally-directed (centripetal) force on a rock at the end of a

string that yoursquore twirling over your headndash the expanding gas in your carrsquos cylinder exerts a force against the piston

Forces have Directionbull In all the previous examples force had a

direction associated with itbull If multiple forces act on an object they

could potentially add or cancel dependingon direction

Force 1Force 2

Total Force Force 1

Force 2

Total Force = 0

12

When net force is not zero

bull When an object experiences a non-zero net force it mustaccelerate

bull Newtonrsquos second lawF = ma Force = mass times acceleration

bull The same force makes a small object accelerate more thanit would a more massive objectndash hit a golf ball and a bowling ball with a golf club and see what

happens

QuestionA 150 lb person is standing still on the edge of a cliff Whatis the total force on the person

A zeroB 150 lbC Canrsquot say from this info

13

QuestionA 150 lb person jumps (or was he pushed) off a cliff and isfalling to their death What is the total force on the person

A zeroB 150 lbC Canrsquot say from this info

But what is acceleration

bull This is getting to be like the ldquohole in thebucketrdquo song but wersquore almost therehellip

bull Acceleration is any change in velocity(speed andor direction of motion)

bull Measured as rate of change of velocityndash velocity is expressed in meters per second (ms)ndash acceleration is meters per second per secondndash expressed as ms2 (meters per second-squared)

14

Putting it back together Units ofEnergy

bull Force is a mass times an accelerationndash mass has units of kilogramsndash acceleration is ms2

ndash force is then kgms2 which we call Newtons (N)

bull Work is a force times a distancendash units are then (kgms2)m = kg m2s2 = Nm = Joules (J)ndash One joule is one Newton of force acting through one meterndash Imperial units of force and distance are pounds and feet so unit of

energy is foot-pound which equals 136 J

bull Energy has the same units as work Joules

A Zoo of Unitsbull The main metric unit of energy is the Joule and most of

the world uses this but many others existbull The calorie is 4184 Joules

ndash raise 1 gram (cc) of water one degree Celsiusbull The Calorie (kilocalorie) is 4184 J (used for food energy)

ndash raise 1 kg (1 liter) of water one degree Celsiusbull The Btu (British thermal unit) is 1055 J (roughly 1 kJ) or

about 14 Calorie or chemical energy of one matchndash raise 1 pound of water one degree Fahrenheit

bull The kilowatt-hour (kWh) is 3600000 J = 3600 kJ or 860Calories (used for electrical energy)ndash one Watt (W) is one Joule per secondndash a kWh is 1000 W for one hour (3600 seconds)

bull Can also use ldquobarrel of oilrdquo ldquoton of coalrdquo 1000 cubic feetof natural gas gram of Uranium or amount of any energycontaining source etc

15

The Physics of Energy Formula List

bull Lots of forms of energy coming fast and furious but to putit in perspective herersquos a list of formulas

P = ΔEΔtPower (rate of energy use)

F = σT4 (temperature to the fourthpower times a constant)

Radiative energy flux

E = mc2 (mass times speed of lightsquared)

Mass energy

ΔE = cpmΔT (mass times change intemperature times heat capacity)

Heat Energy

E = mgh (mass times height times10ms2)

(Grav) Potential Energy

KE = frac12mv2 (mass times velocitysquared)

Kinetic Energy

W = Fd (Force times distance)Work

Energy FormulaEnergy Form

Kinetic Energybull Kinetic Energy the energy of motionbull Moving things carry energy in the amount

KE = frac12mv2

bull Note the v2 dependencemdashthis is whyndash a car at 60 mph is 4 times more dangerous than a car at 30 mphndash hurricane-force winds at 100 mph are much more destructive (4

times) than 50 mph gale-force windsndash a bullet shot from a gun is at least 100 times as destructive as a

thrown bullet even if you can throw it a tenth as fast as you couldshoot it

16

Numerical examples of kineticenergy

bull A baseball (mass is 0145 kg = 145 g) moving at 30 ms(67 mph) has kinetic energy

KE = frac12times(0145 kg)times(30 ms)2

= 6525 kgm2s2 asymp 65 J

bull A quarter (mass = 000567 kg = 567 g) flipped about fourfeet into the air has a speed on reaching your hand of about5 ms The kinetic energy is

KE = frac12times(000567 kg)times(5 ms)2

= 007 kgm2s2 = 007 J

More numerical examples

bull A 1500 kg car moves down the freeway at30 ms (67 mph)

KE = frac12times(1500 kg)times(30 ms)2

= 675000 kgm2s2 = 675 kJConvert to Calories 4184 kJ = 1 Calorie675 kJ (1 Calorie4184 kJ) = 161 Calorie

bull A 2 kg (~44 lb) fish jumps out of the waterwith a speed of 1 ms (22 mph)

KE = frac12times(2 kg)times(1 ms)2

= 1 kgm2s2 = 1 J

17

QuestionKinetic energy is E = 12 m v2 Which has more energy

A 10 kg object going 100 ms

B 100 kg object going 10 ms

C 1 kg object going 1000 ms

D 1000 kg object going 1 ms

1 ms = 22 mph

Gravitational Potential Energybull It takes work to lift a mass against the pull (force) of

gravitybull The force of gravity is mg where m is the mass and g is

the gravitational accelerationF = mg (note similarity to F = ma)

ndash g = 98 ms2 on the surface of the earth or 32 fts2

bull Lifting a height h against the gravitational forcerequires an energy input (work) of

ΔE = W = F h = mghbull Rolling a boulder up a hill and perching it on the edge of a

cliff gives it gravitational potential energy that can be laterreleased when the roadrunner is down below

bull Water in river or hydroelectric plant is using potentialenergy that it got from being lifted up when Sun (solarenergy) evaporated the water

18

QuestionPotential energy is E = 10 m h (metric units) Which hasmore energy

A 1 ton of water at a height of 100 ft

B 100 tons of water at a height of 1 ft

C 200 lb (110 ton) of water at 1000 ft

D All of the above have same energy

1 ms = 22 mph

First Example of Energy Exchangebull When the boulder falls off the cliff it picks up

speed and therefore gains kinetic energybull Where does this energy come from

rArr from the gravitational potential energybull The higher the cliff the more kinetic energy the

boulder will have when it reaches the ground

mgh

becomes

frac12mv2

Energy is conserved sofrac12mv2 = mgh

Can even figure out v since v2 = 2gh

h

19

Examples of GravitationalPotential Energy

bull How much gravitational potential energy does a70 kg high-diver have on the 10 meter platform

mgh = (70 kg)times(10 ms2)times(10 m)= 7000 kgm2s2 = 7 kJ

7 kJ (1 Calorie4182kJ) = 16 CaloriesThis is amount of energy the diver used in climbing the

stairs (actually more than this since some energy waswasted) They got that energy from the food they ate

The Energy of Heatbull Hot things have more energy than their cold

counterpartsbull Heat is really just kinetic energy on microscopic

scales the vibration or otherwise fast motion ofindividual atomsmoleculesndash Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are randombull Heat is frequently quantified by calories (or Btu)

ndash One calorie (4184 J) raises one gram of H2O 1ordmCndash One Calorie (4184 J) raises one kilogram of H2O 1ordmCndash One Btu (1055 J) raises one pound of H2O 1ordmF

20

Energy of Heat continuedbull Food Calories are with the ldquobigrdquo C or kilocalories (kcal)bull Since water has a density of one gram per cubic centimeter 1

cal heats 1 cc of water 1ordmC and likewise 1 kcal (Calorie) heatsone liter of water 1ordmC In British Units 1 Btu heats 1 pound ofwater 1 degree Fahrenheitndash these are useful numbers to hang onto

bull Example to heat a 2-liter bottle of Coke from the 5ordmCrefrigerator temperature to 20ordmC room temperature requires 30Calories or 1225 kJ

bull Drink a pint (16 oz) of ice cold water (or coke) It weighs about1 pound To heat it to body temperature (986 degrees minus 32degrees or change of 666 degrees Takes about 67 BtuConvert to Calories 1 Calorie = 1kJ = 4 Btu so

67 Btu (1 Calorie 4 Btu) = 1675 Calories Since 16 oz ofcoke has 210 Calories and about 17 Calories are used justheating to your body temp you get less calories drinking it cold(or drinking quart of cold water ldquoburnsrdquo 17 Calories)

The Physics of Energy Formula List

P = ΔEΔtPower (rate of energy use)

F = σT4 (temperature to the fourthpower times a constant)

Radiative energy flux

E = mc2 (mass times speed oflight squared)

Mass energy

ΔE = cpmΔT (mass times changein temperature times heatcapacity)

Heat Energy

E = mgh (mass times height times10ms2)

(Grav) Potential Energy

KE = frac12mv2 (mass times velocitysquared)

Kinetic Energy

W = Fd (Force times distance)Work

Energy FormulaEnergy Form

21

Heat Capacitybull Different materials have different capacities to

hold heatndash Add the same energy to different materials and yoursquoll

get different temperature risesndash Quantified as heat capacityndash Water is exceptional with 4184 JkgordmCndash Most materials are about 1000 JkgordmC (including

wood air metals)bull Example to add 10ordmC to a room 3 meters on a side

(cubic) how much energy do we needair density is 13 kgm3 and we have 27 m3 so 35 kg ofair and we need 1000 J per kg per ordmC so we end upneeding 350000 J (= 836 Cal)

Important in designing solar heated houses Also reasonit is cooler near the coast than inland

Powerbull Power is simply energy exchanged

per unit time or how fast you getwork done (Watts = Joulessec)

bull One horsepower = 745 Wbull Perform 100 J of work in 1 s and

call it 100 Wbull Run upstairs raising your 70 kg

(700 N) mass 3 m (2100 J) in 3seconds rarr 700 W output

bull Shuttle puts out a few GW(gigawatts or 109 W) of power

bull A big electrical power plant putsout around a GW That is 1 BillionJoules per second House takes afew kW (kilowatt)

22

QuestionPower is Energy used per second P= energytime Whichhighest power

A Using 100 Calories in 10 minutes

B Using 1000 Calories in 100 minutes

C Using 10 Calories in 1 minute

D Using 1 Calorie in 6 seconds

E All of the above are the same power usage

1 Calorieminute = Watts

Wind Energy

bull Wind can be used as a source of energy (windmills sailingships etc)

bull Really just kinetic energybull Example wind passing through a square meter at 8 meters

per secondndash Each second we have 8 cubic metersndash Air has density of 13 kgm3 so (8 m3)times(13 kgm3) = 104 kg of

air each secondndash frac12mv2 = frac12times(104 kg)times(8 ms)2 = 333 Jndash 333 J every second rarr 333 Watts of available power per square

meter (but to get all of it yoursquod have to stop the wind)bull Stronger winds rarr more power (like v2)

23

Chemical Energy

bull Electrostatic energy (associated with chargedparticles like electrons) is stored in the chemicalbonds of substances

bull Rearranging these bonds can release energy (somereactions require energy to be put in)

bull Typical numbers are 100ndash200 kJ per molendash a mole is 6022times1023 moleculesparticlesndash typical molecules are tens of grams per molerarrworks

out to typical numbers like several thousand Joules pergram or a few Calories per gram (remember 1 Cal = 1kcal = 4187 J)

Chemical Energy Examples

bull Burning a wooden match releases about oneBtu or 1055 Joules (a match is about 03grams) so this is gt3000 Jg nearly 1 Calg

bull Burning coal releases about 20 kJ per gramof chemical energy or roughly 5 Calg

bull Burning gasoline yields about 39 kJ pergram or just over 9 Calg

bull Very few substances over about 11 Calg

24

Energy from Food

bull We get the energy to do the things we do out of food(stored solar energy in the form of chemical energy)

bull Energy sources recognized by our digestive systemsndash Carbohydrates 4 Calories per gramndash Proteins 4 Calories per gramndash Fats 9 Calories per gram (like gasoline) (9 is more than

4 so gain more weight eating same amount of fat thancarbs or protein)

ndash Roughly 3500 Caloriespound in your body fat Less inyour protein (muscle skin etc)

Our Human Energy Budget

bull A 2000 Calorie per daydiet means 2000times4184 J =8368000 J per day

bull 837 MJ in (24 hrday) times(60 minhr)times(60 secmin)= 86400 sec correspondsto 97 Watts of power

bull Even a couch-potato at1500 Calday burns 75 W

bull More active lifestylesrequire greater Caloricintake (more energy)

25

Nutrition Labelsbull Nutrition labels tell you about the

energy content of foodbull Note they use Calories with capitol Cbull Conversions Fat 9 Calg

Carbs 4 CalgProtein 4 Calg

bull This product has 72 Cal from fat 48Cal from carbohydrates and 32 Calfrom proteinndash sum is 152 Calories compare to label

bull 152 Cal = 636 kJ enough to climbabout 1000 meters (64 kg person)

bull 1kwh = 860 Cal or about 14 lb bodyfat

bull 1 gal of gas has 31000 Calories

Mass-energy

bull Einsteinrsquos famous relationE = mc2

relates mass to energybull In effect they are the same thing

ndash one can be transformed into the otherndash physicists speak generally of mass-energy

bull Seldom experienced in daily life directlyndash Happens at large scale in the center of the sun and in

nuclear bombs and reactorsndash Actually does happen at barely detectable level in all

energy transactions but the effect is tiny

26

E = mc2 Examples

bull The energy equivalent of one gram of material(any composition) is (0001 kg)times(30times108 ms)2

= 90times1013 J = 90000000000000 J = 90 TJndash Man thatrsquos bigndash Our global energy budget is equivalent to 1000 kgyr

(thatrsquos about 1 ton per year)bull If one gram of material undergoes a chemical

reaction losing about 9000 J of energy howmuch mass does it lose

9000 J = Δmc2 so Δm = 9000c2 = 9times1039times1016

= 10-13 kg (would we ever notice)

Solar Energy is Nuclear Using E= mc2

bull Thermonuclear fusion reactions in the sunrsquos centerndash Sun is 16 million degrees Celsius in its centerndash Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then heliumndash Reaction per atom 20 million times more energetic than chemical

reactions in general

4 protonsmass = 4029

4He nucleusmass = 40015

2 neutrinos photons (light)

27

E = mc2 in Sun

bull Helium nucleus is lighter than the four protonsbull Mass difference is 4029 - 40015 = 00276 amu

ndash 1 amu (atomic mass unit) is 16605times10-27 kgndash difference of 458times10-29 kgndash multiply by c2 to get 412times10-12 Jndash 1 mole (6022times1023 particles) of protons rarr 25times1012 Jndash typical chemical reactions are 100-200 kJmolendash nuclear fusion is ~20 million times more potent stuffndash Nuclear fusion is energy source of hydrogen bomb

Energy from Lightbull The tremendous energy from the sun is released as light So light

carries energybull Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiationbull Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequencybull Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellipbull All objects emit ldquolightrdquobull The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter moreradiation and color is ldquobluerrdquo

28

Emitted Radiationrsquos Color andIntensity depend on Temperature

Object

YouHeat LampCandle FlameBulb FilamentSunrsquos SurfaceNeutron StarMolecules in deep space

Temperature

~ 30 C~ 500 C~ 1700 C~ 2700 C~ 5500 C~ millions C

lt -272C

Color

Infrared (invisible)Dull redDim orangeYellowBrilliant whiteX-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted lightThe hotter it gets the more intense the radiation (more energy)

ldquoBlackbodyrdquo or Planck Spectrum

29

Same thing on logarithmic scale

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm(note 0degC = 273degK 300degK = 27degC = 81degF)

Okay but how much energybull The power given off of a surface in the form of light is

proportional to the fourth power of temperatureF = σT4 in Watts per square meter

ndash the constant σ is numerically 567times10-8 WordmK4m2

ndash easy to remember constant 5678ndash temperature must be in Kelvin

bull ordmK = ordmC + 273bull ordmC = (59)times(ordmF ndash32)

bull Example radiation from your body(567 times10-8) times(310)4 = 523 Watts per square meter(if naked in the cold of space donrsquot let this happen to you)

30

Radiant Energy continued

bull Example The sun is 5800ordmK on its surface soF = σT4 = (567times10-8)times(5800)4 = 64times107 Wm2

Summing over entire surface area of sun gives39times1026 W

bull Compare to total capacity of energy production onearth 33times1012 Wndash Single power plant typically 05ndash10 GW (109 W)

bull In earthly situations radiated power out partiallybalanced by radiated power in from other sourcesndash Not 523 Wm2 in 70ordmF room more like 100 Wm2

bull goes like σTh4 ndash σTc

4

Electrical Energybull Opposite charges attract so electrons are attracted to

protons This holds atoms togetherbull It takes energy to pull electrons off their atomsbull Electrons want to get back home to their protons They can

only travel through conductors like wires not throughinsulators like plastic paper or wood They will gothrough miles of wire to get home to their protons

bull This is how electricity works The electronrsquos energy canbe stolen as it goes home Can be used in many manyways

bull Note electricity is not a primary source of energy Energy(from burning coal nat gas from hydro wind nuke orsolar) is used to pull of electrons and that energy can bemoved through wires and got back at will

31

And those are the majorplayershellip

bull Wersquove now seen most of the major energyplayersndash work as force times distancendash kinetic energy (wind ocean currents)ndash gravitational potential energy (hydroelectric tidal)ndash chemical energy (fossil fuels batteries food biomass)ndash heat energy (power plants space heating)ndash mass-energy (nuclear sources sunrsquos energy)ndash radiant energy (solar energy)ndash electrical energy (energy of electrons separated from

their atoms)

Conservation and Exchange ofEnergy

Nothing Comes for Free

32

Energy is Conservedbull Conservation of Energy is different from Energy

Conservation the latter being about using energywisely

bull Conservation of Energy means energy is neithercreated nor destroyed The amount of energy inthe Universe is constant

bull Donrsquot we create energy at a power plantndash Oh that this were truemdashno we simply transform

energy at our power plantsbull Doesnrsquot the sun create energy

ndash Nopemdashit exchanges mass for energybull Donrsquot batteries give us new energy

ndash Nope just convert stored chemical energy to electricalenergy Someone had to put that energy in there

height referenceh

Energy Exchangebull Though the total energy of a system is constant

the form of the energy can changebull A simple example is that of a simple pendulum in

which a continual exchange goes on betweenkinetic and potential energy

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

33

Perpetual Motion

bull Why wonrsquot the pendulum swing foreverbull Itrsquos hard to design a system free of energy pathsbull The pendulum slows down by several mechanisms

ndash Friction at the contact point requires force to opposeforce acts through distance rarr work is done

ndash Air resistance must push through air with a force(through a distance) rarr work is done

ndash Gets some air swirling puts kinetic energy into air (notreally fair to separate these last two)

bull Perpetual motion means no loss of energyndash solar system orbits come very close

Some Energy Chains

bull A coffee mug with some gravitational potentialenergy is dropped

bull potential energy turns into kinetic energybull kinetic energy of the mug goes into

ndash ripping the mug apart (chemical breaking bonds)ndash sending the pieces flying (kinetic)ndash into soundndash into heating the floor and pieces through friction as the

pieces slide to a stopbull In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored inthe potential energy)

34

Gasoline Examplebull Put gas in your car containing 9 Calgbull Combust gas turning 9 Calg into kinetic energy of

explosionbull Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a wholebull That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water andsurrounding air) and friction of transmission system(heat) and noise of engine (heating the air) etc

bull Much of energy goes into stirring the air (ends up as heat)bull Apply the brakes and convert kinetic energy into heatbull It all ends up as waste heat ultimately

Bouncing Ballbull Superball has gravitational potential energybull Drop the ball and this becomes kinetic energybull Ball hits ground and compresses (force times

distance) storing energy in the springbull Ball releases this mechanically stored energy

and it goes back into kinetic form (bouncesup)

bull Inefficiencies in ldquospringrdquo end up heating theball and the floor and stirring the air a bit

bull In the end all is heat

35

Why donrsquot we get hotter andhotter

bull If all these processes end up as heat why arenrsquotwe continually getting hotter

bull If earth retained all its heat we would get hotterbull All of earthrsquos heat is radiated away

F = σT4

bull If we dump more power the temperature goes upthe radiated power increases dramaticallyndash comes to equilibrium power dumped = power radiatedndash stable against perturbation T tracks power budget

Rough numbers

bull How much power does the earth radiatebull F = σT4 for T = 288ordmK = 15ordmC is 390 Wm2

bull Summed over entire surface area (4πR2 where R= 6378000 meters) is 20times1017 W

bull Global production is 3times1012 Wbull Solar radiation incident on earth is 18times1017 W

ndash just solar luminosity of 39times1026 W divided bygeometrical fraction that points at earth

bull Amazing coincidence of numbers (or is ithellip)

36

No Energy for Free

bull No matter what you canrsquot create energy out ofnothing it has to come from somewhere

bull We can transform energy from one form toanother we can store energy we can utilizeenergy being conveyed from natural sources

bull The net energy of the entire Universe is constantbull The best we can do is scrape up some useful

crumbs

Examplesbull Unit conversion

ndash 100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Calndash 100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 Jndash 100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWhndash 10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWhndash How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86Calorieshour About what average person eats

ndash Gasoline is $3gal Electricity if $015kWh Which is moreexpensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh)= $008kWh for gasoline Gasoline is cheap in the USA

37

Examplesbull Power vs Energy (P=Etime E = P t t = EP)

ndash Car goes 60 miles in one hour and uses 3 gal of gas What wastotal power in Watts P=Et Power = (3 gal1 hour) = 3galhr(366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W[Alternative method 3 galhr (132000000 J1 gal) (1 hr3600sec) = 110000 Jsec = 110000 W

ndash 1000 W space heater is on for 3 hours How much does it cost ifelectricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr(1kW1000W) = 3kWh ($15kWh) = $45 [Alternative methodE = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000J (1 kWh3600000J) = 3 kWh Again 45 cents

ndash AAA Battery contains 33 Calories of chemical energy How longcan it run a 2 Watt light bulb time = EP time = 33 Calories2W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1hr3600 sec) = 19 hours

QuestionThe US uses about 7 Gbarrels of oil each year This couldbe converted into which of the following units

A Joules B Watts C QBtus D Dollars $ E Any of the above

38

QuestionIf one barrel of oil contains 1700 kWh of energy how manyWatts is 7 Gbarrelyear

A 1400 GW (Giga Watts)

B 14 GW

C 11900 W

D 119 MW

E 1 x 1011 W

QuestionIf the total yearly oil use in the US is about 1400 GW howmany 1000 MW nuclear reactors will need to be built toreplace all oil use with electricity

A Only one will be needed

B Around 14

C Around 140

D Around 1400

E Cant convert Watts to reactors power vs energy

39

More Power Examplesbull How much power does it take to lift 10 kg up 2 meters in 2

secondsmgh = (10 kg)times(10 ms2)times(2 m) = 200J

200 J in 2 seconds rarr 100 Wattsbull If you want to heat the 3 m cubic room by 10ordmC with a

1000 W space heater how long will it takeWe know from before that the room needs to have 360000 J addedto it so at 1000 W = 1000 Js this will take 360 seconds or sixminutes

But the walls need to be warmed up too so it will actually takelonger (and depends on quality of insulation etc)

A note on arithmetic of unitsbull You should carry units in your calculations and multiply and divide them

as if they were numbersbull Example the force of air drag is given bybull Fdrag = frac12cDrAv2

bull cD is a dimensionless drag coefficientbull r is the density of air 13 kgm3

bull A is the cross-sectional area of the body in m2

bull v is the velocity in msbull units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) =

kgmiddotmiddotmm22middotmiddotmm22

m3middotmiddotss22kgmiddotmiddotmm44

m3middotmiddotss22= = kgmiddotmiddotmsms22 = = NewtonsNewtons

2

bull Long ago almost all of our energy came fromfood (delivering muscle power) and almost all ourenergy went into securing food for ourselves

bull Enter the work animal supplementing our musclepower and enabling larger-scale agriculture

bull Next burn wood to run boilers trainsbull 150 years ago muscular effort and firewood

provided most of our energymdashand today this isless than 1 of the story

bull Today much more energy goes intogrowingharvesting food than comes out of food

bull Today in US 86 of our energy comes from fossilfuels (oilnatural gas coal)

Fuzzy on the concept of energy

bull Donrsquot worrymdashwersquoll cover that

3

A note on graphs log vs linearbull Many graphs are on logarithmic scales watch for thisbull This condenses wide-ranging information into a compact

areabull Pay attention because you could warp your intuition if you

donrsquot appreciate the scalebull Log scales work in factors of tenbull A given vertical span represents a constant ratio (eg

factor of ten factor of two etc)bull An exponential increase looks like a straight line on a

logarithmic scale

4

Example Plots

Exponential plot is curved on linear scale and straight on a logarithmic scale

5

A brief history of fossil fuels

bull Here today gone tomorrowbull What will our future hold

ndash Will it be back to a simple lifendash Or will we find new ways to produce all the energy we wantndash Or will it be somewhere in the middle

GlobalEnergyWhereDoes itComeFrom

72287Hydroelectric

then radiatedaway2000000

Sun Abs byEarth

0008003Solar Direct003013Wind01305Geothermal0416

Biomass(burning)

6626Nuclear Energy

22589Natural Gas23292Coal400158Petroleum

Percent ofTotal

1018 Joulesyr(~QBtuyr)Source

Ultimately derivedfrom our sun

Courtesy DavidBodansky (UW)

Btu=1055kJ

6

7

Why do we use so much energy

8

9

We live in a special time and placehellipbull We use almost 100 times the amount used by the rest of the

world (by population)bull This phase has only lasted for the last century or sobull Most of our resources come from fossil fuels presently and

this has a short finite lifetimebull Fossil fuels formed from solar energy over 300 million

years will be used up in a few centuries

2000 2500 3000 3500 4000150010005000

year

ener

gy u

sage

10

Energy the capacity to do work

bull This notion makes sense even in acolloquial contextndash hard to get work done when yoursquore wiped out

(low on energy)ndash work makes you tired yoursquove used up energy

bull But we can make this definition of energymuch more precise by specifying exactlywhat we mean by work

Work =Energy more than justunpleasant tasks

bull In physics the definition of work is the application of aforce through a distance Energy is needed to do it

W = Fd

bull W is the work done = energy usedbull F is the force appliedbull d is the distance through which the force actsbull Only the force that acts in the direction of motion counts

towards work

11

Okay what is Force thenbull Force is a pushingpulling agentbull Examples

ndash gravity exerts a downward force on youndash the floor exerts an upward force on a ball during its bouncendash a car seat exerts a forward force on your body when you accelerate forward from

a stopndash the seat yoursquore sitting in now is exerting an upward force on you (can you feel it)ndash you exert a sideways force on a couch that you slide across the floorndash a string exerts a centrally-directed (centripetal) force on a rock at the end of a

string that yoursquore twirling over your headndash the expanding gas in your carrsquos cylinder exerts a force against the piston

Forces have Directionbull In all the previous examples force had a

direction associated with itbull If multiple forces act on an object they

could potentially add or cancel dependingon direction

Force 1Force 2

Total Force Force 1

Force 2

Total Force = 0

12

When net force is not zero

bull When an object experiences a non-zero net force it mustaccelerate

bull Newtonrsquos second lawF = ma Force = mass times acceleration

bull The same force makes a small object accelerate more thanit would a more massive objectndash hit a golf ball and a bowling ball with a golf club and see what

happens

QuestionA 150 lb person is standing still on the edge of a cliff Whatis the total force on the person

A zeroB 150 lbC Canrsquot say from this info

13

QuestionA 150 lb person jumps (or was he pushed) off a cliff and isfalling to their death What is the total force on the person

A zeroB 150 lbC Canrsquot say from this info

But what is acceleration

bull This is getting to be like the ldquohole in thebucketrdquo song but wersquore almost therehellip

bull Acceleration is any change in velocity(speed andor direction of motion)

bull Measured as rate of change of velocityndash velocity is expressed in meters per second (ms)ndash acceleration is meters per second per secondndash expressed as ms2 (meters per second-squared)

14

Putting it back together Units ofEnergy

bull Force is a mass times an accelerationndash mass has units of kilogramsndash acceleration is ms2

ndash force is then kgms2 which we call Newtons (N)

bull Work is a force times a distancendash units are then (kgms2)m = kg m2s2 = Nm = Joules (J)ndash One joule is one Newton of force acting through one meterndash Imperial units of force and distance are pounds and feet so unit of

energy is foot-pound which equals 136 J

bull Energy has the same units as work Joules

A Zoo of Unitsbull The main metric unit of energy is the Joule and most of

the world uses this but many others existbull The calorie is 4184 Joules

ndash raise 1 gram (cc) of water one degree Celsiusbull The Calorie (kilocalorie) is 4184 J (used for food energy)

ndash raise 1 kg (1 liter) of water one degree Celsiusbull The Btu (British thermal unit) is 1055 J (roughly 1 kJ) or

about 14 Calorie or chemical energy of one matchndash raise 1 pound of water one degree Fahrenheit

bull The kilowatt-hour (kWh) is 3600000 J = 3600 kJ or 860Calories (used for electrical energy)ndash one Watt (W) is one Joule per secondndash a kWh is 1000 W for one hour (3600 seconds)

bull Can also use ldquobarrel of oilrdquo ldquoton of coalrdquo 1000 cubic feetof natural gas gram of Uranium or amount of any energycontaining source etc

15

The Physics of Energy Formula List

bull Lots of forms of energy coming fast and furious but to putit in perspective herersquos a list of formulas

P = ΔEΔtPower (rate of energy use)

F = σT4 (temperature to the fourthpower times a constant)

Radiative energy flux

E = mc2 (mass times speed of lightsquared)

Mass energy

ΔE = cpmΔT (mass times change intemperature times heat capacity)

Heat Energy

E = mgh (mass times height times10ms2)

(Grav) Potential Energy

KE = frac12mv2 (mass times velocitysquared)

Kinetic Energy

W = Fd (Force times distance)Work

Energy FormulaEnergy Form

Kinetic Energybull Kinetic Energy the energy of motionbull Moving things carry energy in the amount

KE = frac12mv2

bull Note the v2 dependencemdashthis is whyndash a car at 60 mph is 4 times more dangerous than a car at 30 mphndash hurricane-force winds at 100 mph are much more destructive (4

times) than 50 mph gale-force windsndash a bullet shot from a gun is at least 100 times as destructive as a

thrown bullet even if you can throw it a tenth as fast as you couldshoot it

16

Numerical examples of kineticenergy

bull A baseball (mass is 0145 kg = 145 g) moving at 30 ms(67 mph) has kinetic energy

KE = frac12times(0145 kg)times(30 ms)2

= 6525 kgm2s2 asymp 65 J

bull A quarter (mass = 000567 kg = 567 g) flipped about fourfeet into the air has a speed on reaching your hand of about5 ms The kinetic energy is

KE = frac12times(000567 kg)times(5 ms)2

= 007 kgm2s2 = 007 J

More numerical examples

bull A 1500 kg car moves down the freeway at30 ms (67 mph)

KE = frac12times(1500 kg)times(30 ms)2

= 675000 kgm2s2 = 675 kJConvert to Calories 4184 kJ = 1 Calorie675 kJ (1 Calorie4184 kJ) = 161 Calorie

bull A 2 kg (~44 lb) fish jumps out of the waterwith a speed of 1 ms (22 mph)

KE = frac12times(2 kg)times(1 ms)2

= 1 kgm2s2 = 1 J

17

QuestionKinetic energy is E = 12 m v2 Which has more energy

A 10 kg object going 100 ms

B 100 kg object going 10 ms

C 1 kg object going 1000 ms

D 1000 kg object going 1 ms

1 ms = 22 mph

Gravitational Potential Energybull It takes work to lift a mass against the pull (force) of

gravitybull The force of gravity is mg where m is the mass and g is

the gravitational accelerationF = mg (note similarity to F = ma)

ndash g = 98 ms2 on the surface of the earth or 32 fts2

bull Lifting a height h against the gravitational forcerequires an energy input (work) of

ΔE = W = F h = mghbull Rolling a boulder up a hill and perching it on the edge of a

cliff gives it gravitational potential energy that can be laterreleased when the roadrunner is down below

bull Water in river or hydroelectric plant is using potentialenergy that it got from being lifted up when Sun (solarenergy) evaporated the water

18

QuestionPotential energy is E = 10 m h (metric units) Which hasmore energy

A 1 ton of water at a height of 100 ft

B 100 tons of water at a height of 1 ft

C 200 lb (110 ton) of water at 1000 ft

D All of the above have same energy

1 ms = 22 mph

First Example of Energy Exchangebull When the boulder falls off the cliff it picks up

speed and therefore gains kinetic energybull Where does this energy come from

rArr from the gravitational potential energybull The higher the cliff the more kinetic energy the

boulder will have when it reaches the ground

mgh

becomes

frac12mv2

Energy is conserved sofrac12mv2 = mgh

Can even figure out v since v2 = 2gh

h

19

Examples of GravitationalPotential Energy

bull How much gravitational potential energy does a70 kg high-diver have on the 10 meter platform

mgh = (70 kg)times(10 ms2)times(10 m)= 7000 kgm2s2 = 7 kJ

7 kJ (1 Calorie4182kJ) = 16 CaloriesThis is amount of energy the diver used in climbing the

stairs (actually more than this since some energy waswasted) They got that energy from the food they ate

The Energy of Heatbull Hot things have more energy than their cold

counterpartsbull Heat is really just kinetic energy on microscopic

scales the vibration or otherwise fast motion ofindividual atomsmoleculesndash Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are randombull Heat is frequently quantified by calories (or Btu)

ndash One calorie (4184 J) raises one gram of H2O 1ordmCndash One Calorie (4184 J) raises one kilogram of H2O 1ordmCndash One Btu (1055 J) raises one pound of H2O 1ordmF

20

Energy of Heat continuedbull Food Calories are with the ldquobigrdquo C or kilocalories (kcal)bull Since water has a density of one gram per cubic centimeter 1

cal heats 1 cc of water 1ordmC and likewise 1 kcal (Calorie) heatsone liter of water 1ordmC In British Units 1 Btu heats 1 pound ofwater 1 degree Fahrenheitndash these are useful numbers to hang onto

bull Example to heat a 2-liter bottle of Coke from the 5ordmCrefrigerator temperature to 20ordmC room temperature requires 30Calories or 1225 kJ

bull Drink a pint (16 oz) of ice cold water (or coke) It weighs about1 pound To heat it to body temperature (986 degrees minus 32degrees or change of 666 degrees Takes about 67 BtuConvert to Calories 1 Calorie = 1kJ = 4 Btu so

67 Btu (1 Calorie 4 Btu) = 1675 Calories Since 16 oz ofcoke has 210 Calories and about 17 Calories are used justheating to your body temp you get less calories drinking it cold(or drinking quart of cold water ldquoburnsrdquo 17 Calories)

The Physics of Energy Formula List

P = ΔEΔtPower (rate of energy use)

F = σT4 (temperature to the fourthpower times a constant)

Radiative energy flux

E = mc2 (mass times speed oflight squared)

Mass energy

ΔE = cpmΔT (mass times changein temperature times heatcapacity)

Heat Energy

E = mgh (mass times height times10ms2)

(Grav) Potential Energy

KE = frac12mv2 (mass times velocitysquared)

Kinetic Energy

W = Fd (Force times distance)Work

Energy FormulaEnergy Form

21

Heat Capacitybull Different materials have different capacities to

hold heatndash Add the same energy to different materials and yoursquoll

get different temperature risesndash Quantified as heat capacityndash Water is exceptional with 4184 JkgordmCndash Most materials are about 1000 JkgordmC (including

wood air metals)bull Example to add 10ordmC to a room 3 meters on a side

(cubic) how much energy do we needair density is 13 kgm3 and we have 27 m3 so 35 kg ofair and we need 1000 J per kg per ordmC so we end upneeding 350000 J (= 836 Cal)

Important in designing solar heated houses Also reasonit is cooler near the coast than inland

Powerbull Power is simply energy exchanged

per unit time or how fast you getwork done (Watts = Joulessec)

bull One horsepower = 745 Wbull Perform 100 J of work in 1 s and

call it 100 Wbull Run upstairs raising your 70 kg

(700 N) mass 3 m (2100 J) in 3seconds rarr 700 W output

bull Shuttle puts out a few GW(gigawatts or 109 W) of power

bull A big electrical power plant putsout around a GW That is 1 BillionJoules per second House takes afew kW (kilowatt)

22

QuestionPower is Energy used per second P= energytime Whichhighest power

A Using 100 Calories in 10 minutes

B Using 1000 Calories in 100 minutes

C Using 10 Calories in 1 minute

D Using 1 Calorie in 6 seconds

E All of the above are the same power usage

1 Calorieminute = Watts

Wind Energy

bull Wind can be used as a source of energy (windmills sailingships etc)

bull Really just kinetic energybull Example wind passing through a square meter at 8 meters

per secondndash Each second we have 8 cubic metersndash Air has density of 13 kgm3 so (8 m3)times(13 kgm3) = 104 kg of

air each secondndash frac12mv2 = frac12times(104 kg)times(8 ms)2 = 333 Jndash 333 J every second rarr 333 Watts of available power per square

meter (but to get all of it yoursquod have to stop the wind)bull Stronger winds rarr more power (like v2)

23

Chemical Energy

bull Electrostatic energy (associated with chargedparticles like electrons) is stored in the chemicalbonds of substances

bull Rearranging these bonds can release energy (somereactions require energy to be put in)

bull Typical numbers are 100ndash200 kJ per molendash a mole is 6022times1023 moleculesparticlesndash typical molecules are tens of grams per molerarrworks

out to typical numbers like several thousand Joules pergram or a few Calories per gram (remember 1 Cal = 1kcal = 4187 J)

Chemical Energy Examples

bull Burning a wooden match releases about oneBtu or 1055 Joules (a match is about 03grams) so this is gt3000 Jg nearly 1 Calg

bull Burning coal releases about 20 kJ per gramof chemical energy or roughly 5 Calg

bull Burning gasoline yields about 39 kJ pergram or just over 9 Calg

bull Very few substances over about 11 Calg

24

Energy from Food

bull We get the energy to do the things we do out of food(stored solar energy in the form of chemical energy)

bull Energy sources recognized by our digestive systemsndash Carbohydrates 4 Calories per gramndash Proteins 4 Calories per gramndash Fats 9 Calories per gram (like gasoline) (9 is more than

4 so gain more weight eating same amount of fat thancarbs or protein)

ndash Roughly 3500 Caloriespound in your body fat Less inyour protein (muscle skin etc)

Our Human Energy Budget

bull A 2000 Calorie per daydiet means 2000times4184 J =8368000 J per day

bull 837 MJ in (24 hrday) times(60 minhr)times(60 secmin)= 86400 sec correspondsto 97 Watts of power

bull Even a couch-potato at1500 Calday burns 75 W

bull More active lifestylesrequire greater Caloricintake (more energy)

25

Nutrition Labelsbull Nutrition labels tell you about the

energy content of foodbull Note they use Calories with capitol Cbull Conversions Fat 9 Calg

Carbs 4 CalgProtein 4 Calg

bull This product has 72 Cal from fat 48Cal from carbohydrates and 32 Calfrom proteinndash sum is 152 Calories compare to label

bull 152 Cal = 636 kJ enough to climbabout 1000 meters (64 kg person)

bull 1kwh = 860 Cal or about 14 lb bodyfat

bull 1 gal of gas has 31000 Calories

Mass-energy

bull Einsteinrsquos famous relationE = mc2

relates mass to energybull In effect they are the same thing

ndash one can be transformed into the otherndash physicists speak generally of mass-energy

bull Seldom experienced in daily life directlyndash Happens at large scale in the center of the sun and in

nuclear bombs and reactorsndash Actually does happen at barely detectable level in all

energy transactions but the effect is tiny

26

E = mc2 Examples

bull The energy equivalent of one gram of material(any composition) is (0001 kg)times(30times108 ms)2

= 90times1013 J = 90000000000000 J = 90 TJndash Man thatrsquos bigndash Our global energy budget is equivalent to 1000 kgyr

(thatrsquos about 1 ton per year)bull If one gram of material undergoes a chemical

reaction losing about 9000 J of energy howmuch mass does it lose

9000 J = Δmc2 so Δm = 9000c2 = 9times1039times1016

= 10-13 kg (would we ever notice)

Solar Energy is Nuclear Using E= mc2

bull Thermonuclear fusion reactions in the sunrsquos centerndash Sun is 16 million degrees Celsius in its centerndash Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then heliumndash Reaction per atom 20 million times more energetic than chemical

reactions in general

4 protonsmass = 4029

4He nucleusmass = 40015

2 neutrinos photons (light)

27

E = mc2 in Sun

bull Helium nucleus is lighter than the four protonsbull Mass difference is 4029 - 40015 = 00276 amu

ndash 1 amu (atomic mass unit) is 16605times10-27 kgndash difference of 458times10-29 kgndash multiply by c2 to get 412times10-12 Jndash 1 mole (6022times1023 particles) of protons rarr 25times1012 Jndash typical chemical reactions are 100-200 kJmolendash nuclear fusion is ~20 million times more potent stuffndash Nuclear fusion is energy source of hydrogen bomb

Energy from Lightbull The tremendous energy from the sun is released as light So light

carries energybull Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiationbull Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequencybull Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellipbull All objects emit ldquolightrdquobull The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter moreradiation and color is ldquobluerrdquo

28

Emitted Radiationrsquos Color andIntensity depend on Temperature

Object

YouHeat LampCandle FlameBulb FilamentSunrsquos SurfaceNeutron StarMolecules in deep space

Temperature

~ 30 C~ 500 C~ 1700 C~ 2700 C~ 5500 C~ millions C

lt -272C

Color

Infrared (invisible)Dull redDim orangeYellowBrilliant whiteX-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted lightThe hotter it gets the more intense the radiation (more energy)

ldquoBlackbodyrdquo or Planck Spectrum

29

Same thing on logarithmic scale

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm(note 0degC = 273degK 300degK = 27degC = 81degF)

Okay but how much energybull The power given off of a surface in the form of light is

proportional to the fourth power of temperatureF = σT4 in Watts per square meter

ndash the constant σ is numerically 567times10-8 WordmK4m2

ndash easy to remember constant 5678ndash temperature must be in Kelvin

bull ordmK = ordmC + 273bull ordmC = (59)times(ordmF ndash32)

bull Example radiation from your body(567 times10-8) times(310)4 = 523 Watts per square meter(if naked in the cold of space donrsquot let this happen to you)

30

Radiant Energy continued

bull Example The sun is 5800ordmK on its surface soF = σT4 = (567times10-8)times(5800)4 = 64times107 Wm2

Summing over entire surface area of sun gives39times1026 W

bull Compare to total capacity of energy production onearth 33times1012 Wndash Single power plant typically 05ndash10 GW (109 W)

bull In earthly situations radiated power out partiallybalanced by radiated power in from other sourcesndash Not 523 Wm2 in 70ordmF room more like 100 Wm2

bull goes like σTh4 ndash σTc

4

Electrical Energybull Opposite charges attract so electrons are attracted to

protons This holds atoms togetherbull It takes energy to pull electrons off their atomsbull Electrons want to get back home to their protons They can

only travel through conductors like wires not throughinsulators like plastic paper or wood They will gothrough miles of wire to get home to their protons

bull This is how electricity works The electronrsquos energy canbe stolen as it goes home Can be used in many manyways

bull Note electricity is not a primary source of energy Energy(from burning coal nat gas from hydro wind nuke orsolar) is used to pull of electrons and that energy can bemoved through wires and got back at will

31

And those are the majorplayershellip

bull Wersquove now seen most of the major energyplayersndash work as force times distancendash kinetic energy (wind ocean currents)ndash gravitational potential energy (hydroelectric tidal)ndash chemical energy (fossil fuels batteries food biomass)ndash heat energy (power plants space heating)ndash mass-energy (nuclear sources sunrsquos energy)ndash radiant energy (solar energy)ndash electrical energy (energy of electrons separated from

their atoms)

Conservation and Exchange ofEnergy

Nothing Comes for Free

32

Energy is Conservedbull Conservation of Energy is different from Energy

Conservation the latter being about using energywisely

bull Conservation of Energy means energy is neithercreated nor destroyed The amount of energy inthe Universe is constant

bull Donrsquot we create energy at a power plantndash Oh that this were truemdashno we simply transform

energy at our power plantsbull Doesnrsquot the sun create energy

ndash Nopemdashit exchanges mass for energybull Donrsquot batteries give us new energy

ndash Nope just convert stored chemical energy to electricalenergy Someone had to put that energy in there

height referenceh

Energy Exchangebull Though the total energy of a system is constant

the form of the energy can changebull A simple example is that of a simple pendulum in

which a continual exchange goes on betweenkinetic and potential energy

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

33

Perpetual Motion

bull Why wonrsquot the pendulum swing foreverbull Itrsquos hard to design a system free of energy pathsbull The pendulum slows down by several mechanisms

ndash Friction at the contact point requires force to opposeforce acts through distance rarr work is done

ndash Air resistance must push through air with a force(through a distance) rarr work is done

ndash Gets some air swirling puts kinetic energy into air (notreally fair to separate these last two)

bull Perpetual motion means no loss of energyndash solar system orbits come very close

Some Energy Chains

bull A coffee mug with some gravitational potentialenergy is dropped

bull potential energy turns into kinetic energybull kinetic energy of the mug goes into

ndash ripping the mug apart (chemical breaking bonds)ndash sending the pieces flying (kinetic)ndash into soundndash into heating the floor and pieces through friction as the

pieces slide to a stopbull In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored inthe potential energy)

34

Gasoline Examplebull Put gas in your car containing 9 Calgbull Combust gas turning 9 Calg into kinetic energy of

explosionbull Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a wholebull That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water andsurrounding air) and friction of transmission system(heat) and noise of engine (heating the air) etc

bull Much of energy goes into stirring the air (ends up as heat)bull Apply the brakes and convert kinetic energy into heatbull It all ends up as waste heat ultimately

Bouncing Ballbull Superball has gravitational potential energybull Drop the ball and this becomes kinetic energybull Ball hits ground and compresses (force times

distance) storing energy in the springbull Ball releases this mechanically stored energy

and it goes back into kinetic form (bouncesup)

bull Inefficiencies in ldquospringrdquo end up heating theball and the floor and stirring the air a bit

bull In the end all is heat

35

Why donrsquot we get hotter andhotter

bull If all these processes end up as heat why arenrsquotwe continually getting hotter

bull If earth retained all its heat we would get hotterbull All of earthrsquos heat is radiated away

F = σT4

bull If we dump more power the temperature goes upthe radiated power increases dramaticallyndash comes to equilibrium power dumped = power radiatedndash stable against perturbation T tracks power budget

Rough numbers

bull How much power does the earth radiatebull F = σT4 for T = 288ordmK = 15ordmC is 390 Wm2

bull Summed over entire surface area (4πR2 where R= 6378000 meters) is 20times1017 W

bull Global production is 3times1012 Wbull Solar radiation incident on earth is 18times1017 W

ndash just solar luminosity of 39times1026 W divided bygeometrical fraction that points at earth

bull Amazing coincidence of numbers (or is ithellip)

36

No Energy for Free

bull No matter what you canrsquot create energy out ofnothing it has to come from somewhere

bull We can transform energy from one form toanother we can store energy we can utilizeenergy being conveyed from natural sources

bull The net energy of the entire Universe is constantbull The best we can do is scrape up some useful

crumbs

Examplesbull Unit conversion

ndash 100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Calndash 100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 Jndash 100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWhndash 10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWhndash How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86Calorieshour About what average person eats

ndash Gasoline is $3gal Electricity if $015kWh Which is moreexpensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh)= $008kWh for gasoline Gasoline is cheap in the USA

37

Examplesbull Power vs Energy (P=Etime E = P t t = EP)

ndash Car goes 60 miles in one hour and uses 3 gal of gas What wastotal power in Watts P=Et Power = (3 gal1 hour) = 3galhr(366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W[Alternative method 3 galhr (132000000 J1 gal) (1 hr3600sec) = 110000 Jsec = 110000 W

ndash 1000 W space heater is on for 3 hours How much does it cost ifelectricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr(1kW1000W) = 3kWh ($15kWh) = $45 [Alternative methodE = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000J (1 kWh3600000J) = 3 kWh Again 45 cents

ndash AAA Battery contains 33 Calories of chemical energy How longcan it run a 2 Watt light bulb time = EP time = 33 Calories2W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1hr3600 sec) = 19 hours

QuestionThe US uses about 7 Gbarrels of oil each year This couldbe converted into which of the following units

A Joules B Watts C QBtus D Dollars $ E Any of the above

38

QuestionIf one barrel of oil contains 1700 kWh of energy how manyWatts is 7 Gbarrelyear

A 1400 GW (Giga Watts)

B 14 GW

C 11900 W

D 119 MW

E 1 x 1011 W

QuestionIf the total yearly oil use in the US is about 1400 GW howmany 1000 MW nuclear reactors will need to be built toreplace all oil use with electricity

A Only one will be needed

B Around 14

C Around 140

D Around 1400

E Cant convert Watts to reactors power vs energy

39

More Power Examplesbull How much power does it take to lift 10 kg up 2 meters in 2

secondsmgh = (10 kg)times(10 ms2)times(2 m) = 200J

200 J in 2 seconds rarr 100 Wattsbull If you want to heat the 3 m cubic room by 10ordmC with a

1000 W space heater how long will it takeWe know from before that the room needs to have 360000 J addedto it so at 1000 W = 1000 Js this will take 360 seconds or sixminutes

But the walls need to be warmed up too so it will actually takelonger (and depends on quality of insulation etc)

A note on arithmetic of unitsbull You should carry units in your calculations and multiply and divide them

as if they were numbersbull Example the force of air drag is given bybull Fdrag = frac12cDrAv2

bull cD is a dimensionless drag coefficientbull r is the density of air 13 kgm3

bull A is the cross-sectional area of the body in m2

bull v is the velocity in msbull units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) =

kgmiddotmiddotmm22middotmiddotmm22

m3middotmiddotss22kgmiddotmiddotmm44

m3middotmiddotss22= = kgmiddotmiddotmsms22 = = NewtonsNewtons

3

A note on graphs log vs linearbull Many graphs are on logarithmic scales watch for thisbull This condenses wide-ranging information into a compact

areabull Pay attention because you could warp your intuition if you

donrsquot appreciate the scalebull Log scales work in factors of tenbull A given vertical span represents a constant ratio (eg

factor of ten factor of two etc)bull An exponential increase looks like a straight line on a

logarithmic scale

4

Example Plots

Exponential plot is curved on linear scale and straight on a logarithmic scale

5

A brief history of fossil fuels

bull Here today gone tomorrowbull What will our future hold

ndash Will it be back to a simple lifendash Or will we find new ways to produce all the energy we wantndash Or will it be somewhere in the middle

GlobalEnergyWhereDoes itComeFrom

72287Hydroelectric

then radiatedaway2000000

Sun Abs byEarth

0008003Solar Direct003013Wind01305Geothermal0416

Biomass(burning)

6626Nuclear Energy

22589Natural Gas23292Coal400158Petroleum

Percent ofTotal

1018 Joulesyr(~QBtuyr)Source

Ultimately derivedfrom our sun

Courtesy DavidBodansky (UW)

Btu=1055kJ

6

7

Why do we use so much energy

8

9

We live in a special time and placehellipbull We use almost 100 times the amount used by the rest of the

world (by population)bull This phase has only lasted for the last century or sobull Most of our resources come from fossil fuels presently and

this has a short finite lifetimebull Fossil fuels formed from solar energy over 300 million

years will be used up in a few centuries

2000 2500 3000 3500 4000150010005000

year

ener

gy u

sage

10

Energy the capacity to do work

bull This notion makes sense even in acolloquial contextndash hard to get work done when yoursquore wiped out

(low on energy)ndash work makes you tired yoursquove used up energy

bull But we can make this definition of energymuch more precise by specifying exactlywhat we mean by work

Work =Energy more than justunpleasant tasks

bull In physics the definition of work is the application of aforce through a distance Energy is needed to do it

W = Fd

bull W is the work done = energy usedbull F is the force appliedbull d is the distance through which the force actsbull Only the force that acts in the direction of motion counts

towards work

11

Okay what is Force thenbull Force is a pushingpulling agentbull Examples

ndash gravity exerts a downward force on youndash the floor exerts an upward force on a ball during its bouncendash a car seat exerts a forward force on your body when you accelerate forward from

a stopndash the seat yoursquore sitting in now is exerting an upward force on you (can you feel it)ndash you exert a sideways force on a couch that you slide across the floorndash a string exerts a centrally-directed (centripetal) force on a rock at the end of a

string that yoursquore twirling over your headndash the expanding gas in your carrsquos cylinder exerts a force against the piston

Forces have Directionbull In all the previous examples force had a

direction associated with itbull If multiple forces act on an object they

could potentially add or cancel dependingon direction

Force 1Force 2

Total Force Force 1

Force 2

Total Force = 0

12

When net force is not zero

bull When an object experiences a non-zero net force it mustaccelerate

bull Newtonrsquos second lawF = ma Force = mass times acceleration

bull The same force makes a small object accelerate more thanit would a more massive objectndash hit a golf ball and a bowling ball with a golf club and see what

happens

QuestionA 150 lb person is standing still on the edge of a cliff Whatis the total force on the person

A zeroB 150 lbC Canrsquot say from this info

13

QuestionA 150 lb person jumps (or was he pushed) off a cliff and isfalling to their death What is the total force on the person

A zeroB 150 lbC Canrsquot say from this info

But what is acceleration

bull This is getting to be like the ldquohole in thebucketrdquo song but wersquore almost therehellip

bull Acceleration is any change in velocity(speed andor direction of motion)

bull Measured as rate of change of velocityndash velocity is expressed in meters per second (ms)ndash acceleration is meters per second per secondndash expressed as ms2 (meters per second-squared)

14

Putting it back together Units ofEnergy

bull Force is a mass times an accelerationndash mass has units of kilogramsndash acceleration is ms2

ndash force is then kgms2 which we call Newtons (N)

bull Work is a force times a distancendash units are then (kgms2)m = kg m2s2 = Nm = Joules (J)ndash One joule is one Newton of force acting through one meterndash Imperial units of force and distance are pounds and feet so unit of

energy is foot-pound which equals 136 J

bull Energy has the same units as work Joules

A Zoo of Unitsbull The main metric unit of energy is the Joule and most of

the world uses this but many others existbull The calorie is 4184 Joules

ndash raise 1 gram (cc) of water one degree Celsiusbull The Calorie (kilocalorie) is 4184 J (used for food energy)

ndash raise 1 kg (1 liter) of water one degree Celsiusbull The Btu (British thermal unit) is 1055 J (roughly 1 kJ) or

about 14 Calorie or chemical energy of one matchndash raise 1 pound of water one degree Fahrenheit

bull The kilowatt-hour (kWh) is 3600000 J = 3600 kJ or 860Calories (used for electrical energy)ndash one Watt (W) is one Joule per secondndash a kWh is 1000 W for one hour (3600 seconds)

bull Can also use ldquobarrel of oilrdquo ldquoton of coalrdquo 1000 cubic feetof natural gas gram of Uranium or amount of any energycontaining source etc

15

The Physics of Energy Formula List

bull Lots of forms of energy coming fast and furious but to putit in perspective herersquos a list of formulas

P = ΔEΔtPower (rate of energy use)

F = σT4 (temperature to the fourthpower times a constant)

Radiative energy flux

E = mc2 (mass times speed of lightsquared)

Mass energy

ΔE = cpmΔT (mass times change intemperature times heat capacity)

Heat Energy

E = mgh (mass times height times10ms2)

(Grav) Potential Energy

KE = frac12mv2 (mass times velocitysquared)

Kinetic Energy

W = Fd (Force times distance)Work

Energy FormulaEnergy Form

Kinetic Energybull Kinetic Energy the energy of motionbull Moving things carry energy in the amount

KE = frac12mv2

bull Note the v2 dependencemdashthis is whyndash a car at 60 mph is 4 times more dangerous than a car at 30 mphndash hurricane-force winds at 100 mph are much more destructive (4

times) than 50 mph gale-force windsndash a bullet shot from a gun is at least 100 times as destructive as a

thrown bullet even if you can throw it a tenth as fast as you couldshoot it

16

Numerical examples of kineticenergy

bull A baseball (mass is 0145 kg = 145 g) moving at 30 ms(67 mph) has kinetic energy

KE = frac12times(0145 kg)times(30 ms)2

= 6525 kgm2s2 asymp 65 J

bull A quarter (mass = 000567 kg = 567 g) flipped about fourfeet into the air has a speed on reaching your hand of about5 ms The kinetic energy is

KE = frac12times(000567 kg)times(5 ms)2

= 007 kgm2s2 = 007 J

More numerical examples

bull A 1500 kg car moves down the freeway at30 ms (67 mph)

KE = frac12times(1500 kg)times(30 ms)2

= 675000 kgm2s2 = 675 kJConvert to Calories 4184 kJ = 1 Calorie675 kJ (1 Calorie4184 kJ) = 161 Calorie

bull A 2 kg (~44 lb) fish jumps out of the waterwith a speed of 1 ms (22 mph)

KE = frac12times(2 kg)times(1 ms)2

= 1 kgm2s2 = 1 J

17

QuestionKinetic energy is E = 12 m v2 Which has more energy

A 10 kg object going 100 ms

B 100 kg object going 10 ms

C 1 kg object going 1000 ms

D 1000 kg object going 1 ms

1 ms = 22 mph

Gravitational Potential Energybull It takes work to lift a mass against the pull (force) of

gravitybull The force of gravity is mg where m is the mass and g is

the gravitational accelerationF = mg (note similarity to F = ma)

ndash g = 98 ms2 on the surface of the earth or 32 fts2

bull Lifting a height h against the gravitational forcerequires an energy input (work) of

ΔE = W = F h = mghbull Rolling a boulder up a hill and perching it on the edge of a

cliff gives it gravitational potential energy that can be laterreleased when the roadrunner is down below

bull Water in river or hydroelectric plant is using potentialenergy that it got from being lifted up when Sun (solarenergy) evaporated the water

18

QuestionPotential energy is E = 10 m h (metric units) Which hasmore energy

A 1 ton of water at a height of 100 ft

B 100 tons of water at a height of 1 ft

C 200 lb (110 ton) of water at 1000 ft

D All of the above have same energy

1 ms = 22 mph

First Example of Energy Exchangebull When the boulder falls off the cliff it picks up

speed and therefore gains kinetic energybull Where does this energy come from

rArr from the gravitational potential energybull The higher the cliff the more kinetic energy the

boulder will have when it reaches the ground

mgh

becomes

frac12mv2

Energy is conserved sofrac12mv2 = mgh

Can even figure out v since v2 = 2gh

h

19

Examples of GravitationalPotential Energy

bull How much gravitational potential energy does a70 kg high-diver have on the 10 meter platform

mgh = (70 kg)times(10 ms2)times(10 m)= 7000 kgm2s2 = 7 kJ

7 kJ (1 Calorie4182kJ) = 16 CaloriesThis is amount of energy the diver used in climbing the

stairs (actually more than this since some energy waswasted) They got that energy from the food they ate

The Energy of Heatbull Hot things have more energy than their cold

counterpartsbull Heat is really just kinetic energy on microscopic

scales the vibration or otherwise fast motion ofindividual atomsmoleculesndash Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are randombull Heat is frequently quantified by calories (or Btu)

ndash One calorie (4184 J) raises one gram of H2O 1ordmCndash One Calorie (4184 J) raises one kilogram of H2O 1ordmCndash One Btu (1055 J) raises one pound of H2O 1ordmF

20

Energy of Heat continuedbull Food Calories are with the ldquobigrdquo C or kilocalories (kcal)bull Since water has a density of one gram per cubic centimeter 1

cal heats 1 cc of water 1ordmC and likewise 1 kcal (Calorie) heatsone liter of water 1ordmC In British Units 1 Btu heats 1 pound ofwater 1 degree Fahrenheitndash these are useful numbers to hang onto

bull Example to heat a 2-liter bottle of Coke from the 5ordmCrefrigerator temperature to 20ordmC room temperature requires 30Calories or 1225 kJ

bull Drink a pint (16 oz) of ice cold water (or coke) It weighs about1 pound To heat it to body temperature (986 degrees minus 32degrees or change of 666 degrees Takes about 67 BtuConvert to Calories 1 Calorie = 1kJ = 4 Btu so

67 Btu (1 Calorie 4 Btu) = 1675 Calories Since 16 oz ofcoke has 210 Calories and about 17 Calories are used justheating to your body temp you get less calories drinking it cold(or drinking quart of cold water ldquoburnsrdquo 17 Calories)

The Physics of Energy Formula List

P = ΔEΔtPower (rate of energy use)

F = σT4 (temperature to the fourthpower times a constant)

Radiative energy flux

E = mc2 (mass times speed oflight squared)

Mass energy

ΔE = cpmΔT (mass times changein temperature times heatcapacity)

Heat Energy

E = mgh (mass times height times10ms2)

(Grav) Potential Energy

KE = frac12mv2 (mass times velocitysquared)

Kinetic Energy

W = Fd (Force times distance)Work

Energy FormulaEnergy Form

21

Heat Capacitybull Different materials have different capacities to

hold heatndash Add the same energy to different materials and yoursquoll

get different temperature risesndash Quantified as heat capacityndash Water is exceptional with 4184 JkgordmCndash Most materials are about 1000 JkgordmC (including

wood air metals)bull Example to add 10ordmC to a room 3 meters on a side

(cubic) how much energy do we needair density is 13 kgm3 and we have 27 m3 so 35 kg ofair and we need 1000 J per kg per ordmC so we end upneeding 350000 J (= 836 Cal)

Important in designing solar heated houses Also reasonit is cooler near the coast than inland

Powerbull Power is simply energy exchanged

per unit time or how fast you getwork done (Watts = Joulessec)

bull One horsepower = 745 Wbull Perform 100 J of work in 1 s and

call it 100 Wbull Run upstairs raising your 70 kg

(700 N) mass 3 m (2100 J) in 3seconds rarr 700 W output

bull Shuttle puts out a few GW(gigawatts or 109 W) of power

bull A big electrical power plant putsout around a GW That is 1 BillionJoules per second House takes afew kW (kilowatt)

22

QuestionPower is Energy used per second P= energytime Whichhighest power

A Using 100 Calories in 10 minutes

B Using 1000 Calories in 100 minutes

C Using 10 Calories in 1 minute

D Using 1 Calorie in 6 seconds

E All of the above are the same power usage

1 Calorieminute = Watts

Wind Energy

bull Wind can be used as a source of energy (windmills sailingships etc)

bull Really just kinetic energybull Example wind passing through a square meter at 8 meters

per secondndash Each second we have 8 cubic metersndash Air has density of 13 kgm3 so (8 m3)times(13 kgm3) = 104 kg of

air each secondndash frac12mv2 = frac12times(104 kg)times(8 ms)2 = 333 Jndash 333 J every second rarr 333 Watts of available power per square

meter (but to get all of it yoursquod have to stop the wind)bull Stronger winds rarr more power (like v2)

23

Chemical Energy

bull Electrostatic energy (associated with chargedparticles like electrons) is stored in the chemicalbonds of substances

bull Rearranging these bonds can release energy (somereactions require energy to be put in)

bull Typical numbers are 100ndash200 kJ per molendash a mole is 6022times1023 moleculesparticlesndash typical molecules are tens of grams per molerarrworks

out to typical numbers like several thousand Joules pergram or a few Calories per gram (remember 1 Cal = 1kcal = 4187 J)

Chemical Energy Examples

bull Burning a wooden match releases about oneBtu or 1055 Joules (a match is about 03grams) so this is gt3000 Jg nearly 1 Calg

bull Burning coal releases about 20 kJ per gramof chemical energy or roughly 5 Calg

bull Burning gasoline yields about 39 kJ pergram or just over 9 Calg

bull Very few substances over about 11 Calg

24

Energy from Food

bull We get the energy to do the things we do out of food(stored solar energy in the form of chemical energy)

bull Energy sources recognized by our digestive systemsndash Carbohydrates 4 Calories per gramndash Proteins 4 Calories per gramndash Fats 9 Calories per gram (like gasoline) (9 is more than

4 so gain more weight eating same amount of fat thancarbs or protein)

ndash Roughly 3500 Caloriespound in your body fat Less inyour protein (muscle skin etc)

Our Human Energy Budget

bull A 2000 Calorie per daydiet means 2000times4184 J =8368000 J per day

bull 837 MJ in (24 hrday) times(60 minhr)times(60 secmin)= 86400 sec correspondsto 97 Watts of power

bull Even a couch-potato at1500 Calday burns 75 W

bull More active lifestylesrequire greater Caloricintake (more energy)

25

Nutrition Labelsbull Nutrition labels tell you about the

energy content of foodbull Note they use Calories with capitol Cbull Conversions Fat 9 Calg

Carbs 4 CalgProtein 4 Calg

bull This product has 72 Cal from fat 48Cal from carbohydrates and 32 Calfrom proteinndash sum is 152 Calories compare to label

bull 152 Cal = 636 kJ enough to climbabout 1000 meters (64 kg person)

bull 1kwh = 860 Cal or about 14 lb bodyfat

bull 1 gal of gas has 31000 Calories

Mass-energy

bull Einsteinrsquos famous relationE = mc2

relates mass to energybull In effect they are the same thing

ndash one can be transformed into the otherndash physicists speak generally of mass-energy

bull Seldom experienced in daily life directlyndash Happens at large scale in the center of the sun and in

nuclear bombs and reactorsndash Actually does happen at barely detectable level in all

energy transactions but the effect is tiny

26

E = mc2 Examples

bull The energy equivalent of one gram of material(any composition) is (0001 kg)times(30times108 ms)2

= 90times1013 J = 90000000000000 J = 90 TJndash Man thatrsquos bigndash Our global energy budget is equivalent to 1000 kgyr

(thatrsquos about 1 ton per year)bull If one gram of material undergoes a chemical

reaction losing about 9000 J of energy howmuch mass does it lose

9000 J = Δmc2 so Δm = 9000c2 = 9times1039times1016

= 10-13 kg (would we ever notice)

Solar Energy is Nuclear Using E= mc2

bull Thermonuclear fusion reactions in the sunrsquos centerndash Sun is 16 million degrees Celsius in its centerndash Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then heliumndash Reaction per atom 20 million times more energetic than chemical

reactions in general

4 protonsmass = 4029

4He nucleusmass = 40015

2 neutrinos photons (light)

27

E = mc2 in Sun

bull Helium nucleus is lighter than the four protonsbull Mass difference is 4029 - 40015 = 00276 amu

ndash 1 amu (atomic mass unit) is 16605times10-27 kgndash difference of 458times10-29 kgndash multiply by c2 to get 412times10-12 Jndash 1 mole (6022times1023 particles) of protons rarr 25times1012 Jndash typical chemical reactions are 100-200 kJmolendash nuclear fusion is ~20 million times more potent stuffndash Nuclear fusion is energy source of hydrogen bomb

Energy from Lightbull The tremendous energy from the sun is released as light So light

carries energybull Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiationbull Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequencybull Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellipbull All objects emit ldquolightrdquobull The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter moreradiation and color is ldquobluerrdquo

28

Emitted Radiationrsquos Color andIntensity depend on Temperature

Object

YouHeat LampCandle FlameBulb FilamentSunrsquos SurfaceNeutron StarMolecules in deep space

Temperature

~ 30 C~ 500 C~ 1700 C~ 2700 C~ 5500 C~ millions C

lt -272C

Color

Infrared (invisible)Dull redDim orangeYellowBrilliant whiteX-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted lightThe hotter it gets the more intense the radiation (more energy)

ldquoBlackbodyrdquo or Planck Spectrum

29

Same thing on logarithmic scale

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm(note 0degC = 273degK 300degK = 27degC = 81degF)

Okay but how much energybull The power given off of a surface in the form of light is

proportional to the fourth power of temperatureF = σT4 in Watts per square meter

ndash the constant σ is numerically 567times10-8 WordmK4m2

ndash easy to remember constant 5678ndash temperature must be in Kelvin

bull ordmK = ordmC + 273bull ordmC = (59)times(ordmF ndash32)

bull Example radiation from your body(567 times10-8) times(310)4 = 523 Watts per square meter(if naked in the cold of space donrsquot let this happen to you)

30

Radiant Energy continued

bull Example The sun is 5800ordmK on its surface soF = σT4 = (567times10-8)times(5800)4 = 64times107 Wm2

Summing over entire surface area of sun gives39times1026 W

bull Compare to total capacity of energy production onearth 33times1012 Wndash Single power plant typically 05ndash10 GW (109 W)

bull In earthly situations radiated power out partiallybalanced by radiated power in from other sourcesndash Not 523 Wm2 in 70ordmF room more like 100 Wm2

bull goes like σTh4 ndash σTc

4

Electrical Energybull Opposite charges attract so electrons are attracted to

protons This holds atoms togetherbull It takes energy to pull electrons off their atomsbull Electrons want to get back home to their protons They can

only travel through conductors like wires not throughinsulators like plastic paper or wood They will gothrough miles of wire to get home to their protons

bull This is how electricity works The electronrsquos energy canbe stolen as it goes home Can be used in many manyways

bull Note electricity is not a primary source of energy Energy(from burning coal nat gas from hydro wind nuke orsolar) is used to pull of electrons and that energy can bemoved through wires and got back at will

31

And those are the majorplayershellip

bull Wersquove now seen most of the major energyplayersndash work as force times distancendash kinetic energy (wind ocean currents)ndash gravitational potential energy (hydroelectric tidal)ndash chemical energy (fossil fuels batteries food biomass)ndash heat energy (power plants space heating)ndash mass-energy (nuclear sources sunrsquos energy)ndash radiant energy (solar energy)ndash electrical energy (energy of electrons separated from

their atoms)

Conservation and Exchange ofEnergy

Nothing Comes for Free

32

Energy is Conservedbull Conservation of Energy is different from Energy

Conservation the latter being about using energywisely

bull Conservation of Energy means energy is neithercreated nor destroyed The amount of energy inthe Universe is constant

bull Donrsquot we create energy at a power plantndash Oh that this were truemdashno we simply transform

energy at our power plantsbull Doesnrsquot the sun create energy

ndash Nopemdashit exchanges mass for energybull Donrsquot batteries give us new energy

ndash Nope just convert stored chemical energy to electricalenergy Someone had to put that energy in there

height referenceh

Energy Exchangebull Though the total energy of a system is constant

the form of the energy can changebull A simple example is that of a simple pendulum in

which a continual exchange goes on betweenkinetic and potential energy

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

33

Perpetual Motion

bull Why wonrsquot the pendulum swing foreverbull Itrsquos hard to design a system free of energy pathsbull The pendulum slows down by several mechanisms

ndash Friction at the contact point requires force to opposeforce acts through distance rarr work is done

ndash Air resistance must push through air with a force(through a distance) rarr work is done

ndash Gets some air swirling puts kinetic energy into air (notreally fair to separate these last two)

bull Perpetual motion means no loss of energyndash solar system orbits come very close

Some Energy Chains

bull A coffee mug with some gravitational potentialenergy is dropped

bull potential energy turns into kinetic energybull kinetic energy of the mug goes into

ndash ripping the mug apart (chemical breaking bonds)ndash sending the pieces flying (kinetic)ndash into soundndash into heating the floor and pieces through friction as the

pieces slide to a stopbull In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored inthe potential energy)

34

Gasoline Examplebull Put gas in your car containing 9 Calgbull Combust gas turning 9 Calg into kinetic energy of

explosionbull Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a wholebull That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water andsurrounding air) and friction of transmission system(heat) and noise of engine (heating the air) etc

bull Much of energy goes into stirring the air (ends up as heat)bull Apply the brakes and convert kinetic energy into heatbull It all ends up as waste heat ultimately

Bouncing Ballbull Superball has gravitational potential energybull Drop the ball and this becomes kinetic energybull Ball hits ground and compresses (force times

distance) storing energy in the springbull Ball releases this mechanically stored energy

and it goes back into kinetic form (bouncesup)

bull Inefficiencies in ldquospringrdquo end up heating theball and the floor and stirring the air a bit

bull In the end all is heat

35

Why donrsquot we get hotter andhotter

bull If all these processes end up as heat why arenrsquotwe continually getting hotter

bull If earth retained all its heat we would get hotterbull All of earthrsquos heat is radiated away

F = σT4

bull If we dump more power the temperature goes upthe radiated power increases dramaticallyndash comes to equilibrium power dumped = power radiatedndash stable against perturbation T tracks power budget

Rough numbers

bull How much power does the earth radiatebull F = σT4 for T = 288ordmK = 15ordmC is 390 Wm2

bull Summed over entire surface area (4πR2 where R= 6378000 meters) is 20times1017 W

bull Global production is 3times1012 Wbull Solar radiation incident on earth is 18times1017 W

ndash just solar luminosity of 39times1026 W divided bygeometrical fraction that points at earth

bull Amazing coincidence of numbers (or is ithellip)

36

No Energy for Free

bull No matter what you canrsquot create energy out ofnothing it has to come from somewhere

bull We can transform energy from one form toanother we can store energy we can utilizeenergy being conveyed from natural sources

bull The net energy of the entire Universe is constantbull The best we can do is scrape up some useful

crumbs

Examplesbull Unit conversion

ndash 100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Calndash 100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 Jndash 100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWhndash 10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWhndash How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86Calorieshour About what average person eats

ndash Gasoline is $3gal Electricity if $015kWh Which is moreexpensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh)= $008kWh for gasoline Gasoline is cheap in the USA

37

Examplesbull Power vs Energy (P=Etime E = P t t = EP)

ndash Car goes 60 miles in one hour and uses 3 gal of gas What wastotal power in Watts P=Et Power = (3 gal1 hour) = 3galhr(366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W[Alternative method 3 galhr (132000000 J1 gal) (1 hr3600sec) = 110000 Jsec = 110000 W

ndash 1000 W space heater is on for 3 hours How much does it cost ifelectricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr(1kW1000W) = 3kWh ($15kWh) = $45 [Alternative methodE = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000J (1 kWh3600000J) = 3 kWh Again 45 cents

ndash AAA Battery contains 33 Calories of chemical energy How longcan it run a 2 Watt light bulb time = EP time = 33 Calories2W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1hr3600 sec) = 19 hours

QuestionThe US uses about 7 Gbarrels of oil each year This couldbe converted into which of the following units

A Joules B Watts C QBtus D Dollars $ E Any of the above

38

QuestionIf one barrel of oil contains 1700 kWh of energy how manyWatts is 7 Gbarrelyear

A 1400 GW (Giga Watts)

B 14 GW

C 11900 W

D 119 MW

E 1 x 1011 W

QuestionIf the total yearly oil use in the US is about 1400 GW howmany 1000 MW nuclear reactors will need to be built toreplace all oil use with electricity

A Only one will be needed

B Around 14

C Around 140

D Around 1400

E Cant convert Watts to reactors power vs energy

39

More Power Examplesbull How much power does it take to lift 10 kg up 2 meters in 2

secondsmgh = (10 kg)times(10 ms2)times(2 m) = 200J

200 J in 2 seconds rarr 100 Wattsbull If you want to heat the 3 m cubic room by 10ordmC with a

1000 W space heater how long will it takeWe know from before that the room needs to have 360000 J addedto it so at 1000 W = 1000 Js this will take 360 seconds or sixminutes

But the walls need to be warmed up too so it will actually takelonger (and depends on quality of insulation etc)

A note on arithmetic of unitsbull You should carry units in your calculations and multiply and divide them

as if they were numbersbull Example the force of air drag is given bybull Fdrag = frac12cDrAv2

bull cD is a dimensionless drag coefficientbull r is the density of air 13 kgm3

bull A is the cross-sectional area of the body in m2

bull v is the velocity in msbull units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) =

kgmiddotmiddotmm22middotmiddotmm22

m3middotmiddotss22kgmiddotmiddotmm44

m3middotmiddotss22= = kgmiddotmiddotmsms22 = = NewtonsNewtons

4

Example Plots

Exponential plot is curved on linear scale and straight on a logarithmic scale

5

A brief history of fossil fuels

bull Here today gone tomorrowbull What will our future hold

ndash Will it be back to a simple lifendash Or will we find new ways to produce all the energy we wantndash Or will it be somewhere in the middle

GlobalEnergyWhereDoes itComeFrom

72287Hydroelectric

then radiatedaway2000000

Sun Abs byEarth

0008003Solar Direct003013Wind01305Geothermal0416

Biomass(burning)

6626Nuclear Energy

22589Natural Gas23292Coal400158Petroleum

Percent ofTotal

1018 Joulesyr(~QBtuyr)Source

Ultimately derivedfrom our sun

Courtesy DavidBodansky (UW)

Btu=1055kJ

6

7

Why do we use so much energy

8

9

We live in a special time and placehellipbull We use almost 100 times the amount used by the rest of the

world (by population)bull This phase has only lasted for the last century or sobull Most of our resources come from fossil fuels presently and

this has a short finite lifetimebull Fossil fuels formed from solar energy over 300 million

years will be used up in a few centuries

2000 2500 3000 3500 4000150010005000

year

ener

gy u

sage

10

Energy the capacity to do work

bull This notion makes sense even in acolloquial contextndash hard to get work done when yoursquore wiped out

(low on energy)ndash work makes you tired yoursquove used up energy

bull But we can make this definition of energymuch more precise by specifying exactlywhat we mean by work

Work =Energy more than justunpleasant tasks

bull In physics the definition of work is the application of aforce through a distance Energy is needed to do it

W = Fd

bull W is the work done = energy usedbull F is the force appliedbull d is the distance through which the force actsbull Only the force that acts in the direction of motion counts

towards work

11

Okay what is Force thenbull Force is a pushingpulling agentbull Examples

ndash gravity exerts a downward force on youndash the floor exerts an upward force on a ball during its bouncendash a car seat exerts a forward force on your body when you accelerate forward from

a stopndash the seat yoursquore sitting in now is exerting an upward force on you (can you feel it)ndash you exert a sideways force on a couch that you slide across the floorndash a string exerts a centrally-directed (centripetal) force on a rock at the end of a

string that yoursquore twirling over your headndash the expanding gas in your carrsquos cylinder exerts a force against the piston

Forces have Directionbull In all the previous examples force had a

direction associated with itbull If multiple forces act on an object they

could potentially add or cancel dependingon direction

Force 1Force 2

Total Force Force 1

Force 2

Total Force = 0

12

When net force is not zero

bull When an object experiences a non-zero net force it mustaccelerate

bull Newtonrsquos second lawF = ma Force = mass times acceleration

bull The same force makes a small object accelerate more thanit would a more massive objectndash hit a golf ball and a bowling ball with a golf club and see what

happens

QuestionA 150 lb person is standing still on the edge of a cliff Whatis the total force on the person

A zeroB 150 lbC Canrsquot say from this info

13

QuestionA 150 lb person jumps (or was he pushed) off a cliff and isfalling to their death What is the total force on the person

A zeroB 150 lbC Canrsquot say from this info

But what is acceleration

bull This is getting to be like the ldquohole in thebucketrdquo song but wersquore almost therehellip

bull Acceleration is any change in velocity(speed andor direction of motion)

bull Measured as rate of change of velocityndash velocity is expressed in meters per second (ms)ndash acceleration is meters per second per secondndash expressed as ms2 (meters per second-squared)

14

Putting it back together Units ofEnergy

bull Force is a mass times an accelerationndash mass has units of kilogramsndash acceleration is ms2

ndash force is then kgms2 which we call Newtons (N)

bull Work is a force times a distancendash units are then (kgms2)m = kg m2s2 = Nm = Joules (J)ndash One joule is one Newton of force acting through one meterndash Imperial units of force and distance are pounds and feet so unit of

energy is foot-pound which equals 136 J

bull Energy has the same units as work Joules

A Zoo of Unitsbull The main metric unit of energy is the Joule and most of

the world uses this but many others existbull The calorie is 4184 Joules

ndash raise 1 gram (cc) of water one degree Celsiusbull The Calorie (kilocalorie) is 4184 J (used for food energy)

ndash raise 1 kg (1 liter) of water one degree Celsiusbull The Btu (British thermal unit) is 1055 J (roughly 1 kJ) or

about 14 Calorie or chemical energy of one matchndash raise 1 pound of water one degree Fahrenheit

bull The kilowatt-hour (kWh) is 3600000 J = 3600 kJ or 860Calories (used for electrical energy)ndash one Watt (W) is one Joule per secondndash a kWh is 1000 W for one hour (3600 seconds)

bull Can also use ldquobarrel of oilrdquo ldquoton of coalrdquo 1000 cubic feetof natural gas gram of Uranium or amount of any energycontaining source etc

15

The Physics of Energy Formula List

bull Lots of forms of energy coming fast and furious but to putit in perspective herersquos a list of formulas

P = ΔEΔtPower (rate of energy use)

F = σT4 (temperature to the fourthpower times a constant)

Radiative energy flux

E = mc2 (mass times speed of lightsquared)

Mass energy

ΔE = cpmΔT (mass times change intemperature times heat capacity)

Heat Energy

E = mgh (mass times height times10ms2)

(Grav) Potential Energy

KE = frac12mv2 (mass times velocitysquared)

Kinetic Energy

W = Fd (Force times distance)Work

Energy FormulaEnergy Form

Kinetic Energybull Kinetic Energy the energy of motionbull Moving things carry energy in the amount

KE = frac12mv2

bull Note the v2 dependencemdashthis is whyndash a car at 60 mph is 4 times more dangerous than a car at 30 mphndash hurricane-force winds at 100 mph are much more destructive (4

times) than 50 mph gale-force windsndash a bullet shot from a gun is at least 100 times as destructive as a

thrown bullet even if you can throw it a tenth as fast as you couldshoot it

16

Numerical examples of kineticenergy

bull A baseball (mass is 0145 kg = 145 g) moving at 30 ms(67 mph) has kinetic energy

KE = frac12times(0145 kg)times(30 ms)2

= 6525 kgm2s2 asymp 65 J

bull A quarter (mass = 000567 kg = 567 g) flipped about fourfeet into the air has a speed on reaching your hand of about5 ms The kinetic energy is

KE = frac12times(000567 kg)times(5 ms)2

= 007 kgm2s2 = 007 J

More numerical examples

bull A 1500 kg car moves down the freeway at30 ms (67 mph)

KE = frac12times(1500 kg)times(30 ms)2

= 675000 kgm2s2 = 675 kJConvert to Calories 4184 kJ = 1 Calorie675 kJ (1 Calorie4184 kJ) = 161 Calorie

bull A 2 kg (~44 lb) fish jumps out of the waterwith a speed of 1 ms (22 mph)

KE = frac12times(2 kg)times(1 ms)2

= 1 kgm2s2 = 1 J

17

QuestionKinetic energy is E = 12 m v2 Which has more energy

A 10 kg object going 100 ms

B 100 kg object going 10 ms

C 1 kg object going 1000 ms

D 1000 kg object going 1 ms

1 ms = 22 mph

Gravitational Potential Energybull It takes work to lift a mass against the pull (force) of

gravitybull The force of gravity is mg where m is the mass and g is

the gravitational accelerationF = mg (note similarity to F = ma)

ndash g = 98 ms2 on the surface of the earth or 32 fts2

bull Lifting a height h against the gravitational forcerequires an energy input (work) of

ΔE = W = F h = mghbull Rolling a boulder up a hill and perching it on the edge of a

cliff gives it gravitational potential energy that can be laterreleased when the roadrunner is down below

bull Water in river or hydroelectric plant is using potentialenergy that it got from being lifted up when Sun (solarenergy) evaporated the water

18

QuestionPotential energy is E = 10 m h (metric units) Which hasmore energy

A 1 ton of water at a height of 100 ft

B 100 tons of water at a height of 1 ft

C 200 lb (110 ton) of water at 1000 ft

D All of the above have same energy

1 ms = 22 mph

First Example of Energy Exchangebull When the boulder falls off the cliff it picks up

speed and therefore gains kinetic energybull Where does this energy come from

rArr from the gravitational potential energybull The higher the cliff the more kinetic energy the

boulder will have when it reaches the ground

mgh

becomes

frac12mv2

Energy is conserved sofrac12mv2 = mgh

Can even figure out v since v2 = 2gh

h

19

Examples of GravitationalPotential Energy

bull How much gravitational potential energy does a70 kg high-diver have on the 10 meter platform

mgh = (70 kg)times(10 ms2)times(10 m)= 7000 kgm2s2 = 7 kJ

7 kJ (1 Calorie4182kJ) = 16 CaloriesThis is amount of energy the diver used in climbing the

stairs (actually more than this since some energy waswasted) They got that energy from the food they ate

The Energy of Heatbull Hot things have more energy than their cold

counterpartsbull Heat is really just kinetic energy on microscopic

scales the vibration or otherwise fast motion ofindividual atomsmoleculesndash Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are randombull Heat is frequently quantified by calories (or Btu)

ndash One calorie (4184 J) raises one gram of H2O 1ordmCndash One Calorie (4184 J) raises one kilogram of H2O 1ordmCndash One Btu (1055 J) raises one pound of H2O 1ordmF

20

Energy of Heat continuedbull Food Calories are with the ldquobigrdquo C or kilocalories (kcal)bull Since water has a density of one gram per cubic centimeter 1

cal heats 1 cc of water 1ordmC and likewise 1 kcal (Calorie) heatsone liter of water 1ordmC In British Units 1 Btu heats 1 pound ofwater 1 degree Fahrenheitndash these are useful numbers to hang onto

bull Example to heat a 2-liter bottle of Coke from the 5ordmCrefrigerator temperature to 20ordmC room temperature requires 30Calories or 1225 kJ

bull Drink a pint (16 oz) of ice cold water (or coke) It weighs about1 pound To heat it to body temperature (986 degrees minus 32degrees or change of 666 degrees Takes about 67 BtuConvert to Calories 1 Calorie = 1kJ = 4 Btu so

67 Btu (1 Calorie 4 Btu) = 1675 Calories Since 16 oz ofcoke has 210 Calories and about 17 Calories are used justheating to your body temp you get less calories drinking it cold(or drinking quart of cold water ldquoburnsrdquo 17 Calories)

The Physics of Energy Formula List

P = ΔEΔtPower (rate of energy use)

F = σT4 (temperature to the fourthpower times a constant)

Radiative energy flux

E = mc2 (mass times speed oflight squared)

Mass energy

ΔE = cpmΔT (mass times changein temperature times heatcapacity)

Heat Energy

E = mgh (mass times height times10ms2)

(Grav) Potential Energy

KE = frac12mv2 (mass times velocitysquared)

Kinetic Energy

W = Fd (Force times distance)Work

Energy FormulaEnergy Form

21

Heat Capacitybull Different materials have different capacities to

hold heatndash Add the same energy to different materials and yoursquoll

get different temperature risesndash Quantified as heat capacityndash Water is exceptional with 4184 JkgordmCndash Most materials are about 1000 JkgordmC (including

wood air metals)bull Example to add 10ordmC to a room 3 meters on a side

(cubic) how much energy do we needair density is 13 kgm3 and we have 27 m3 so 35 kg ofair and we need 1000 J per kg per ordmC so we end upneeding 350000 J (= 836 Cal)

Important in designing solar heated houses Also reasonit is cooler near the coast than inland

Powerbull Power is simply energy exchanged

per unit time or how fast you getwork done (Watts = Joulessec)

bull One horsepower = 745 Wbull Perform 100 J of work in 1 s and

call it 100 Wbull Run upstairs raising your 70 kg

(700 N) mass 3 m (2100 J) in 3seconds rarr 700 W output

bull Shuttle puts out a few GW(gigawatts or 109 W) of power

bull A big electrical power plant putsout around a GW That is 1 BillionJoules per second House takes afew kW (kilowatt)

22

QuestionPower is Energy used per second P= energytime Whichhighest power

A Using 100 Calories in 10 minutes

B Using 1000 Calories in 100 minutes

C Using 10 Calories in 1 minute

D Using 1 Calorie in 6 seconds

E All of the above are the same power usage

1 Calorieminute = Watts

Wind Energy

bull Wind can be used as a source of energy (windmills sailingships etc)

bull Really just kinetic energybull Example wind passing through a square meter at 8 meters

per secondndash Each second we have 8 cubic metersndash Air has density of 13 kgm3 so (8 m3)times(13 kgm3) = 104 kg of

air each secondndash frac12mv2 = frac12times(104 kg)times(8 ms)2 = 333 Jndash 333 J every second rarr 333 Watts of available power per square

meter (but to get all of it yoursquod have to stop the wind)bull Stronger winds rarr more power (like v2)

23

Chemical Energy

bull Electrostatic energy (associated with chargedparticles like electrons) is stored in the chemicalbonds of substances

bull Rearranging these bonds can release energy (somereactions require energy to be put in)

bull Typical numbers are 100ndash200 kJ per molendash a mole is 6022times1023 moleculesparticlesndash typical molecules are tens of grams per molerarrworks

out to typical numbers like several thousand Joules pergram or a few Calories per gram (remember 1 Cal = 1kcal = 4187 J)

Chemical Energy Examples

bull Burning a wooden match releases about oneBtu or 1055 Joules (a match is about 03grams) so this is gt3000 Jg nearly 1 Calg

bull Burning coal releases about 20 kJ per gramof chemical energy or roughly 5 Calg

bull Burning gasoline yields about 39 kJ pergram or just over 9 Calg

bull Very few substances over about 11 Calg

24

Energy from Food

bull We get the energy to do the things we do out of food(stored solar energy in the form of chemical energy)

bull Energy sources recognized by our digestive systemsndash Carbohydrates 4 Calories per gramndash Proteins 4 Calories per gramndash Fats 9 Calories per gram (like gasoline) (9 is more than

4 so gain more weight eating same amount of fat thancarbs or protein)

ndash Roughly 3500 Caloriespound in your body fat Less inyour protein (muscle skin etc)

Our Human Energy Budget

bull A 2000 Calorie per daydiet means 2000times4184 J =8368000 J per day

bull 837 MJ in (24 hrday) times(60 minhr)times(60 secmin)= 86400 sec correspondsto 97 Watts of power

bull Even a couch-potato at1500 Calday burns 75 W

bull More active lifestylesrequire greater Caloricintake (more energy)

25

Nutrition Labelsbull Nutrition labels tell you about the

energy content of foodbull Note they use Calories with capitol Cbull Conversions Fat 9 Calg

Carbs 4 CalgProtein 4 Calg

bull This product has 72 Cal from fat 48Cal from carbohydrates and 32 Calfrom proteinndash sum is 152 Calories compare to label

bull 152 Cal = 636 kJ enough to climbabout 1000 meters (64 kg person)

bull 1kwh = 860 Cal or about 14 lb bodyfat

bull 1 gal of gas has 31000 Calories

Mass-energy

bull Einsteinrsquos famous relationE = mc2

relates mass to energybull In effect they are the same thing

ndash one can be transformed into the otherndash physicists speak generally of mass-energy

bull Seldom experienced in daily life directlyndash Happens at large scale in the center of the sun and in

nuclear bombs and reactorsndash Actually does happen at barely detectable level in all

energy transactions but the effect is tiny

26

E = mc2 Examples

bull The energy equivalent of one gram of material(any composition) is (0001 kg)times(30times108 ms)2

= 90times1013 J = 90000000000000 J = 90 TJndash Man thatrsquos bigndash Our global energy budget is equivalent to 1000 kgyr

(thatrsquos about 1 ton per year)bull If one gram of material undergoes a chemical

reaction losing about 9000 J of energy howmuch mass does it lose

9000 J = Δmc2 so Δm = 9000c2 = 9times1039times1016

= 10-13 kg (would we ever notice)

Solar Energy is Nuclear Using E= mc2

bull Thermonuclear fusion reactions in the sunrsquos centerndash Sun is 16 million degrees Celsius in its centerndash Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then heliumndash Reaction per atom 20 million times more energetic than chemical

reactions in general

4 protonsmass = 4029

4He nucleusmass = 40015

2 neutrinos photons (light)

27

E = mc2 in Sun

bull Helium nucleus is lighter than the four protonsbull Mass difference is 4029 - 40015 = 00276 amu

ndash 1 amu (atomic mass unit) is 16605times10-27 kgndash difference of 458times10-29 kgndash multiply by c2 to get 412times10-12 Jndash 1 mole (6022times1023 particles) of protons rarr 25times1012 Jndash typical chemical reactions are 100-200 kJmolendash nuclear fusion is ~20 million times more potent stuffndash Nuclear fusion is energy source of hydrogen bomb

Energy from Lightbull The tremendous energy from the sun is released as light So light

carries energybull Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiationbull Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequencybull Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellipbull All objects emit ldquolightrdquobull The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter moreradiation and color is ldquobluerrdquo

28

Emitted Radiationrsquos Color andIntensity depend on Temperature

Object

YouHeat LampCandle FlameBulb FilamentSunrsquos SurfaceNeutron StarMolecules in deep space

Temperature

~ 30 C~ 500 C~ 1700 C~ 2700 C~ 5500 C~ millions C

lt -272C

Color

Infrared (invisible)Dull redDim orangeYellowBrilliant whiteX-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted lightThe hotter it gets the more intense the radiation (more energy)

ldquoBlackbodyrdquo or Planck Spectrum

29

Same thing on logarithmic scale

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm(note 0degC = 273degK 300degK = 27degC = 81degF)

Okay but how much energybull The power given off of a surface in the form of light is

proportional to the fourth power of temperatureF = σT4 in Watts per square meter

ndash the constant σ is numerically 567times10-8 WordmK4m2

ndash easy to remember constant 5678ndash temperature must be in Kelvin

bull ordmK = ordmC + 273bull ordmC = (59)times(ordmF ndash32)

bull Example radiation from your body(567 times10-8) times(310)4 = 523 Watts per square meter(if naked in the cold of space donrsquot let this happen to you)

30

Radiant Energy continued

bull Example The sun is 5800ordmK on its surface soF = σT4 = (567times10-8)times(5800)4 = 64times107 Wm2

Summing over entire surface area of sun gives39times1026 W

bull Compare to total capacity of energy production onearth 33times1012 Wndash Single power plant typically 05ndash10 GW (109 W)

bull In earthly situations radiated power out partiallybalanced by radiated power in from other sourcesndash Not 523 Wm2 in 70ordmF room more like 100 Wm2

bull goes like σTh4 ndash σTc

4

Electrical Energybull Opposite charges attract so electrons are attracted to

protons This holds atoms togetherbull It takes energy to pull electrons off their atomsbull Electrons want to get back home to their protons They can

only travel through conductors like wires not throughinsulators like plastic paper or wood They will gothrough miles of wire to get home to their protons

bull This is how electricity works The electronrsquos energy canbe stolen as it goes home Can be used in many manyways

bull Note electricity is not a primary source of energy Energy(from burning coal nat gas from hydro wind nuke orsolar) is used to pull of electrons and that energy can bemoved through wires and got back at will

31

And those are the majorplayershellip

bull Wersquove now seen most of the major energyplayersndash work as force times distancendash kinetic energy (wind ocean currents)ndash gravitational potential energy (hydroelectric tidal)ndash chemical energy (fossil fuels batteries food biomass)ndash heat energy (power plants space heating)ndash mass-energy (nuclear sources sunrsquos energy)ndash radiant energy (solar energy)ndash electrical energy (energy of electrons separated from

their atoms)

Conservation and Exchange ofEnergy

Nothing Comes for Free

32

Energy is Conservedbull Conservation of Energy is different from Energy

Conservation the latter being about using energywisely

bull Conservation of Energy means energy is neithercreated nor destroyed The amount of energy inthe Universe is constant

bull Donrsquot we create energy at a power plantndash Oh that this were truemdashno we simply transform

energy at our power plantsbull Doesnrsquot the sun create energy

ndash Nopemdashit exchanges mass for energybull Donrsquot batteries give us new energy

ndash Nope just convert stored chemical energy to electricalenergy Someone had to put that energy in there

height referenceh

Energy Exchangebull Though the total energy of a system is constant

the form of the energy can changebull A simple example is that of a simple pendulum in

which a continual exchange goes on betweenkinetic and potential energy

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

33

Perpetual Motion

bull Why wonrsquot the pendulum swing foreverbull Itrsquos hard to design a system free of energy pathsbull The pendulum slows down by several mechanisms

ndash Friction at the contact point requires force to opposeforce acts through distance rarr work is done

ndash Air resistance must push through air with a force(through a distance) rarr work is done

ndash Gets some air swirling puts kinetic energy into air (notreally fair to separate these last two)

bull Perpetual motion means no loss of energyndash solar system orbits come very close

Some Energy Chains

bull A coffee mug with some gravitational potentialenergy is dropped

bull potential energy turns into kinetic energybull kinetic energy of the mug goes into

ndash ripping the mug apart (chemical breaking bonds)ndash sending the pieces flying (kinetic)ndash into soundndash into heating the floor and pieces through friction as the

pieces slide to a stopbull In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored inthe potential energy)

34

Gasoline Examplebull Put gas in your car containing 9 Calgbull Combust gas turning 9 Calg into kinetic energy of

explosionbull Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a wholebull That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water andsurrounding air) and friction of transmission system(heat) and noise of engine (heating the air) etc

bull Much of energy goes into stirring the air (ends up as heat)bull Apply the brakes and convert kinetic energy into heatbull It all ends up as waste heat ultimately

Bouncing Ballbull Superball has gravitational potential energybull Drop the ball and this becomes kinetic energybull Ball hits ground and compresses (force times

distance) storing energy in the springbull Ball releases this mechanically stored energy

and it goes back into kinetic form (bouncesup)

bull Inefficiencies in ldquospringrdquo end up heating theball and the floor and stirring the air a bit

bull In the end all is heat

35

Why donrsquot we get hotter andhotter

bull If all these processes end up as heat why arenrsquotwe continually getting hotter

bull If earth retained all its heat we would get hotterbull All of earthrsquos heat is radiated away

F = σT4

bull If we dump more power the temperature goes upthe radiated power increases dramaticallyndash comes to equilibrium power dumped = power radiatedndash stable against perturbation T tracks power budget

Rough numbers

bull How much power does the earth radiatebull F = σT4 for T = 288ordmK = 15ordmC is 390 Wm2

bull Summed over entire surface area (4πR2 where R= 6378000 meters) is 20times1017 W

bull Global production is 3times1012 Wbull Solar radiation incident on earth is 18times1017 W

ndash just solar luminosity of 39times1026 W divided bygeometrical fraction that points at earth

bull Amazing coincidence of numbers (or is ithellip)

36

No Energy for Free

bull No matter what you canrsquot create energy out ofnothing it has to come from somewhere

bull We can transform energy from one form toanother we can store energy we can utilizeenergy being conveyed from natural sources

bull The net energy of the entire Universe is constantbull The best we can do is scrape up some useful

crumbs

Examplesbull Unit conversion

ndash 100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Calndash 100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 Jndash 100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWhndash 10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWhndash How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86Calorieshour About what average person eats

ndash Gasoline is $3gal Electricity if $015kWh Which is moreexpensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh)= $008kWh for gasoline Gasoline is cheap in the USA

37

Examplesbull Power vs Energy (P=Etime E = P t t = EP)

ndash Car goes 60 miles in one hour and uses 3 gal of gas What wastotal power in Watts P=Et Power = (3 gal1 hour) = 3galhr(366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W[Alternative method 3 galhr (132000000 J1 gal) (1 hr3600sec) = 110000 Jsec = 110000 W

ndash 1000 W space heater is on for 3 hours How much does it cost ifelectricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr(1kW1000W) = 3kWh ($15kWh) = $45 [Alternative methodE = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000J (1 kWh3600000J) = 3 kWh Again 45 cents

ndash AAA Battery contains 33 Calories of chemical energy How longcan it run a 2 Watt light bulb time = EP time = 33 Calories2W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1hr3600 sec) = 19 hours

QuestionThe US uses about 7 Gbarrels of oil each year This couldbe converted into which of the following units

A Joules B Watts C QBtus D Dollars $ E Any of the above

38

QuestionIf one barrel of oil contains 1700 kWh of energy how manyWatts is 7 Gbarrelyear

A 1400 GW (Giga Watts)

B 14 GW

C 11900 W

D 119 MW

E 1 x 1011 W

QuestionIf the total yearly oil use in the US is about 1400 GW howmany 1000 MW nuclear reactors will need to be built toreplace all oil use with electricity

A Only one will be needed

B Around 14

C Around 140

D Around 1400

E Cant convert Watts to reactors power vs energy

39

More Power Examplesbull How much power does it take to lift 10 kg up 2 meters in 2

secondsmgh = (10 kg)times(10 ms2)times(2 m) = 200J

200 J in 2 seconds rarr 100 Wattsbull If you want to heat the 3 m cubic room by 10ordmC with a

1000 W space heater how long will it takeWe know from before that the room needs to have 360000 J addedto it so at 1000 W = 1000 Js this will take 360 seconds or sixminutes

But the walls need to be warmed up too so it will actually takelonger (and depends on quality of insulation etc)

A note on arithmetic of unitsbull You should carry units in your calculations and multiply and divide them

as if they were numbersbull Example the force of air drag is given bybull Fdrag = frac12cDrAv2

bull cD is a dimensionless drag coefficientbull r is the density of air 13 kgm3

bull A is the cross-sectional area of the body in m2

bull v is the velocity in msbull units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) =

kgmiddotmiddotmm22middotmiddotmm22

m3middotmiddotss22kgmiddotmiddotmm44

m3middotmiddotss22= = kgmiddotmiddotmsms22 = = NewtonsNewtons

5

A brief history of fossil fuels

bull Here today gone tomorrowbull What will our future hold

ndash Will it be back to a simple lifendash Or will we find new ways to produce all the energy we wantndash Or will it be somewhere in the middle

GlobalEnergyWhereDoes itComeFrom

72287Hydroelectric

then radiatedaway2000000

Sun Abs byEarth

0008003Solar Direct003013Wind01305Geothermal0416

Biomass(burning)

6626Nuclear Energy

22589Natural Gas23292Coal400158Petroleum

Percent ofTotal

1018 Joulesyr(~QBtuyr)Source

Ultimately derivedfrom our sun

Courtesy DavidBodansky (UW)

Btu=1055kJ

6

7

Why do we use so much energy

8

9

We live in a special time and placehellipbull We use almost 100 times the amount used by the rest of the

world (by population)bull This phase has only lasted for the last century or sobull Most of our resources come from fossil fuels presently and

this has a short finite lifetimebull Fossil fuels formed from solar energy over 300 million

years will be used up in a few centuries

2000 2500 3000 3500 4000150010005000

year

ener

gy u

sage

10

Energy the capacity to do work

bull This notion makes sense even in acolloquial contextndash hard to get work done when yoursquore wiped out

(low on energy)ndash work makes you tired yoursquove used up energy

bull But we can make this definition of energymuch more precise by specifying exactlywhat we mean by work

Work =Energy more than justunpleasant tasks

bull In physics the definition of work is the application of aforce through a distance Energy is needed to do it

W = Fd

bull W is the work done = energy usedbull F is the force appliedbull d is the distance through which the force actsbull Only the force that acts in the direction of motion counts

towards work

11

Okay what is Force thenbull Force is a pushingpulling agentbull Examples

ndash gravity exerts a downward force on youndash the floor exerts an upward force on a ball during its bouncendash a car seat exerts a forward force on your body when you accelerate forward from

a stopndash the seat yoursquore sitting in now is exerting an upward force on you (can you feel it)ndash you exert a sideways force on a couch that you slide across the floorndash a string exerts a centrally-directed (centripetal) force on a rock at the end of a

string that yoursquore twirling over your headndash the expanding gas in your carrsquos cylinder exerts a force against the piston

Forces have Directionbull In all the previous examples force had a

direction associated with itbull If multiple forces act on an object they

could potentially add or cancel dependingon direction

Force 1Force 2

Total Force Force 1

Force 2

Total Force = 0

12

When net force is not zero

bull When an object experiences a non-zero net force it mustaccelerate

bull Newtonrsquos second lawF = ma Force = mass times acceleration

bull The same force makes a small object accelerate more thanit would a more massive objectndash hit a golf ball and a bowling ball with a golf club and see what

happens

QuestionA 150 lb person is standing still on the edge of a cliff Whatis the total force on the person

A zeroB 150 lbC Canrsquot say from this info

13

QuestionA 150 lb person jumps (or was he pushed) off a cliff and isfalling to their death What is the total force on the person

A zeroB 150 lbC Canrsquot say from this info

But what is acceleration

bull This is getting to be like the ldquohole in thebucketrdquo song but wersquore almost therehellip

bull Acceleration is any change in velocity(speed andor direction of motion)

bull Measured as rate of change of velocityndash velocity is expressed in meters per second (ms)ndash acceleration is meters per second per secondndash expressed as ms2 (meters per second-squared)

14

Putting it back together Units ofEnergy

bull Force is a mass times an accelerationndash mass has units of kilogramsndash acceleration is ms2

ndash force is then kgms2 which we call Newtons (N)

bull Work is a force times a distancendash units are then (kgms2)m = kg m2s2 = Nm = Joules (J)ndash One joule is one Newton of force acting through one meterndash Imperial units of force and distance are pounds and feet so unit of

energy is foot-pound which equals 136 J

bull Energy has the same units as work Joules

A Zoo of Unitsbull The main metric unit of energy is the Joule and most of

the world uses this but many others existbull The calorie is 4184 Joules

ndash raise 1 gram (cc) of water one degree Celsiusbull The Calorie (kilocalorie) is 4184 J (used for food energy)

ndash raise 1 kg (1 liter) of water one degree Celsiusbull The Btu (British thermal unit) is 1055 J (roughly 1 kJ) or

about 14 Calorie or chemical energy of one matchndash raise 1 pound of water one degree Fahrenheit

bull The kilowatt-hour (kWh) is 3600000 J = 3600 kJ or 860Calories (used for electrical energy)ndash one Watt (W) is one Joule per secondndash a kWh is 1000 W for one hour (3600 seconds)

bull Can also use ldquobarrel of oilrdquo ldquoton of coalrdquo 1000 cubic feetof natural gas gram of Uranium or amount of any energycontaining source etc

15

The Physics of Energy Formula List

bull Lots of forms of energy coming fast and furious but to putit in perspective herersquos a list of formulas

P = ΔEΔtPower (rate of energy use)

F = σT4 (temperature to the fourthpower times a constant)

Radiative energy flux

E = mc2 (mass times speed of lightsquared)

Mass energy

ΔE = cpmΔT (mass times change intemperature times heat capacity)

Heat Energy

E = mgh (mass times height times10ms2)

(Grav) Potential Energy

KE = frac12mv2 (mass times velocitysquared)

Kinetic Energy

W = Fd (Force times distance)Work

Energy FormulaEnergy Form

Kinetic Energybull Kinetic Energy the energy of motionbull Moving things carry energy in the amount

KE = frac12mv2

bull Note the v2 dependencemdashthis is whyndash a car at 60 mph is 4 times more dangerous than a car at 30 mphndash hurricane-force winds at 100 mph are much more destructive (4

times) than 50 mph gale-force windsndash a bullet shot from a gun is at least 100 times as destructive as a

thrown bullet even if you can throw it a tenth as fast as you couldshoot it

16

Numerical examples of kineticenergy

bull A baseball (mass is 0145 kg = 145 g) moving at 30 ms(67 mph) has kinetic energy

KE = frac12times(0145 kg)times(30 ms)2

= 6525 kgm2s2 asymp 65 J

bull A quarter (mass = 000567 kg = 567 g) flipped about fourfeet into the air has a speed on reaching your hand of about5 ms The kinetic energy is

KE = frac12times(000567 kg)times(5 ms)2

= 007 kgm2s2 = 007 J

More numerical examples

bull A 1500 kg car moves down the freeway at30 ms (67 mph)

KE = frac12times(1500 kg)times(30 ms)2

= 675000 kgm2s2 = 675 kJConvert to Calories 4184 kJ = 1 Calorie675 kJ (1 Calorie4184 kJ) = 161 Calorie

bull A 2 kg (~44 lb) fish jumps out of the waterwith a speed of 1 ms (22 mph)

KE = frac12times(2 kg)times(1 ms)2

= 1 kgm2s2 = 1 J

17

QuestionKinetic energy is E = 12 m v2 Which has more energy

A 10 kg object going 100 ms

B 100 kg object going 10 ms

C 1 kg object going 1000 ms

D 1000 kg object going 1 ms

1 ms = 22 mph

Gravitational Potential Energybull It takes work to lift a mass against the pull (force) of

gravitybull The force of gravity is mg where m is the mass and g is

the gravitational accelerationF = mg (note similarity to F = ma)

ndash g = 98 ms2 on the surface of the earth or 32 fts2

bull Lifting a height h against the gravitational forcerequires an energy input (work) of

ΔE = W = F h = mghbull Rolling a boulder up a hill and perching it on the edge of a

cliff gives it gravitational potential energy that can be laterreleased when the roadrunner is down below

bull Water in river or hydroelectric plant is using potentialenergy that it got from being lifted up when Sun (solarenergy) evaporated the water

18

QuestionPotential energy is E = 10 m h (metric units) Which hasmore energy

A 1 ton of water at a height of 100 ft

B 100 tons of water at a height of 1 ft

C 200 lb (110 ton) of water at 1000 ft

D All of the above have same energy

1 ms = 22 mph

First Example of Energy Exchangebull When the boulder falls off the cliff it picks up

speed and therefore gains kinetic energybull Where does this energy come from

rArr from the gravitational potential energybull The higher the cliff the more kinetic energy the

boulder will have when it reaches the ground

mgh

becomes

frac12mv2

Energy is conserved sofrac12mv2 = mgh

Can even figure out v since v2 = 2gh

h

19

Examples of GravitationalPotential Energy

bull How much gravitational potential energy does a70 kg high-diver have on the 10 meter platform

mgh = (70 kg)times(10 ms2)times(10 m)= 7000 kgm2s2 = 7 kJ

7 kJ (1 Calorie4182kJ) = 16 CaloriesThis is amount of energy the diver used in climbing the

stairs (actually more than this since some energy waswasted) They got that energy from the food they ate

The Energy of Heatbull Hot things have more energy than their cold

counterpartsbull Heat is really just kinetic energy on microscopic

scales the vibration or otherwise fast motion ofindividual atomsmoleculesndash Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are randombull Heat is frequently quantified by calories (or Btu)

ndash One calorie (4184 J) raises one gram of H2O 1ordmCndash One Calorie (4184 J) raises one kilogram of H2O 1ordmCndash One Btu (1055 J) raises one pound of H2O 1ordmF

20

Energy of Heat continuedbull Food Calories are with the ldquobigrdquo C or kilocalories (kcal)bull Since water has a density of one gram per cubic centimeter 1

cal heats 1 cc of water 1ordmC and likewise 1 kcal (Calorie) heatsone liter of water 1ordmC In British Units 1 Btu heats 1 pound ofwater 1 degree Fahrenheitndash these are useful numbers to hang onto

bull Example to heat a 2-liter bottle of Coke from the 5ordmCrefrigerator temperature to 20ordmC room temperature requires 30Calories or 1225 kJ

bull Drink a pint (16 oz) of ice cold water (or coke) It weighs about1 pound To heat it to body temperature (986 degrees minus 32degrees or change of 666 degrees Takes about 67 BtuConvert to Calories 1 Calorie = 1kJ = 4 Btu so

67 Btu (1 Calorie 4 Btu) = 1675 Calories Since 16 oz ofcoke has 210 Calories and about 17 Calories are used justheating to your body temp you get less calories drinking it cold(or drinking quart of cold water ldquoburnsrdquo 17 Calories)

The Physics of Energy Formula List

P = ΔEΔtPower (rate of energy use)

F = σT4 (temperature to the fourthpower times a constant)

Radiative energy flux

E = mc2 (mass times speed oflight squared)

Mass energy

ΔE = cpmΔT (mass times changein temperature times heatcapacity)

Heat Energy

E = mgh (mass times height times10ms2)

(Grav) Potential Energy

KE = frac12mv2 (mass times velocitysquared)

Kinetic Energy

W = Fd (Force times distance)Work

Energy FormulaEnergy Form

21

Heat Capacitybull Different materials have different capacities to

hold heatndash Add the same energy to different materials and yoursquoll

get different temperature risesndash Quantified as heat capacityndash Water is exceptional with 4184 JkgordmCndash Most materials are about 1000 JkgordmC (including

wood air metals)bull Example to add 10ordmC to a room 3 meters on a side

(cubic) how much energy do we needair density is 13 kgm3 and we have 27 m3 so 35 kg ofair and we need 1000 J per kg per ordmC so we end upneeding 350000 J (= 836 Cal)

Important in designing solar heated houses Also reasonit is cooler near the coast than inland

Powerbull Power is simply energy exchanged

per unit time or how fast you getwork done (Watts = Joulessec)

bull One horsepower = 745 Wbull Perform 100 J of work in 1 s and

call it 100 Wbull Run upstairs raising your 70 kg

(700 N) mass 3 m (2100 J) in 3seconds rarr 700 W output

bull Shuttle puts out a few GW(gigawatts or 109 W) of power

bull A big electrical power plant putsout around a GW That is 1 BillionJoules per second House takes afew kW (kilowatt)

22

QuestionPower is Energy used per second P= energytime Whichhighest power

A Using 100 Calories in 10 minutes

B Using 1000 Calories in 100 minutes

C Using 10 Calories in 1 minute

D Using 1 Calorie in 6 seconds

E All of the above are the same power usage

1 Calorieminute = Watts

Wind Energy

bull Wind can be used as a source of energy (windmills sailingships etc)

bull Really just kinetic energybull Example wind passing through a square meter at 8 meters

per secondndash Each second we have 8 cubic metersndash Air has density of 13 kgm3 so (8 m3)times(13 kgm3) = 104 kg of

air each secondndash frac12mv2 = frac12times(104 kg)times(8 ms)2 = 333 Jndash 333 J every second rarr 333 Watts of available power per square

meter (but to get all of it yoursquod have to stop the wind)bull Stronger winds rarr more power (like v2)

23

Chemical Energy

bull Electrostatic energy (associated with chargedparticles like electrons) is stored in the chemicalbonds of substances

bull Rearranging these bonds can release energy (somereactions require energy to be put in)

bull Typical numbers are 100ndash200 kJ per molendash a mole is 6022times1023 moleculesparticlesndash typical molecules are tens of grams per molerarrworks

out to typical numbers like several thousand Joules pergram or a few Calories per gram (remember 1 Cal = 1kcal = 4187 J)

Chemical Energy Examples

bull Burning a wooden match releases about oneBtu or 1055 Joules (a match is about 03grams) so this is gt3000 Jg nearly 1 Calg

bull Burning coal releases about 20 kJ per gramof chemical energy or roughly 5 Calg

bull Burning gasoline yields about 39 kJ pergram or just over 9 Calg

bull Very few substances over about 11 Calg

24

Energy from Food

bull We get the energy to do the things we do out of food(stored solar energy in the form of chemical energy)

bull Energy sources recognized by our digestive systemsndash Carbohydrates 4 Calories per gramndash Proteins 4 Calories per gramndash Fats 9 Calories per gram (like gasoline) (9 is more than

4 so gain more weight eating same amount of fat thancarbs or protein)

ndash Roughly 3500 Caloriespound in your body fat Less inyour protein (muscle skin etc)

Our Human Energy Budget

bull A 2000 Calorie per daydiet means 2000times4184 J =8368000 J per day

bull 837 MJ in (24 hrday) times(60 minhr)times(60 secmin)= 86400 sec correspondsto 97 Watts of power

bull Even a couch-potato at1500 Calday burns 75 W

bull More active lifestylesrequire greater Caloricintake (more energy)

25

Nutrition Labelsbull Nutrition labels tell you about the

energy content of foodbull Note they use Calories with capitol Cbull Conversions Fat 9 Calg

Carbs 4 CalgProtein 4 Calg

bull This product has 72 Cal from fat 48Cal from carbohydrates and 32 Calfrom proteinndash sum is 152 Calories compare to label

bull 152 Cal = 636 kJ enough to climbabout 1000 meters (64 kg person)

bull 1kwh = 860 Cal or about 14 lb bodyfat

bull 1 gal of gas has 31000 Calories

Mass-energy

bull Einsteinrsquos famous relationE = mc2

relates mass to energybull In effect they are the same thing

ndash one can be transformed into the otherndash physicists speak generally of mass-energy

bull Seldom experienced in daily life directlyndash Happens at large scale in the center of the sun and in

nuclear bombs and reactorsndash Actually does happen at barely detectable level in all

energy transactions but the effect is tiny

26

E = mc2 Examples

bull The energy equivalent of one gram of material(any composition) is (0001 kg)times(30times108 ms)2

= 90times1013 J = 90000000000000 J = 90 TJndash Man thatrsquos bigndash Our global energy budget is equivalent to 1000 kgyr

(thatrsquos about 1 ton per year)bull If one gram of material undergoes a chemical

reaction losing about 9000 J of energy howmuch mass does it lose

9000 J = Δmc2 so Δm = 9000c2 = 9times1039times1016

= 10-13 kg (would we ever notice)

Solar Energy is Nuclear Using E= mc2

bull Thermonuclear fusion reactions in the sunrsquos centerndash Sun is 16 million degrees Celsius in its centerndash Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then heliumndash Reaction per atom 20 million times more energetic than chemical

reactions in general

4 protonsmass = 4029

4He nucleusmass = 40015

2 neutrinos photons (light)

27

E = mc2 in Sun

bull Helium nucleus is lighter than the four protonsbull Mass difference is 4029 - 40015 = 00276 amu

ndash 1 amu (atomic mass unit) is 16605times10-27 kgndash difference of 458times10-29 kgndash multiply by c2 to get 412times10-12 Jndash 1 mole (6022times1023 particles) of protons rarr 25times1012 Jndash typical chemical reactions are 100-200 kJmolendash nuclear fusion is ~20 million times more potent stuffndash Nuclear fusion is energy source of hydrogen bomb

Energy from Lightbull The tremendous energy from the sun is released as light So light

carries energybull Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiationbull Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequencybull Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellipbull All objects emit ldquolightrdquobull The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter moreradiation and color is ldquobluerrdquo

28

Emitted Radiationrsquos Color andIntensity depend on Temperature

Object

YouHeat LampCandle FlameBulb FilamentSunrsquos SurfaceNeutron StarMolecules in deep space

Temperature

~ 30 C~ 500 C~ 1700 C~ 2700 C~ 5500 C~ millions C

lt -272C

Color

Infrared (invisible)Dull redDim orangeYellowBrilliant whiteX-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted lightThe hotter it gets the more intense the radiation (more energy)

ldquoBlackbodyrdquo or Planck Spectrum

29

Same thing on logarithmic scale

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm(note 0degC = 273degK 300degK = 27degC = 81degF)

Okay but how much energybull The power given off of a surface in the form of light is

proportional to the fourth power of temperatureF = σT4 in Watts per square meter

ndash the constant σ is numerically 567times10-8 WordmK4m2

ndash easy to remember constant 5678ndash temperature must be in Kelvin

bull ordmK = ordmC + 273bull ordmC = (59)times(ordmF ndash32)

bull Example radiation from your body(567 times10-8) times(310)4 = 523 Watts per square meter(if naked in the cold of space donrsquot let this happen to you)

30

Radiant Energy continued

bull Example The sun is 5800ordmK on its surface soF = σT4 = (567times10-8)times(5800)4 = 64times107 Wm2

Summing over entire surface area of sun gives39times1026 W

bull Compare to total capacity of energy production onearth 33times1012 Wndash Single power plant typically 05ndash10 GW (109 W)

bull In earthly situations radiated power out partiallybalanced by radiated power in from other sourcesndash Not 523 Wm2 in 70ordmF room more like 100 Wm2

bull goes like σTh4 ndash σTc

4

Electrical Energybull Opposite charges attract so electrons are attracted to

protons This holds atoms togetherbull It takes energy to pull electrons off their atomsbull Electrons want to get back home to their protons They can

only travel through conductors like wires not throughinsulators like plastic paper or wood They will gothrough miles of wire to get home to their protons

bull This is how electricity works The electronrsquos energy canbe stolen as it goes home Can be used in many manyways

bull Note electricity is not a primary source of energy Energy(from burning coal nat gas from hydro wind nuke orsolar) is used to pull of electrons and that energy can bemoved through wires and got back at will

31

And those are the majorplayershellip

bull Wersquove now seen most of the major energyplayersndash work as force times distancendash kinetic energy (wind ocean currents)ndash gravitational potential energy (hydroelectric tidal)ndash chemical energy (fossil fuels batteries food biomass)ndash heat energy (power plants space heating)ndash mass-energy (nuclear sources sunrsquos energy)ndash radiant energy (solar energy)ndash electrical energy (energy of electrons separated from

their atoms)

Conservation and Exchange ofEnergy

Nothing Comes for Free

32

Energy is Conservedbull Conservation of Energy is different from Energy

Conservation the latter being about using energywisely

bull Conservation of Energy means energy is neithercreated nor destroyed The amount of energy inthe Universe is constant

bull Donrsquot we create energy at a power plantndash Oh that this were truemdashno we simply transform

energy at our power plantsbull Doesnrsquot the sun create energy

ndash Nopemdashit exchanges mass for energybull Donrsquot batteries give us new energy

ndash Nope just convert stored chemical energy to electricalenergy Someone had to put that energy in there

height referenceh

Energy Exchangebull Though the total energy of a system is constant

the form of the energy can changebull A simple example is that of a simple pendulum in

which a continual exchange goes on betweenkinetic and potential energy

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

33

Perpetual Motion

bull Why wonrsquot the pendulum swing foreverbull Itrsquos hard to design a system free of energy pathsbull The pendulum slows down by several mechanisms

ndash Friction at the contact point requires force to opposeforce acts through distance rarr work is done

ndash Air resistance must push through air with a force(through a distance) rarr work is done

ndash Gets some air swirling puts kinetic energy into air (notreally fair to separate these last two)

bull Perpetual motion means no loss of energyndash solar system orbits come very close

Some Energy Chains

bull A coffee mug with some gravitational potentialenergy is dropped

bull potential energy turns into kinetic energybull kinetic energy of the mug goes into

ndash ripping the mug apart (chemical breaking bonds)ndash sending the pieces flying (kinetic)ndash into soundndash into heating the floor and pieces through friction as the

pieces slide to a stopbull In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored inthe potential energy)

34

Gasoline Examplebull Put gas in your car containing 9 Calgbull Combust gas turning 9 Calg into kinetic energy of

explosionbull Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a wholebull That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water andsurrounding air) and friction of transmission system(heat) and noise of engine (heating the air) etc

bull Much of energy goes into stirring the air (ends up as heat)bull Apply the brakes and convert kinetic energy into heatbull It all ends up as waste heat ultimately

Bouncing Ballbull Superball has gravitational potential energybull Drop the ball and this becomes kinetic energybull Ball hits ground and compresses (force times

distance) storing energy in the springbull Ball releases this mechanically stored energy

and it goes back into kinetic form (bouncesup)

bull Inefficiencies in ldquospringrdquo end up heating theball and the floor and stirring the air a bit

bull In the end all is heat

35

Why donrsquot we get hotter andhotter

bull If all these processes end up as heat why arenrsquotwe continually getting hotter

bull If earth retained all its heat we would get hotterbull All of earthrsquos heat is radiated away

F = σT4

bull If we dump more power the temperature goes upthe radiated power increases dramaticallyndash comes to equilibrium power dumped = power radiatedndash stable against perturbation T tracks power budget

Rough numbers

bull How much power does the earth radiatebull F = σT4 for T = 288ordmK = 15ordmC is 390 Wm2

bull Summed over entire surface area (4πR2 where R= 6378000 meters) is 20times1017 W

bull Global production is 3times1012 Wbull Solar radiation incident on earth is 18times1017 W

ndash just solar luminosity of 39times1026 W divided bygeometrical fraction that points at earth

bull Amazing coincidence of numbers (or is ithellip)

36

No Energy for Free

bull No matter what you canrsquot create energy out ofnothing it has to come from somewhere

bull We can transform energy from one form toanother we can store energy we can utilizeenergy being conveyed from natural sources

bull The net energy of the entire Universe is constantbull The best we can do is scrape up some useful

crumbs

Examplesbull Unit conversion

ndash 100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Calndash 100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 Jndash 100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWhndash 10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWhndash How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86Calorieshour About what average person eats

ndash Gasoline is $3gal Electricity if $015kWh Which is moreexpensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh)= $008kWh for gasoline Gasoline is cheap in the USA

37

Examplesbull Power vs Energy (P=Etime E = P t t = EP)

ndash Car goes 60 miles in one hour and uses 3 gal of gas What wastotal power in Watts P=Et Power = (3 gal1 hour) = 3galhr(366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W[Alternative method 3 galhr (132000000 J1 gal) (1 hr3600sec) = 110000 Jsec = 110000 W

ndash 1000 W space heater is on for 3 hours How much does it cost ifelectricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr(1kW1000W) = 3kWh ($15kWh) = $45 [Alternative methodE = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000J (1 kWh3600000J) = 3 kWh Again 45 cents

ndash AAA Battery contains 33 Calories of chemical energy How longcan it run a 2 Watt light bulb time = EP time = 33 Calories2W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1hr3600 sec) = 19 hours

QuestionThe US uses about 7 Gbarrels of oil each year This couldbe converted into which of the following units

A Joules B Watts C QBtus D Dollars $ E Any of the above

38

QuestionIf one barrel of oil contains 1700 kWh of energy how manyWatts is 7 Gbarrelyear

A 1400 GW (Giga Watts)

B 14 GW

C 11900 W

D 119 MW

E 1 x 1011 W

QuestionIf the total yearly oil use in the US is about 1400 GW howmany 1000 MW nuclear reactors will need to be built toreplace all oil use with electricity

A Only one will be needed

B Around 14

C Around 140

D Around 1400

E Cant convert Watts to reactors power vs energy

39

More Power Examplesbull How much power does it take to lift 10 kg up 2 meters in 2

secondsmgh = (10 kg)times(10 ms2)times(2 m) = 200J

200 J in 2 seconds rarr 100 Wattsbull If you want to heat the 3 m cubic room by 10ordmC with a

1000 W space heater how long will it takeWe know from before that the room needs to have 360000 J addedto it so at 1000 W = 1000 Js this will take 360 seconds or sixminutes

But the walls need to be warmed up too so it will actually takelonger (and depends on quality of insulation etc)

A note on arithmetic of unitsbull You should carry units in your calculations and multiply and divide them

as if they were numbersbull Example the force of air drag is given bybull Fdrag = frac12cDrAv2

bull cD is a dimensionless drag coefficientbull r is the density of air 13 kgm3

bull A is the cross-sectional area of the body in m2

bull v is the velocity in msbull units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) =

kgmiddotmiddotmm22middotmiddotmm22

m3middotmiddotss22kgmiddotmiddotmm44

m3middotmiddotss22= = kgmiddotmiddotmsms22 = = NewtonsNewtons

6

7

Why do we use so much energy

8

9

We live in a special time and placehellipbull We use almost 100 times the amount used by the rest of the

world (by population)bull This phase has only lasted for the last century or sobull Most of our resources come from fossil fuels presently and

this has a short finite lifetimebull Fossil fuels formed from solar energy over 300 million

years will be used up in a few centuries

2000 2500 3000 3500 4000150010005000

year

ener

gy u

sage

10

Energy the capacity to do work

bull This notion makes sense even in acolloquial contextndash hard to get work done when yoursquore wiped out

(low on energy)ndash work makes you tired yoursquove used up energy

bull But we can make this definition of energymuch more precise by specifying exactlywhat we mean by work

Work =Energy more than justunpleasant tasks

bull In physics the definition of work is the application of aforce through a distance Energy is needed to do it

W = Fd

bull W is the work done = energy usedbull F is the force appliedbull d is the distance through which the force actsbull Only the force that acts in the direction of motion counts

towards work

11

Okay what is Force thenbull Force is a pushingpulling agentbull Examples

ndash gravity exerts a downward force on youndash the floor exerts an upward force on a ball during its bouncendash a car seat exerts a forward force on your body when you accelerate forward from

a stopndash the seat yoursquore sitting in now is exerting an upward force on you (can you feel it)ndash you exert a sideways force on a couch that you slide across the floorndash a string exerts a centrally-directed (centripetal) force on a rock at the end of a

string that yoursquore twirling over your headndash the expanding gas in your carrsquos cylinder exerts a force against the piston

Forces have Directionbull In all the previous examples force had a

direction associated with itbull If multiple forces act on an object they

could potentially add or cancel dependingon direction

Force 1Force 2

Total Force Force 1

Force 2

Total Force = 0

12

When net force is not zero

bull When an object experiences a non-zero net force it mustaccelerate

bull Newtonrsquos second lawF = ma Force = mass times acceleration

bull The same force makes a small object accelerate more thanit would a more massive objectndash hit a golf ball and a bowling ball with a golf club and see what

happens

QuestionA 150 lb person is standing still on the edge of a cliff Whatis the total force on the person

A zeroB 150 lbC Canrsquot say from this info

13

QuestionA 150 lb person jumps (or was he pushed) off a cliff and isfalling to their death What is the total force on the person

A zeroB 150 lbC Canrsquot say from this info

But what is acceleration

bull This is getting to be like the ldquohole in thebucketrdquo song but wersquore almost therehellip

bull Acceleration is any change in velocity(speed andor direction of motion)

bull Measured as rate of change of velocityndash velocity is expressed in meters per second (ms)ndash acceleration is meters per second per secondndash expressed as ms2 (meters per second-squared)

14

Putting it back together Units ofEnergy

bull Force is a mass times an accelerationndash mass has units of kilogramsndash acceleration is ms2

ndash force is then kgms2 which we call Newtons (N)

bull Work is a force times a distancendash units are then (kgms2)m = kg m2s2 = Nm = Joules (J)ndash One joule is one Newton of force acting through one meterndash Imperial units of force and distance are pounds and feet so unit of

energy is foot-pound which equals 136 J

bull Energy has the same units as work Joules

A Zoo of Unitsbull The main metric unit of energy is the Joule and most of

the world uses this but many others existbull The calorie is 4184 Joules

ndash raise 1 gram (cc) of water one degree Celsiusbull The Calorie (kilocalorie) is 4184 J (used for food energy)

ndash raise 1 kg (1 liter) of water one degree Celsiusbull The Btu (British thermal unit) is 1055 J (roughly 1 kJ) or

about 14 Calorie or chemical energy of one matchndash raise 1 pound of water one degree Fahrenheit

bull The kilowatt-hour (kWh) is 3600000 J = 3600 kJ or 860Calories (used for electrical energy)ndash one Watt (W) is one Joule per secondndash a kWh is 1000 W for one hour (3600 seconds)

bull Can also use ldquobarrel of oilrdquo ldquoton of coalrdquo 1000 cubic feetof natural gas gram of Uranium or amount of any energycontaining source etc

15

The Physics of Energy Formula List

bull Lots of forms of energy coming fast and furious but to putit in perspective herersquos a list of formulas

P = ΔEΔtPower (rate of energy use)

F = σT4 (temperature to the fourthpower times a constant)

Radiative energy flux

E = mc2 (mass times speed of lightsquared)

Mass energy

ΔE = cpmΔT (mass times change intemperature times heat capacity)

Heat Energy

E = mgh (mass times height times10ms2)

(Grav) Potential Energy

KE = frac12mv2 (mass times velocitysquared)

Kinetic Energy

W = Fd (Force times distance)Work

Energy FormulaEnergy Form

Kinetic Energybull Kinetic Energy the energy of motionbull Moving things carry energy in the amount

KE = frac12mv2

bull Note the v2 dependencemdashthis is whyndash a car at 60 mph is 4 times more dangerous than a car at 30 mphndash hurricane-force winds at 100 mph are much more destructive (4

times) than 50 mph gale-force windsndash a bullet shot from a gun is at least 100 times as destructive as a

thrown bullet even if you can throw it a tenth as fast as you couldshoot it

16

Numerical examples of kineticenergy

bull A baseball (mass is 0145 kg = 145 g) moving at 30 ms(67 mph) has kinetic energy

KE = frac12times(0145 kg)times(30 ms)2

= 6525 kgm2s2 asymp 65 J

bull A quarter (mass = 000567 kg = 567 g) flipped about fourfeet into the air has a speed on reaching your hand of about5 ms The kinetic energy is

KE = frac12times(000567 kg)times(5 ms)2

= 007 kgm2s2 = 007 J

More numerical examples

bull A 1500 kg car moves down the freeway at30 ms (67 mph)

KE = frac12times(1500 kg)times(30 ms)2

= 675000 kgm2s2 = 675 kJConvert to Calories 4184 kJ = 1 Calorie675 kJ (1 Calorie4184 kJ) = 161 Calorie

bull A 2 kg (~44 lb) fish jumps out of the waterwith a speed of 1 ms (22 mph)

KE = frac12times(2 kg)times(1 ms)2

= 1 kgm2s2 = 1 J

17

QuestionKinetic energy is E = 12 m v2 Which has more energy

A 10 kg object going 100 ms

B 100 kg object going 10 ms

C 1 kg object going 1000 ms

D 1000 kg object going 1 ms

1 ms = 22 mph

Gravitational Potential Energybull It takes work to lift a mass against the pull (force) of

gravitybull The force of gravity is mg where m is the mass and g is

the gravitational accelerationF = mg (note similarity to F = ma)

ndash g = 98 ms2 on the surface of the earth or 32 fts2

bull Lifting a height h against the gravitational forcerequires an energy input (work) of

ΔE = W = F h = mghbull Rolling a boulder up a hill and perching it on the edge of a

cliff gives it gravitational potential energy that can be laterreleased when the roadrunner is down below

bull Water in river or hydroelectric plant is using potentialenergy that it got from being lifted up when Sun (solarenergy) evaporated the water

18

QuestionPotential energy is E = 10 m h (metric units) Which hasmore energy

A 1 ton of water at a height of 100 ft

B 100 tons of water at a height of 1 ft

C 200 lb (110 ton) of water at 1000 ft

D All of the above have same energy

1 ms = 22 mph

First Example of Energy Exchangebull When the boulder falls off the cliff it picks up

speed and therefore gains kinetic energybull Where does this energy come from

rArr from the gravitational potential energybull The higher the cliff the more kinetic energy the

boulder will have when it reaches the ground

mgh

becomes

frac12mv2

Energy is conserved sofrac12mv2 = mgh

Can even figure out v since v2 = 2gh

h

19

Examples of GravitationalPotential Energy

bull How much gravitational potential energy does a70 kg high-diver have on the 10 meter platform

mgh = (70 kg)times(10 ms2)times(10 m)= 7000 kgm2s2 = 7 kJ

7 kJ (1 Calorie4182kJ) = 16 CaloriesThis is amount of energy the diver used in climbing the

stairs (actually more than this since some energy waswasted) They got that energy from the food they ate

The Energy of Heatbull Hot things have more energy than their cold

counterpartsbull Heat is really just kinetic energy on microscopic

scales the vibration or otherwise fast motion ofindividual atomsmoleculesndash Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are randombull Heat is frequently quantified by calories (or Btu)

ndash One calorie (4184 J) raises one gram of H2O 1ordmCndash One Calorie (4184 J) raises one kilogram of H2O 1ordmCndash One Btu (1055 J) raises one pound of H2O 1ordmF

20

Energy of Heat continuedbull Food Calories are with the ldquobigrdquo C or kilocalories (kcal)bull Since water has a density of one gram per cubic centimeter 1

cal heats 1 cc of water 1ordmC and likewise 1 kcal (Calorie) heatsone liter of water 1ordmC In British Units 1 Btu heats 1 pound ofwater 1 degree Fahrenheitndash these are useful numbers to hang onto

bull Example to heat a 2-liter bottle of Coke from the 5ordmCrefrigerator temperature to 20ordmC room temperature requires 30Calories or 1225 kJ

bull Drink a pint (16 oz) of ice cold water (or coke) It weighs about1 pound To heat it to body temperature (986 degrees minus 32degrees or change of 666 degrees Takes about 67 BtuConvert to Calories 1 Calorie = 1kJ = 4 Btu so

67 Btu (1 Calorie 4 Btu) = 1675 Calories Since 16 oz ofcoke has 210 Calories and about 17 Calories are used justheating to your body temp you get less calories drinking it cold(or drinking quart of cold water ldquoburnsrdquo 17 Calories)

The Physics of Energy Formula List

P = ΔEΔtPower (rate of energy use)

F = σT4 (temperature to the fourthpower times a constant)

Radiative energy flux

E = mc2 (mass times speed oflight squared)

Mass energy

ΔE = cpmΔT (mass times changein temperature times heatcapacity)

Heat Energy

E = mgh (mass times height times10ms2)

(Grav) Potential Energy

KE = frac12mv2 (mass times velocitysquared)

Kinetic Energy

W = Fd (Force times distance)Work

Energy FormulaEnergy Form

21

Heat Capacitybull Different materials have different capacities to

hold heatndash Add the same energy to different materials and yoursquoll

get different temperature risesndash Quantified as heat capacityndash Water is exceptional with 4184 JkgordmCndash Most materials are about 1000 JkgordmC (including

wood air metals)bull Example to add 10ordmC to a room 3 meters on a side

(cubic) how much energy do we needair density is 13 kgm3 and we have 27 m3 so 35 kg ofair and we need 1000 J per kg per ordmC so we end upneeding 350000 J (= 836 Cal)

Important in designing solar heated houses Also reasonit is cooler near the coast than inland

Powerbull Power is simply energy exchanged

per unit time or how fast you getwork done (Watts = Joulessec)

bull One horsepower = 745 Wbull Perform 100 J of work in 1 s and

call it 100 Wbull Run upstairs raising your 70 kg

(700 N) mass 3 m (2100 J) in 3seconds rarr 700 W output

bull Shuttle puts out a few GW(gigawatts or 109 W) of power

bull A big electrical power plant putsout around a GW That is 1 BillionJoules per second House takes afew kW (kilowatt)

22

QuestionPower is Energy used per second P= energytime Whichhighest power

A Using 100 Calories in 10 minutes

B Using 1000 Calories in 100 minutes

C Using 10 Calories in 1 minute

D Using 1 Calorie in 6 seconds

E All of the above are the same power usage

1 Calorieminute = Watts

Wind Energy

bull Wind can be used as a source of energy (windmills sailingships etc)

bull Really just kinetic energybull Example wind passing through a square meter at 8 meters

per secondndash Each second we have 8 cubic metersndash Air has density of 13 kgm3 so (8 m3)times(13 kgm3) = 104 kg of

air each secondndash frac12mv2 = frac12times(104 kg)times(8 ms)2 = 333 Jndash 333 J every second rarr 333 Watts of available power per square

meter (but to get all of it yoursquod have to stop the wind)bull Stronger winds rarr more power (like v2)

23

Chemical Energy

bull Electrostatic energy (associated with chargedparticles like electrons) is stored in the chemicalbonds of substances

bull Rearranging these bonds can release energy (somereactions require energy to be put in)

bull Typical numbers are 100ndash200 kJ per molendash a mole is 6022times1023 moleculesparticlesndash typical molecules are tens of grams per molerarrworks

out to typical numbers like several thousand Joules pergram or a few Calories per gram (remember 1 Cal = 1kcal = 4187 J)

Chemical Energy Examples

bull Burning a wooden match releases about oneBtu or 1055 Joules (a match is about 03grams) so this is gt3000 Jg nearly 1 Calg

bull Burning coal releases about 20 kJ per gramof chemical energy or roughly 5 Calg

bull Burning gasoline yields about 39 kJ pergram or just over 9 Calg

bull Very few substances over about 11 Calg

24

Energy from Food

bull We get the energy to do the things we do out of food(stored solar energy in the form of chemical energy)

bull Energy sources recognized by our digestive systemsndash Carbohydrates 4 Calories per gramndash Proteins 4 Calories per gramndash Fats 9 Calories per gram (like gasoline) (9 is more than

4 so gain more weight eating same amount of fat thancarbs or protein)

ndash Roughly 3500 Caloriespound in your body fat Less inyour protein (muscle skin etc)

Our Human Energy Budget

bull A 2000 Calorie per daydiet means 2000times4184 J =8368000 J per day

bull 837 MJ in (24 hrday) times(60 minhr)times(60 secmin)= 86400 sec correspondsto 97 Watts of power

bull Even a couch-potato at1500 Calday burns 75 W

bull More active lifestylesrequire greater Caloricintake (more energy)

25

Nutrition Labelsbull Nutrition labels tell you about the

energy content of foodbull Note they use Calories with capitol Cbull Conversions Fat 9 Calg

Carbs 4 CalgProtein 4 Calg

bull This product has 72 Cal from fat 48Cal from carbohydrates and 32 Calfrom proteinndash sum is 152 Calories compare to label

bull 152 Cal = 636 kJ enough to climbabout 1000 meters (64 kg person)

bull 1kwh = 860 Cal or about 14 lb bodyfat

bull 1 gal of gas has 31000 Calories

Mass-energy

bull Einsteinrsquos famous relationE = mc2

relates mass to energybull In effect they are the same thing

ndash one can be transformed into the otherndash physicists speak generally of mass-energy

bull Seldom experienced in daily life directlyndash Happens at large scale in the center of the sun and in

nuclear bombs and reactorsndash Actually does happen at barely detectable level in all

energy transactions but the effect is tiny

26

E = mc2 Examples

bull The energy equivalent of one gram of material(any composition) is (0001 kg)times(30times108 ms)2

= 90times1013 J = 90000000000000 J = 90 TJndash Man thatrsquos bigndash Our global energy budget is equivalent to 1000 kgyr

(thatrsquos about 1 ton per year)bull If one gram of material undergoes a chemical

reaction losing about 9000 J of energy howmuch mass does it lose

9000 J = Δmc2 so Δm = 9000c2 = 9times1039times1016

= 10-13 kg (would we ever notice)

Solar Energy is Nuclear Using E= mc2

bull Thermonuclear fusion reactions in the sunrsquos centerndash Sun is 16 million degrees Celsius in its centerndash Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then heliumndash Reaction per atom 20 million times more energetic than chemical

reactions in general

4 protonsmass = 4029

4He nucleusmass = 40015

2 neutrinos photons (light)

27

E = mc2 in Sun

bull Helium nucleus is lighter than the four protonsbull Mass difference is 4029 - 40015 = 00276 amu

ndash 1 amu (atomic mass unit) is 16605times10-27 kgndash difference of 458times10-29 kgndash multiply by c2 to get 412times10-12 Jndash 1 mole (6022times1023 particles) of protons rarr 25times1012 Jndash typical chemical reactions are 100-200 kJmolendash nuclear fusion is ~20 million times more potent stuffndash Nuclear fusion is energy source of hydrogen bomb

Energy from Lightbull The tremendous energy from the sun is released as light So light

carries energybull Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiationbull Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequencybull Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellipbull All objects emit ldquolightrdquobull The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter moreradiation and color is ldquobluerrdquo

28

Emitted Radiationrsquos Color andIntensity depend on Temperature

Object

YouHeat LampCandle FlameBulb FilamentSunrsquos SurfaceNeutron StarMolecules in deep space

Temperature

~ 30 C~ 500 C~ 1700 C~ 2700 C~ 5500 C~ millions C

lt -272C

Color

Infrared (invisible)Dull redDim orangeYellowBrilliant whiteX-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted lightThe hotter it gets the more intense the radiation (more energy)

ldquoBlackbodyrdquo or Planck Spectrum

29

Same thing on logarithmic scale

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm(note 0degC = 273degK 300degK = 27degC = 81degF)

Okay but how much energybull The power given off of a surface in the form of light is

proportional to the fourth power of temperatureF = σT4 in Watts per square meter

ndash the constant σ is numerically 567times10-8 WordmK4m2

ndash easy to remember constant 5678ndash temperature must be in Kelvin

bull ordmK = ordmC + 273bull ordmC = (59)times(ordmF ndash32)

bull Example radiation from your body(567 times10-8) times(310)4 = 523 Watts per square meter(if naked in the cold of space donrsquot let this happen to you)

30

Radiant Energy continued

bull Example The sun is 5800ordmK on its surface soF = σT4 = (567times10-8)times(5800)4 = 64times107 Wm2

Summing over entire surface area of sun gives39times1026 W

bull Compare to total capacity of energy production onearth 33times1012 Wndash Single power plant typically 05ndash10 GW (109 W)

bull In earthly situations radiated power out partiallybalanced by radiated power in from other sourcesndash Not 523 Wm2 in 70ordmF room more like 100 Wm2

bull goes like σTh4 ndash σTc

4

Electrical Energybull Opposite charges attract so electrons are attracted to

protons This holds atoms togetherbull It takes energy to pull electrons off their atomsbull Electrons want to get back home to their protons They can

only travel through conductors like wires not throughinsulators like plastic paper or wood They will gothrough miles of wire to get home to their protons

bull This is how electricity works The electronrsquos energy canbe stolen as it goes home Can be used in many manyways

bull Note electricity is not a primary source of energy Energy(from burning coal nat gas from hydro wind nuke orsolar) is used to pull of electrons and that energy can bemoved through wires and got back at will

31

And those are the majorplayershellip

bull Wersquove now seen most of the major energyplayersndash work as force times distancendash kinetic energy (wind ocean currents)ndash gravitational potential energy (hydroelectric tidal)ndash chemical energy (fossil fuels batteries food biomass)ndash heat energy (power plants space heating)ndash mass-energy (nuclear sources sunrsquos energy)ndash radiant energy (solar energy)ndash electrical energy (energy of electrons separated from

their atoms)

Conservation and Exchange ofEnergy

Nothing Comes for Free

32

Energy is Conservedbull Conservation of Energy is different from Energy

Conservation the latter being about using energywisely

bull Conservation of Energy means energy is neithercreated nor destroyed The amount of energy inthe Universe is constant

bull Donrsquot we create energy at a power plantndash Oh that this were truemdashno we simply transform

energy at our power plantsbull Doesnrsquot the sun create energy

ndash Nopemdashit exchanges mass for energybull Donrsquot batteries give us new energy

ndash Nope just convert stored chemical energy to electricalenergy Someone had to put that energy in there

height referenceh

Energy Exchangebull Though the total energy of a system is constant

the form of the energy can changebull A simple example is that of a simple pendulum in

which a continual exchange goes on betweenkinetic and potential energy

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

33

Perpetual Motion

bull Why wonrsquot the pendulum swing foreverbull Itrsquos hard to design a system free of energy pathsbull The pendulum slows down by several mechanisms

ndash Friction at the contact point requires force to opposeforce acts through distance rarr work is done

ndash Air resistance must push through air with a force(through a distance) rarr work is done

ndash Gets some air swirling puts kinetic energy into air (notreally fair to separate these last two)

bull Perpetual motion means no loss of energyndash solar system orbits come very close

Some Energy Chains

bull A coffee mug with some gravitational potentialenergy is dropped

bull potential energy turns into kinetic energybull kinetic energy of the mug goes into

ndash ripping the mug apart (chemical breaking bonds)ndash sending the pieces flying (kinetic)ndash into soundndash into heating the floor and pieces through friction as the

pieces slide to a stopbull In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored inthe potential energy)

34

Gasoline Examplebull Put gas in your car containing 9 Calgbull Combust gas turning 9 Calg into kinetic energy of

explosionbull Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a wholebull That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water andsurrounding air) and friction of transmission system(heat) and noise of engine (heating the air) etc

bull Much of energy goes into stirring the air (ends up as heat)bull Apply the brakes and convert kinetic energy into heatbull It all ends up as waste heat ultimately

Bouncing Ballbull Superball has gravitational potential energybull Drop the ball and this becomes kinetic energybull Ball hits ground and compresses (force times

distance) storing energy in the springbull Ball releases this mechanically stored energy

and it goes back into kinetic form (bouncesup)

bull Inefficiencies in ldquospringrdquo end up heating theball and the floor and stirring the air a bit

bull In the end all is heat

35

Why donrsquot we get hotter andhotter

bull If all these processes end up as heat why arenrsquotwe continually getting hotter

bull If earth retained all its heat we would get hotterbull All of earthrsquos heat is radiated away

F = σT4

bull If we dump more power the temperature goes upthe radiated power increases dramaticallyndash comes to equilibrium power dumped = power radiatedndash stable against perturbation T tracks power budget

Rough numbers

bull How much power does the earth radiatebull F = σT4 for T = 288ordmK = 15ordmC is 390 Wm2

bull Summed over entire surface area (4πR2 where R= 6378000 meters) is 20times1017 W

bull Global production is 3times1012 Wbull Solar radiation incident on earth is 18times1017 W

ndash just solar luminosity of 39times1026 W divided bygeometrical fraction that points at earth

bull Amazing coincidence of numbers (or is ithellip)

36

No Energy for Free

bull No matter what you canrsquot create energy out ofnothing it has to come from somewhere

bull We can transform energy from one form toanother we can store energy we can utilizeenergy being conveyed from natural sources

bull The net energy of the entire Universe is constantbull The best we can do is scrape up some useful

crumbs

Examplesbull Unit conversion

ndash 100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Calndash 100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 Jndash 100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWhndash 10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWhndash How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86Calorieshour About what average person eats

ndash Gasoline is $3gal Electricity if $015kWh Which is moreexpensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh)= $008kWh for gasoline Gasoline is cheap in the USA

37

Examplesbull Power vs Energy (P=Etime E = P t t = EP)

ndash Car goes 60 miles in one hour and uses 3 gal of gas What wastotal power in Watts P=Et Power = (3 gal1 hour) = 3galhr(366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W[Alternative method 3 galhr (132000000 J1 gal) (1 hr3600sec) = 110000 Jsec = 110000 W

ndash 1000 W space heater is on for 3 hours How much does it cost ifelectricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr(1kW1000W) = 3kWh ($15kWh) = $45 [Alternative methodE = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000J (1 kWh3600000J) = 3 kWh Again 45 cents

ndash AAA Battery contains 33 Calories of chemical energy How longcan it run a 2 Watt light bulb time = EP time = 33 Calories2W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1hr3600 sec) = 19 hours

QuestionThe US uses about 7 Gbarrels of oil each year This couldbe converted into which of the following units

A Joules B Watts C QBtus D Dollars $ E Any of the above

38

QuestionIf one barrel of oil contains 1700 kWh of energy how manyWatts is 7 Gbarrelyear

A 1400 GW (Giga Watts)

B 14 GW

C 11900 W

D 119 MW

E 1 x 1011 W

QuestionIf the total yearly oil use in the US is about 1400 GW howmany 1000 MW nuclear reactors will need to be built toreplace all oil use with electricity

A Only one will be needed

B Around 14

C Around 140

D Around 1400

E Cant convert Watts to reactors power vs energy

39

More Power Examplesbull How much power does it take to lift 10 kg up 2 meters in 2

secondsmgh = (10 kg)times(10 ms2)times(2 m) = 200J

200 J in 2 seconds rarr 100 Wattsbull If you want to heat the 3 m cubic room by 10ordmC with a

1000 W space heater how long will it takeWe know from before that the room needs to have 360000 J addedto it so at 1000 W = 1000 Js this will take 360 seconds or sixminutes

But the walls need to be warmed up too so it will actually takelonger (and depends on quality of insulation etc)

A note on arithmetic of unitsbull You should carry units in your calculations and multiply and divide them

as if they were numbersbull Example the force of air drag is given bybull Fdrag = frac12cDrAv2

bull cD is a dimensionless drag coefficientbull r is the density of air 13 kgm3

bull A is the cross-sectional area of the body in m2

bull v is the velocity in msbull units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) =

kgmiddotmiddotmm22middotmiddotmm22

m3middotmiddotss22kgmiddotmiddotmm44

m3middotmiddotss22= = kgmiddotmiddotmsms22 = = NewtonsNewtons

7

Why do we use so much energy

8

9

We live in a special time and placehellipbull We use almost 100 times the amount used by the rest of the

world (by population)bull This phase has only lasted for the last century or sobull Most of our resources come from fossil fuels presently and

this has a short finite lifetimebull Fossil fuels formed from solar energy over 300 million

years will be used up in a few centuries

2000 2500 3000 3500 4000150010005000

year

ener

gy u

sage

10

Energy the capacity to do work

bull This notion makes sense even in acolloquial contextndash hard to get work done when yoursquore wiped out

(low on energy)ndash work makes you tired yoursquove used up energy

bull But we can make this definition of energymuch more precise by specifying exactlywhat we mean by work

Work =Energy more than justunpleasant tasks

bull In physics the definition of work is the application of aforce through a distance Energy is needed to do it

W = Fd

bull W is the work done = energy usedbull F is the force appliedbull d is the distance through which the force actsbull Only the force that acts in the direction of motion counts

towards work

11

Okay what is Force thenbull Force is a pushingpulling agentbull Examples

ndash gravity exerts a downward force on youndash the floor exerts an upward force on a ball during its bouncendash a car seat exerts a forward force on your body when you accelerate forward from

a stopndash the seat yoursquore sitting in now is exerting an upward force on you (can you feel it)ndash you exert a sideways force on a couch that you slide across the floorndash a string exerts a centrally-directed (centripetal) force on a rock at the end of a

string that yoursquore twirling over your headndash the expanding gas in your carrsquos cylinder exerts a force against the piston

Forces have Directionbull In all the previous examples force had a

direction associated with itbull If multiple forces act on an object they

could potentially add or cancel dependingon direction

Force 1Force 2

Total Force Force 1

Force 2

Total Force = 0

12

When net force is not zero

bull When an object experiences a non-zero net force it mustaccelerate

bull Newtonrsquos second lawF = ma Force = mass times acceleration

bull The same force makes a small object accelerate more thanit would a more massive objectndash hit a golf ball and a bowling ball with a golf club and see what

happens

QuestionA 150 lb person is standing still on the edge of a cliff Whatis the total force on the person

A zeroB 150 lbC Canrsquot say from this info

13

QuestionA 150 lb person jumps (or was he pushed) off a cliff and isfalling to their death What is the total force on the person

A zeroB 150 lbC Canrsquot say from this info

But what is acceleration

bull This is getting to be like the ldquohole in thebucketrdquo song but wersquore almost therehellip

bull Acceleration is any change in velocity(speed andor direction of motion)

bull Measured as rate of change of velocityndash velocity is expressed in meters per second (ms)ndash acceleration is meters per second per secondndash expressed as ms2 (meters per second-squared)

14

Putting it back together Units ofEnergy

bull Force is a mass times an accelerationndash mass has units of kilogramsndash acceleration is ms2

ndash force is then kgms2 which we call Newtons (N)

bull Work is a force times a distancendash units are then (kgms2)m = kg m2s2 = Nm = Joules (J)ndash One joule is one Newton of force acting through one meterndash Imperial units of force and distance are pounds and feet so unit of

energy is foot-pound which equals 136 J

bull Energy has the same units as work Joules

A Zoo of Unitsbull The main metric unit of energy is the Joule and most of

the world uses this but many others existbull The calorie is 4184 Joules

ndash raise 1 gram (cc) of water one degree Celsiusbull The Calorie (kilocalorie) is 4184 J (used for food energy)

ndash raise 1 kg (1 liter) of water one degree Celsiusbull The Btu (British thermal unit) is 1055 J (roughly 1 kJ) or

about 14 Calorie or chemical energy of one matchndash raise 1 pound of water one degree Fahrenheit

bull The kilowatt-hour (kWh) is 3600000 J = 3600 kJ or 860Calories (used for electrical energy)ndash one Watt (W) is one Joule per secondndash a kWh is 1000 W for one hour (3600 seconds)

bull Can also use ldquobarrel of oilrdquo ldquoton of coalrdquo 1000 cubic feetof natural gas gram of Uranium or amount of any energycontaining source etc

15

The Physics of Energy Formula List

bull Lots of forms of energy coming fast and furious but to putit in perspective herersquos a list of formulas

P = ΔEΔtPower (rate of energy use)

F = σT4 (temperature to the fourthpower times a constant)

Radiative energy flux

E = mc2 (mass times speed of lightsquared)

Mass energy

ΔE = cpmΔT (mass times change intemperature times heat capacity)

Heat Energy

E = mgh (mass times height times10ms2)

(Grav) Potential Energy

KE = frac12mv2 (mass times velocitysquared)

Kinetic Energy

W = Fd (Force times distance)Work

Energy FormulaEnergy Form

Kinetic Energybull Kinetic Energy the energy of motionbull Moving things carry energy in the amount

KE = frac12mv2

bull Note the v2 dependencemdashthis is whyndash a car at 60 mph is 4 times more dangerous than a car at 30 mphndash hurricane-force winds at 100 mph are much more destructive (4

times) than 50 mph gale-force windsndash a bullet shot from a gun is at least 100 times as destructive as a

thrown bullet even if you can throw it a tenth as fast as you couldshoot it

16

Numerical examples of kineticenergy

bull A baseball (mass is 0145 kg = 145 g) moving at 30 ms(67 mph) has kinetic energy

KE = frac12times(0145 kg)times(30 ms)2

= 6525 kgm2s2 asymp 65 J

bull A quarter (mass = 000567 kg = 567 g) flipped about fourfeet into the air has a speed on reaching your hand of about5 ms The kinetic energy is

KE = frac12times(000567 kg)times(5 ms)2

= 007 kgm2s2 = 007 J

More numerical examples

bull A 1500 kg car moves down the freeway at30 ms (67 mph)

KE = frac12times(1500 kg)times(30 ms)2

= 675000 kgm2s2 = 675 kJConvert to Calories 4184 kJ = 1 Calorie675 kJ (1 Calorie4184 kJ) = 161 Calorie

bull A 2 kg (~44 lb) fish jumps out of the waterwith a speed of 1 ms (22 mph)

KE = frac12times(2 kg)times(1 ms)2

= 1 kgm2s2 = 1 J

17

QuestionKinetic energy is E = 12 m v2 Which has more energy

A 10 kg object going 100 ms

B 100 kg object going 10 ms

C 1 kg object going 1000 ms

D 1000 kg object going 1 ms

1 ms = 22 mph

Gravitational Potential Energybull It takes work to lift a mass against the pull (force) of

gravitybull The force of gravity is mg where m is the mass and g is

the gravitational accelerationF = mg (note similarity to F = ma)

ndash g = 98 ms2 on the surface of the earth or 32 fts2

bull Lifting a height h against the gravitational forcerequires an energy input (work) of

ΔE = W = F h = mghbull Rolling a boulder up a hill and perching it on the edge of a

cliff gives it gravitational potential energy that can be laterreleased when the roadrunner is down below

bull Water in river or hydroelectric plant is using potentialenergy that it got from being lifted up when Sun (solarenergy) evaporated the water

18

QuestionPotential energy is E = 10 m h (metric units) Which hasmore energy

A 1 ton of water at a height of 100 ft

B 100 tons of water at a height of 1 ft

C 200 lb (110 ton) of water at 1000 ft

D All of the above have same energy

1 ms = 22 mph

First Example of Energy Exchangebull When the boulder falls off the cliff it picks up

speed and therefore gains kinetic energybull Where does this energy come from

rArr from the gravitational potential energybull The higher the cliff the more kinetic energy the

boulder will have when it reaches the ground

mgh

becomes

frac12mv2

Energy is conserved sofrac12mv2 = mgh

Can even figure out v since v2 = 2gh

h

19

Examples of GravitationalPotential Energy

bull How much gravitational potential energy does a70 kg high-diver have on the 10 meter platform

mgh = (70 kg)times(10 ms2)times(10 m)= 7000 kgm2s2 = 7 kJ

7 kJ (1 Calorie4182kJ) = 16 CaloriesThis is amount of energy the diver used in climbing the

stairs (actually more than this since some energy waswasted) They got that energy from the food they ate

The Energy of Heatbull Hot things have more energy than their cold

counterpartsbull Heat is really just kinetic energy on microscopic

scales the vibration or otherwise fast motion ofindividual atomsmoleculesndash Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are randombull Heat is frequently quantified by calories (or Btu)

ndash One calorie (4184 J) raises one gram of H2O 1ordmCndash One Calorie (4184 J) raises one kilogram of H2O 1ordmCndash One Btu (1055 J) raises one pound of H2O 1ordmF

20

Energy of Heat continuedbull Food Calories are with the ldquobigrdquo C or kilocalories (kcal)bull Since water has a density of one gram per cubic centimeter 1

cal heats 1 cc of water 1ordmC and likewise 1 kcal (Calorie) heatsone liter of water 1ordmC In British Units 1 Btu heats 1 pound ofwater 1 degree Fahrenheitndash these are useful numbers to hang onto

bull Example to heat a 2-liter bottle of Coke from the 5ordmCrefrigerator temperature to 20ordmC room temperature requires 30Calories or 1225 kJ

bull Drink a pint (16 oz) of ice cold water (or coke) It weighs about1 pound To heat it to body temperature (986 degrees minus 32degrees or change of 666 degrees Takes about 67 BtuConvert to Calories 1 Calorie = 1kJ = 4 Btu so

67 Btu (1 Calorie 4 Btu) = 1675 Calories Since 16 oz ofcoke has 210 Calories and about 17 Calories are used justheating to your body temp you get less calories drinking it cold(or drinking quart of cold water ldquoburnsrdquo 17 Calories)

The Physics of Energy Formula List

P = ΔEΔtPower (rate of energy use)

F = σT4 (temperature to the fourthpower times a constant)

Radiative energy flux

E = mc2 (mass times speed oflight squared)

Mass energy

ΔE = cpmΔT (mass times changein temperature times heatcapacity)

Heat Energy

E = mgh (mass times height times10ms2)

(Grav) Potential Energy

KE = frac12mv2 (mass times velocitysquared)

Kinetic Energy

W = Fd (Force times distance)Work

Energy FormulaEnergy Form

21

Heat Capacitybull Different materials have different capacities to

hold heatndash Add the same energy to different materials and yoursquoll

get different temperature risesndash Quantified as heat capacityndash Water is exceptional with 4184 JkgordmCndash Most materials are about 1000 JkgordmC (including

wood air metals)bull Example to add 10ordmC to a room 3 meters on a side

(cubic) how much energy do we needair density is 13 kgm3 and we have 27 m3 so 35 kg ofair and we need 1000 J per kg per ordmC so we end upneeding 350000 J (= 836 Cal)

Important in designing solar heated houses Also reasonit is cooler near the coast than inland

Powerbull Power is simply energy exchanged

per unit time or how fast you getwork done (Watts = Joulessec)

bull One horsepower = 745 Wbull Perform 100 J of work in 1 s and

call it 100 Wbull Run upstairs raising your 70 kg

(700 N) mass 3 m (2100 J) in 3seconds rarr 700 W output

bull Shuttle puts out a few GW(gigawatts or 109 W) of power

bull A big electrical power plant putsout around a GW That is 1 BillionJoules per second House takes afew kW (kilowatt)

22

QuestionPower is Energy used per second P= energytime Whichhighest power

A Using 100 Calories in 10 minutes

B Using 1000 Calories in 100 minutes

C Using 10 Calories in 1 minute

D Using 1 Calorie in 6 seconds

E All of the above are the same power usage

1 Calorieminute = Watts

Wind Energy

bull Wind can be used as a source of energy (windmills sailingships etc)

bull Really just kinetic energybull Example wind passing through a square meter at 8 meters

per secondndash Each second we have 8 cubic metersndash Air has density of 13 kgm3 so (8 m3)times(13 kgm3) = 104 kg of

air each secondndash frac12mv2 = frac12times(104 kg)times(8 ms)2 = 333 Jndash 333 J every second rarr 333 Watts of available power per square

meter (but to get all of it yoursquod have to stop the wind)bull Stronger winds rarr more power (like v2)

23

Chemical Energy

bull Electrostatic energy (associated with chargedparticles like electrons) is stored in the chemicalbonds of substances

bull Rearranging these bonds can release energy (somereactions require energy to be put in)

bull Typical numbers are 100ndash200 kJ per molendash a mole is 6022times1023 moleculesparticlesndash typical molecules are tens of grams per molerarrworks

out to typical numbers like several thousand Joules pergram or a few Calories per gram (remember 1 Cal = 1kcal = 4187 J)

Chemical Energy Examples

bull Burning a wooden match releases about oneBtu or 1055 Joules (a match is about 03grams) so this is gt3000 Jg nearly 1 Calg

bull Burning coal releases about 20 kJ per gramof chemical energy or roughly 5 Calg

bull Burning gasoline yields about 39 kJ pergram or just over 9 Calg

bull Very few substances over about 11 Calg

24

Energy from Food

bull We get the energy to do the things we do out of food(stored solar energy in the form of chemical energy)

bull Energy sources recognized by our digestive systemsndash Carbohydrates 4 Calories per gramndash Proteins 4 Calories per gramndash Fats 9 Calories per gram (like gasoline) (9 is more than

4 so gain more weight eating same amount of fat thancarbs or protein)

ndash Roughly 3500 Caloriespound in your body fat Less inyour protein (muscle skin etc)

Our Human Energy Budget

bull A 2000 Calorie per daydiet means 2000times4184 J =8368000 J per day

bull 837 MJ in (24 hrday) times(60 minhr)times(60 secmin)= 86400 sec correspondsto 97 Watts of power

bull Even a couch-potato at1500 Calday burns 75 W

bull More active lifestylesrequire greater Caloricintake (more energy)

25

Nutrition Labelsbull Nutrition labels tell you about the

energy content of foodbull Note they use Calories with capitol Cbull Conversions Fat 9 Calg

Carbs 4 CalgProtein 4 Calg

bull This product has 72 Cal from fat 48Cal from carbohydrates and 32 Calfrom proteinndash sum is 152 Calories compare to label

bull 152 Cal = 636 kJ enough to climbabout 1000 meters (64 kg person)

bull 1kwh = 860 Cal or about 14 lb bodyfat

bull 1 gal of gas has 31000 Calories

Mass-energy

bull Einsteinrsquos famous relationE = mc2

relates mass to energybull In effect they are the same thing

ndash one can be transformed into the otherndash physicists speak generally of mass-energy

bull Seldom experienced in daily life directlyndash Happens at large scale in the center of the sun and in

nuclear bombs and reactorsndash Actually does happen at barely detectable level in all

energy transactions but the effect is tiny

26

E = mc2 Examples

bull The energy equivalent of one gram of material(any composition) is (0001 kg)times(30times108 ms)2

= 90times1013 J = 90000000000000 J = 90 TJndash Man thatrsquos bigndash Our global energy budget is equivalent to 1000 kgyr

(thatrsquos about 1 ton per year)bull If one gram of material undergoes a chemical

reaction losing about 9000 J of energy howmuch mass does it lose

9000 J = Δmc2 so Δm = 9000c2 = 9times1039times1016

= 10-13 kg (would we ever notice)

Solar Energy is Nuclear Using E= mc2

bull Thermonuclear fusion reactions in the sunrsquos centerndash Sun is 16 million degrees Celsius in its centerndash Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then heliumndash Reaction per atom 20 million times more energetic than chemical

reactions in general

4 protonsmass = 4029

4He nucleusmass = 40015

2 neutrinos photons (light)

27

E = mc2 in Sun

bull Helium nucleus is lighter than the four protonsbull Mass difference is 4029 - 40015 = 00276 amu

ndash 1 amu (atomic mass unit) is 16605times10-27 kgndash difference of 458times10-29 kgndash multiply by c2 to get 412times10-12 Jndash 1 mole (6022times1023 particles) of protons rarr 25times1012 Jndash typical chemical reactions are 100-200 kJmolendash nuclear fusion is ~20 million times more potent stuffndash Nuclear fusion is energy source of hydrogen bomb

Energy from Lightbull The tremendous energy from the sun is released as light So light

carries energybull Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiationbull Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequencybull Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellipbull All objects emit ldquolightrdquobull The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter moreradiation and color is ldquobluerrdquo

28

Emitted Radiationrsquos Color andIntensity depend on Temperature

Object

YouHeat LampCandle FlameBulb FilamentSunrsquos SurfaceNeutron StarMolecules in deep space

Temperature

~ 30 C~ 500 C~ 1700 C~ 2700 C~ 5500 C~ millions C

lt -272C

Color

Infrared (invisible)Dull redDim orangeYellowBrilliant whiteX-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted lightThe hotter it gets the more intense the radiation (more energy)

ldquoBlackbodyrdquo or Planck Spectrum

29

Same thing on logarithmic scale

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm(note 0degC = 273degK 300degK = 27degC = 81degF)

Okay but how much energybull The power given off of a surface in the form of light is

proportional to the fourth power of temperatureF = σT4 in Watts per square meter

ndash the constant σ is numerically 567times10-8 WordmK4m2

ndash easy to remember constant 5678ndash temperature must be in Kelvin

bull ordmK = ordmC + 273bull ordmC = (59)times(ordmF ndash32)

bull Example radiation from your body(567 times10-8) times(310)4 = 523 Watts per square meter(if naked in the cold of space donrsquot let this happen to you)

30

Radiant Energy continued

bull Example The sun is 5800ordmK on its surface soF = σT4 = (567times10-8)times(5800)4 = 64times107 Wm2

Summing over entire surface area of sun gives39times1026 W

bull Compare to total capacity of energy production onearth 33times1012 Wndash Single power plant typically 05ndash10 GW (109 W)

bull In earthly situations radiated power out partiallybalanced by radiated power in from other sourcesndash Not 523 Wm2 in 70ordmF room more like 100 Wm2

bull goes like σTh4 ndash σTc

4

Electrical Energybull Opposite charges attract so electrons are attracted to

protons This holds atoms togetherbull It takes energy to pull electrons off their atomsbull Electrons want to get back home to their protons They can

only travel through conductors like wires not throughinsulators like plastic paper or wood They will gothrough miles of wire to get home to their protons

bull This is how electricity works The electronrsquos energy canbe stolen as it goes home Can be used in many manyways

bull Note electricity is not a primary source of energy Energy(from burning coal nat gas from hydro wind nuke orsolar) is used to pull of electrons and that energy can bemoved through wires and got back at will

31

And those are the majorplayershellip

bull Wersquove now seen most of the major energyplayersndash work as force times distancendash kinetic energy (wind ocean currents)ndash gravitational potential energy (hydroelectric tidal)ndash chemical energy (fossil fuels batteries food biomass)ndash heat energy (power plants space heating)ndash mass-energy (nuclear sources sunrsquos energy)ndash radiant energy (solar energy)ndash electrical energy (energy of electrons separated from

their atoms)

Conservation and Exchange ofEnergy

Nothing Comes for Free

32

Energy is Conservedbull Conservation of Energy is different from Energy

Conservation the latter being about using energywisely

bull Conservation of Energy means energy is neithercreated nor destroyed The amount of energy inthe Universe is constant

bull Donrsquot we create energy at a power plantndash Oh that this were truemdashno we simply transform

energy at our power plantsbull Doesnrsquot the sun create energy

ndash Nopemdashit exchanges mass for energybull Donrsquot batteries give us new energy

ndash Nope just convert stored chemical energy to electricalenergy Someone had to put that energy in there

height referenceh

Energy Exchangebull Though the total energy of a system is constant

the form of the energy can changebull A simple example is that of a simple pendulum in

which a continual exchange goes on betweenkinetic and potential energy

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

33

Perpetual Motion

bull Why wonrsquot the pendulum swing foreverbull Itrsquos hard to design a system free of energy pathsbull The pendulum slows down by several mechanisms

ndash Friction at the contact point requires force to opposeforce acts through distance rarr work is done

ndash Air resistance must push through air with a force(through a distance) rarr work is done

ndash Gets some air swirling puts kinetic energy into air (notreally fair to separate these last two)

bull Perpetual motion means no loss of energyndash solar system orbits come very close

Some Energy Chains

bull A coffee mug with some gravitational potentialenergy is dropped

bull potential energy turns into kinetic energybull kinetic energy of the mug goes into

ndash ripping the mug apart (chemical breaking bonds)ndash sending the pieces flying (kinetic)ndash into soundndash into heating the floor and pieces through friction as the

pieces slide to a stopbull In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored inthe potential energy)

34

Gasoline Examplebull Put gas in your car containing 9 Calgbull Combust gas turning 9 Calg into kinetic energy of

explosionbull Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a wholebull That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water andsurrounding air) and friction of transmission system(heat) and noise of engine (heating the air) etc

bull Much of energy goes into stirring the air (ends up as heat)bull Apply the brakes and convert kinetic energy into heatbull It all ends up as waste heat ultimately

Bouncing Ballbull Superball has gravitational potential energybull Drop the ball and this becomes kinetic energybull Ball hits ground and compresses (force times

distance) storing energy in the springbull Ball releases this mechanically stored energy

and it goes back into kinetic form (bouncesup)

bull Inefficiencies in ldquospringrdquo end up heating theball and the floor and stirring the air a bit

bull In the end all is heat

35

Why donrsquot we get hotter andhotter

bull If all these processes end up as heat why arenrsquotwe continually getting hotter

bull If earth retained all its heat we would get hotterbull All of earthrsquos heat is radiated away

F = σT4

bull If we dump more power the temperature goes upthe radiated power increases dramaticallyndash comes to equilibrium power dumped = power radiatedndash stable against perturbation T tracks power budget

Rough numbers

bull How much power does the earth radiatebull F = σT4 for T = 288ordmK = 15ordmC is 390 Wm2

bull Summed over entire surface area (4πR2 where R= 6378000 meters) is 20times1017 W

bull Global production is 3times1012 Wbull Solar radiation incident on earth is 18times1017 W

ndash just solar luminosity of 39times1026 W divided bygeometrical fraction that points at earth

bull Amazing coincidence of numbers (or is ithellip)

36

No Energy for Free

bull No matter what you canrsquot create energy out ofnothing it has to come from somewhere

bull We can transform energy from one form toanother we can store energy we can utilizeenergy being conveyed from natural sources

bull The net energy of the entire Universe is constantbull The best we can do is scrape up some useful

crumbs

Examplesbull Unit conversion

ndash 100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Calndash 100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 Jndash 100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWhndash 10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWhndash How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86Calorieshour About what average person eats

ndash Gasoline is $3gal Electricity if $015kWh Which is moreexpensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh)= $008kWh for gasoline Gasoline is cheap in the USA

37

Examplesbull Power vs Energy (P=Etime E = P t t = EP)

ndash Car goes 60 miles in one hour and uses 3 gal of gas What wastotal power in Watts P=Et Power = (3 gal1 hour) = 3galhr(366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W[Alternative method 3 galhr (132000000 J1 gal) (1 hr3600sec) = 110000 Jsec = 110000 W

ndash 1000 W space heater is on for 3 hours How much does it cost ifelectricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr(1kW1000W) = 3kWh ($15kWh) = $45 [Alternative methodE = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000J (1 kWh3600000J) = 3 kWh Again 45 cents

ndash AAA Battery contains 33 Calories of chemical energy How longcan it run a 2 Watt light bulb time = EP time = 33 Calories2W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1hr3600 sec) = 19 hours

QuestionThe US uses about 7 Gbarrels of oil each year This couldbe converted into which of the following units

A Joules B Watts C QBtus D Dollars $ E Any of the above

38

QuestionIf one barrel of oil contains 1700 kWh of energy how manyWatts is 7 Gbarrelyear

A 1400 GW (Giga Watts)

B 14 GW

C 11900 W

D 119 MW

E 1 x 1011 W

QuestionIf the total yearly oil use in the US is about 1400 GW howmany 1000 MW nuclear reactors will need to be built toreplace all oil use with electricity

A Only one will be needed

B Around 14

C Around 140

D Around 1400

E Cant convert Watts to reactors power vs energy

39

More Power Examplesbull How much power does it take to lift 10 kg up 2 meters in 2

secondsmgh = (10 kg)times(10 ms2)times(2 m) = 200J

200 J in 2 seconds rarr 100 Wattsbull If you want to heat the 3 m cubic room by 10ordmC with a

1000 W space heater how long will it takeWe know from before that the room needs to have 360000 J addedto it so at 1000 W = 1000 Js this will take 360 seconds or sixminutes

But the walls need to be warmed up too so it will actually takelonger (and depends on quality of insulation etc)

A note on arithmetic of unitsbull You should carry units in your calculations and multiply and divide them

as if they were numbersbull Example the force of air drag is given bybull Fdrag = frac12cDrAv2

bull cD is a dimensionless drag coefficientbull r is the density of air 13 kgm3

bull A is the cross-sectional area of the body in m2

bull v is the velocity in msbull units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) =

kgmiddotmiddotmm22middotmiddotmm22

m3middotmiddotss22kgmiddotmiddotmm44

m3middotmiddotss22= = kgmiddotmiddotmsms22 = = NewtonsNewtons

8

9

We live in a special time and placehellipbull We use almost 100 times the amount used by the rest of the

world (by population)bull This phase has only lasted for the last century or sobull Most of our resources come from fossil fuels presently and

this has a short finite lifetimebull Fossil fuels formed from solar energy over 300 million

years will be used up in a few centuries

2000 2500 3000 3500 4000150010005000

year

ener

gy u

sage

10

Energy the capacity to do work

bull This notion makes sense even in acolloquial contextndash hard to get work done when yoursquore wiped out

(low on energy)ndash work makes you tired yoursquove used up energy

bull But we can make this definition of energymuch more precise by specifying exactlywhat we mean by work

Work =Energy more than justunpleasant tasks

bull In physics the definition of work is the application of aforce through a distance Energy is needed to do it

W = Fd

bull W is the work done = energy usedbull F is the force appliedbull d is the distance through which the force actsbull Only the force that acts in the direction of motion counts

towards work

11

Okay what is Force thenbull Force is a pushingpulling agentbull Examples

ndash gravity exerts a downward force on youndash the floor exerts an upward force on a ball during its bouncendash a car seat exerts a forward force on your body when you accelerate forward from

a stopndash the seat yoursquore sitting in now is exerting an upward force on you (can you feel it)ndash you exert a sideways force on a couch that you slide across the floorndash a string exerts a centrally-directed (centripetal) force on a rock at the end of a

string that yoursquore twirling over your headndash the expanding gas in your carrsquos cylinder exerts a force against the piston

Forces have Directionbull In all the previous examples force had a

direction associated with itbull If multiple forces act on an object they

could potentially add or cancel dependingon direction

Force 1Force 2

Total Force Force 1

Force 2

Total Force = 0

12

When net force is not zero

bull When an object experiences a non-zero net force it mustaccelerate

bull Newtonrsquos second lawF = ma Force = mass times acceleration

bull The same force makes a small object accelerate more thanit would a more massive objectndash hit a golf ball and a bowling ball with a golf club and see what

happens

QuestionA 150 lb person is standing still on the edge of a cliff Whatis the total force on the person

A zeroB 150 lbC Canrsquot say from this info

13

QuestionA 150 lb person jumps (or was he pushed) off a cliff and isfalling to their death What is the total force on the person

A zeroB 150 lbC Canrsquot say from this info

But what is acceleration

bull This is getting to be like the ldquohole in thebucketrdquo song but wersquore almost therehellip

bull Acceleration is any change in velocity(speed andor direction of motion)

bull Measured as rate of change of velocityndash velocity is expressed in meters per second (ms)ndash acceleration is meters per second per secondndash expressed as ms2 (meters per second-squared)

14

Putting it back together Units ofEnergy

bull Force is a mass times an accelerationndash mass has units of kilogramsndash acceleration is ms2

ndash force is then kgms2 which we call Newtons (N)

bull Work is a force times a distancendash units are then (kgms2)m = kg m2s2 = Nm = Joules (J)ndash One joule is one Newton of force acting through one meterndash Imperial units of force and distance are pounds and feet so unit of

energy is foot-pound which equals 136 J

bull Energy has the same units as work Joules

A Zoo of Unitsbull The main metric unit of energy is the Joule and most of

the world uses this but many others existbull The calorie is 4184 Joules

ndash raise 1 gram (cc) of water one degree Celsiusbull The Calorie (kilocalorie) is 4184 J (used for food energy)

ndash raise 1 kg (1 liter) of water one degree Celsiusbull The Btu (British thermal unit) is 1055 J (roughly 1 kJ) or

about 14 Calorie or chemical energy of one matchndash raise 1 pound of water one degree Fahrenheit

bull The kilowatt-hour (kWh) is 3600000 J = 3600 kJ or 860Calories (used for electrical energy)ndash one Watt (W) is one Joule per secondndash a kWh is 1000 W for one hour (3600 seconds)

bull Can also use ldquobarrel of oilrdquo ldquoton of coalrdquo 1000 cubic feetof natural gas gram of Uranium or amount of any energycontaining source etc

15

The Physics of Energy Formula List

bull Lots of forms of energy coming fast and furious but to putit in perspective herersquos a list of formulas

P = ΔEΔtPower (rate of energy use)

F = σT4 (temperature to the fourthpower times a constant)

Radiative energy flux

E = mc2 (mass times speed of lightsquared)

Mass energy

ΔE = cpmΔT (mass times change intemperature times heat capacity)

Heat Energy

E = mgh (mass times height times10ms2)

(Grav) Potential Energy

KE = frac12mv2 (mass times velocitysquared)

Kinetic Energy

W = Fd (Force times distance)Work

Energy FormulaEnergy Form

Kinetic Energybull Kinetic Energy the energy of motionbull Moving things carry energy in the amount

KE = frac12mv2

bull Note the v2 dependencemdashthis is whyndash a car at 60 mph is 4 times more dangerous than a car at 30 mphndash hurricane-force winds at 100 mph are much more destructive (4

times) than 50 mph gale-force windsndash a bullet shot from a gun is at least 100 times as destructive as a

thrown bullet even if you can throw it a tenth as fast as you couldshoot it

16

Numerical examples of kineticenergy

bull A baseball (mass is 0145 kg = 145 g) moving at 30 ms(67 mph) has kinetic energy

KE = frac12times(0145 kg)times(30 ms)2

= 6525 kgm2s2 asymp 65 J

bull A quarter (mass = 000567 kg = 567 g) flipped about fourfeet into the air has a speed on reaching your hand of about5 ms The kinetic energy is

KE = frac12times(000567 kg)times(5 ms)2

= 007 kgm2s2 = 007 J

More numerical examples

bull A 1500 kg car moves down the freeway at30 ms (67 mph)

KE = frac12times(1500 kg)times(30 ms)2

= 675000 kgm2s2 = 675 kJConvert to Calories 4184 kJ = 1 Calorie675 kJ (1 Calorie4184 kJ) = 161 Calorie

bull A 2 kg (~44 lb) fish jumps out of the waterwith a speed of 1 ms (22 mph)

KE = frac12times(2 kg)times(1 ms)2

= 1 kgm2s2 = 1 J

17

QuestionKinetic energy is E = 12 m v2 Which has more energy

A 10 kg object going 100 ms

B 100 kg object going 10 ms

C 1 kg object going 1000 ms

D 1000 kg object going 1 ms

1 ms = 22 mph

Gravitational Potential Energybull It takes work to lift a mass against the pull (force) of

gravitybull The force of gravity is mg where m is the mass and g is

the gravitational accelerationF = mg (note similarity to F = ma)

ndash g = 98 ms2 on the surface of the earth or 32 fts2

bull Lifting a height h against the gravitational forcerequires an energy input (work) of

ΔE = W = F h = mghbull Rolling a boulder up a hill and perching it on the edge of a

cliff gives it gravitational potential energy that can be laterreleased when the roadrunner is down below

bull Water in river or hydroelectric plant is using potentialenergy that it got from being lifted up when Sun (solarenergy) evaporated the water

18

QuestionPotential energy is E = 10 m h (metric units) Which hasmore energy

A 1 ton of water at a height of 100 ft

B 100 tons of water at a height of 1 ft

C 200 lb (110 ton) of water at 1000 ft

D All of the above have same energy

1 ms = 22 mph

First Example of Energy Exchangebull When the boulder falls off the cliff it picks up

speed and therefore gains kinetic energybull Where does this energy come from

rArr from the gravitational potential energybull The higher the cliff the more kinetic energy the

boulder will have when it reaches the ground

mgh

becomes

frac12mv2

Energy is conserved sofrac12mv2 = mgh

Can even figure out v since v2 = 2gh

h

19

Examples of GravitationalPotential Energy

bull How much gravitational potential energy does a70 kg high-diver have on the 10 meter platform

mgh = (70 kg)times(10 ms2)times(10 m)= 7000 kgm2s2 = 7 kJ

7 kJ (1 Calorie4182kJ) = 16 CaloriesThis is amount of energy the diver used in climbing the

stairs (actually more than this since some energy waswasted) They got that energy from the food they ate

The Energy of Heatbull Hot things have more energy than their cold

counterpartsbull Heat is really just kinetic energy on microscopic

scales the vibration or otherwise fast motion ofindividual atomsmoleculesndash Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are randombull Heat is frequently quantified by calories (or Btu)

ndash One calorie (4184 J) raises one gram of H2O 1ordmCndash One Calorie (4184 J) raises one kilogram of H2O 1ordmCndash One Btu (1055 J) raises one pound of H2O 1ordmF

20

Energy of Heat continuedbull Food Calories are with the ldquobigrdquo C or kilocalories (kcal)bull Since water has a density of one gram per cubic centimeter 1

cal heats 1 cc of water 1ordmC and likewise 1 kcal (Calorie) heatsone liter of water 1ordmC In British Units 1 Btu heats 1 pound ofwater 1 degree Fahrenheitndash these are useful numbers to hang onto

bull Example to heat a 2-liter bottle of Coke from the 5ordmCrefrigerator temperature to 20ordmC room temperature requires 30Calories or 1225 kJ

bull Drink a pint (16 oz) of ice cold water (or coke) It weighs about1 pound To heat it to body temperature (986 degrees minus 32degrees or change of 666 degrees Takes about 67 BtuConvert to Calories 1 Calorie = 1kJ = 4 Btu so

67 Btu (1 Calorie 4 Btu) = 1675 Calories Since 16 oz ofcoke has 210 Calories and about 17 Calories are used justheating to your body temp you get less calories drinking it cold(or drinking quart of cold water ldquoburnsrdquo 17 Calories)

The Physics of Energy Formula List

P = ΔEΔtPower (rate of energy use)

F = σT4 (temperature to the fourthpower times a constant)

Radiative energy flux

E = mc2 (mass times speed oflight squared)

Mass energy

ΔE = cpmΔT (mass times changein temperature times heatcapacity)

Heat Energy

E = mgh (mass times height times10ms2)

(Grav) Potential Energy

KE = frac12mv2 (mass times velocitysquared)

Kinetic Energy

W = Fd (Force times distance)Work

Energy FormulaEnergy Form

21

Heat Capacitybull Different materials have different capacities to

hold heatndash Add the same energy to different materials and yoursquoll

get different temperature risesndash Quantified as heat capacityndash Water is exceptional with 4184 JkgordmCndash Most materials are about 1000 JkgordmC (including

wood air metals)bull Example to add 10ordmC to a room 3 meters on a side

(cubic) how much energy do we needair density is 13 kgm3 and we have 27 m3 so 35 kg ofair and we need 1000 J per kg per ordmC so we end upneeding 350000 J (= 836 Cal)

Important in designing solar heated houses Also reasonit is cooler near the coast than inland

Powerbull Power is simply energy exchanged

per unit time or how fast you getwork done (Watts = Joulessec)

bull One horsepower = 745 Wbull Perform 100 J of work in 1 s and

call it 100 Wbull Run upstairs raising your 70 kg

(700 N) mass 3 m (2100 J) in 3seconds rarr 700 W output

bull Shuttle puts out a few GW(gigawatts or 109 W) of power

bull A big electrical power plant putsout around a GW That is 1 BillionJoules per second House takes afew kW (kilowatt)

22

QuestionPower is Energy used per second P= energytime Whichhighest power

A Using 100 Calories in 10 minutes

B Using 1000 Calories in 100 minutes

C Using 10 Calories in 1 minute

D Using 1 Calorie in 6 seconds

E All of the above are the same power usage

1 Calorieminute = Watts

Wind Energy

bull Wind can be used as a source of energy (windmills sailingships etc)

bull Really just kinetic energybull Example wind passing through a square meter at 8 meters

per secondndash Each second we have 8 cubic metersndash Air has density of 13 kgm3 so (8 m3)times(13 kgm3) = 104 kg of

air each secondndash frac12mv2 = frac12times(104 kg)times(8 ms)2 = 333 Jndash 333 J every second rarr 333 Watts of available power per square

meter (but to get all of it yoursquod have to stop the wind)bull Stronger winds rarr more power (like v2)

23

Chemical Energy

bull Electrostatic energy (associated with chargedparticles like electrons) is stored in the chemicalbonds of substances

bull Rearranging these bonds can release energy (somereactions require energy to be put in)

bull Typical numbers are 100ndash200 kJ per molendash a mole is 6022times1023 moleculesparticlesndash typical molecules are tens of grams per molerarrworks

out to typical numbers like several thousand Joules pergram or a few Calories per gram (remember 1 Cal = 1kcal = 4187 J)

Chemical Energy Examples

bull Burning a wooden match releases about oneBtu or 1055 Joules (a match is about 03grams) so this is gt3000 Jg nearly 1 Calg

bull Burning coal releases about 20 kJ per gramof chemical energy or roughly 5 Calg

bull Burning gasoline yields about 39 kJ pergram or just over 9 Calg

bull Very few substances over about 11 Calg

24

Energy from Food

bull We get the energy to do the things we do out of food(stored solar energy in the form of chemical energy)

bull Energy sources recognized by our digestive systemsndash Carbohydrates 4 Calories per gramndash Proteins 4 Calories per gramndash Fats 9 Calories per gram (like gasoline) (9 is more than

4 so gain more weight eating same amount of fat thancarbs or protein)

ndash Roughly 3500 Caloriespound in your body fat Less inyour protein (muscle skin etc)

Our Human Energy Budget

bull A 2000 Calorie per daydiet means 2000times4184 J =8368000 J per day

bull 837 MJ in (24 hrday) times(60 minhr)times(60 secmin)= 86400 sec correspondsto 97 Watts of power

bull Even a couch-potato at1500 Calday burns 75 W

bull More active lifestylesrequire greater Caloricintake (more energy)

25

Nutrition Labelsbull Nutrition labels tell you about the

energy content of foodbull Note they use Calories with capitol Cbull Conversions Fat 9 Calg

Carbs 4 CalgProtein 4 Calg

bull This product has 72 Cal from fat 48Cal from carbohydrates and 32 Calfrom proteinndash sum is 152 Calories compare to label

bull 152 Cal = 636 kJ enough to climbabout 1000 meters (64 kg person)

bull 1kwh = 860 Cal or about 14 lb bodyfat

bull 1 gal of gas has 31000 Calories

Mass-energy

bull Einsteinrsquos famous relationE = mc2

relates mass to energybull In effect they are the same thing

ndash one can be transformed into the otherndash physicists speak generally of mass-energy

bull Seldom experienced in daily life directlyndash Happens at large scale in the center of the sun and in

nuclear bombs and reactorsndash Actually does happen at barely detectable level in all

energy transactions but the effect is tiny

26

E = mc2 Examples

bull The energy equivalent of one gram of material(any composition) is (0001 kg)times(30times108 ms)2

= 90times1013 J = 90000000000000 J = 90 TJndash Man thatrsquos bigndash Our global energy budget is equivalent to 1000 kgyr

(thatrsquos about 1 ton per year)bull If one gram of material undergoes a chemical

reaction losing about 9000 J of energy howmuch mass does it lose

9000 J = Δmc2 so Δm = 9000c2 = 9times1039times1016

= 10-13 kg (would we ever notice)

Solar Energy is Nuclear Using E= mc2

bull Thermonuclear fusion reactions in the sunrsquos centerndash Sun is 16 million degrees Celsius in its centerndash Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then heliumndash Reaction per atom 20 million times more energetic than chemical

reactions in general

4 protonsmass = 4029

4He nucleusmass = 40015

2 neutrinos photons (light)

27

E = mc2 in Sun

bull Helium nucleus is lighter than the four protonsbull Mass difference is 4029 - 40015 = 00276 amu

ndash 1 amu (atomic mass unit) is 16605times10-27 kgndash difference of 458times10-29 kgndash multiply by c2 to get 412times10-12 Jndash 1 mole (6022times1023 particles) of protons rarr 25times1012 Jndash typical chemical reactions are 100-200 kJmolendash nuclear fusion is ~20 million times more potent stuffndash Nuclear fusion is energy source of hydrogen bomb

Energy from Lightbull The tremendous energy from the sun is released as light So light

carries energybull Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiationbull Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequencybull Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellipbull All objects emit ldquolightrdquobull The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter moreradiation and color is ldquobluerrdquo

28

Emitted Radiationrsquos Color andIntensity depend on Temperature

Object

YouHeat LampCandle FlameBulb FilamentSunrsquos SurfaceNeutron StarMolecules in deep space

Temperature

~ 30 C~ 500 C~ 1700 C~ 2700 C~ 5500 C~ millions C

lt -272C

Color

Infrared (invisible)Dull redDim orangeYellowBrilliant whiteX-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted lightThe hotter it gets the more intense the radiation (more energy)

ldquoBlackbodyrdquo or Planck Spectrum

29

Same thing on logarithmic scale

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm(note 0degC = 273degK 300degK = 27degC = 81degF)

Okay but how much energybull The power given off of a surface in the form of light is

proportional to the fourth power of temperatureF = σT4 in Watts per square meter

ndash the constant σ is numerically 567times10-8 WordmK4m2

ndash easy to remember constant 5678ndash temperature must be in Kelvin

bull ordmK = ordmC + 273bull ordmC = (59)times(ordmF ndash32)

bull Example radiation from your body(567 times10-8) times(310)4 = 523 Watts per square meter(if naked in the cold of space donrsquot let this happen to you)

30

Radiant Energy continued

bull Example The sun is 5800ordmK on its surface soF = σT4 = (567times10-8)times(5800)4 = 64times107 Wm2

Summing over entire surface area of sun gives39times1026 W

bull Compare to total capacity of energy production onearth 33times1012 Wndash Single power plant typically 05ndash10 GW (109 W)

bull In earthly situations radiated power out partiallybalanced by radiated power in from other sourcesndash Not 523 Wm2 in 70ordmF room more like 100 Wm2

bull goes like σTh4 ndash σTc

4

Electrical Energybull Opposite charges attract so electrons are attracted to

protons This holds atoms togetherbull It takes energy to pull electrons off their atomsbull Electrons want to get back home to their protons They can

only travel through conductors like wires not throughinsulators like plastic paper or wood They will gothrough miles of wire to get home to their protons

bull This is how electricity works The electronrsquos energy canbe stolen as it goes home Can be used in many manyways

bull Note electricity is not a primary source of energy Energy(from burning coal nat gas from hydro wind nuke orsolar) is used to pull of electrons and that energy can bemoved through wires and got back at will

31

And those are the majorplayershellip

bull Wersquove now seen most of the major energyplayersndash work as force times distancendash kinetic energy (wind ocean currents)ndash gravitational potential energy (hydroelectric tidal)ndash chemical energy (fossil fuels batteries food biomass)ndash heat energy (power plants space heating)ndash mass-energy (nuclear sources sunrsquos energy)ndash radiant energy (solar energy)ndash electrical energy (energy of electrons separated from

their atoms)

Conservation and Exchange ofEnergy

Nothing Comes for Free

32

Energy is Conservedbull Conservation of Energy is different from Energy

Conservation the latter being about using energywisely

bull Conservation of Energy means energy is neithercreated nor destroyed The amount of energy inthe Universe is constant

bull Donrsquot we create energy at a power plantndash Oh that this were truemdashno we simply transform

energy at our power plantsbull Doesnrsquot the sun create energy

ndash Nopemdashit exchanges mass for energybull Donrsquot batteries give us new energy

ndash Nope just convert stored chemical energy to electricalenergy Someone had to put that energy in there

height referenceh

Energy Exchangebull Though the total energy of a system is constant

the form of the energy can changebull A simple example is that of a simple pendulum in

which a continual exchange goes on betweenkinetic and potential energy

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

33

Perpetual Motion

bull Why wonrsquot the pendulum swing foreverbull Itrsquos hard to design a system free of energy pathsbull The pendulum slows down by several mechanisms

ndash Friction at the contact point requires force to opposeforce acts through distance rarr work is done

ndash Air resistance must push through air with a force(through a distance) rarr work is done

ndash Gets some air swirling puts kinetic energy into air (notreally fair to separate these last two)

bull Perpetual motion means no loss of energyndash solar system orbits come very close

Some Energy Chains

bull A coffee mug with some gravitational potentialenergy is dropped

bull potential energy turns into kinetic energybull kinetic energy of the mug goes into

ndash ripping the mug apart (chemical breaking bonds)ndash sending the pieces flying (kinetic)ndash into soundndash into heating the floor and pieces through friction as the

pieces slide to a stopbull In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored inthe potential energy)

34

Gasoline Examplebull Put gas in your car containing 9 Calgbull Combust gas turning 9 Calg into kinetic energy of

explosionbull Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a wholebull That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water andsurrounding air) and friction of transmission system(heat) and noise of engine (heating the air) etc

bull Much of energy goes into stirring the air (ends up as heat)bull Apply the brakes and convert kinetic energy into heatbull It all ends up as waste heat ultimately

Bouncing Ballbull Superball has gravitational potential energybull Drop the ball and this becomes kinetic energybull Ball hits ground and compresses (force times

distance) storing energy in the springbull Ball releases this mechanically stored energy

and it goes back into kinetic form (bouncesup)

bull Inefficiencies in ldquospringrdquo end up heating theball and the floor and stirring the air a bit

bull In the end all is heat

35

Why donrsquot we get hotter andhotter

bull If all these processes end up as heat why arenrsquotwe continually getting hotter

bull If earth retained all its heat we would get hotterbull All of earthrsquos heat is radiated away

F = σT4

bull If we dump more power the temperature goes upthe radiated power increases dramaticallyndash comes to equilibrium power dumped = power radiatedndash stable against perturbation T tracks power budget

Rough numbers

bull How much power does the earth radiatebull F = σT4 for T = 288ordmK = 15ordmC is 390 Wm2

bull Summed over entire surface area (4πR2 where R= 6378000 meters) is 20times1017 W

bull Global production is 3times1012 Wbull Solar radiation incident on earth is 18times1017 W

ndash just solar luminosity of 39times1026 W divided bygeometrical fraction that points at earth

bull Amazing coincidence of numbers (or is ithellip)

36

No Energy for Free

bull No matter what you canrsquot create energy out ofnothing it has to come from somewhere

bull We can transform energy from one form toanother we can store energy we can utilizeenergy being conveyed from natural sources

bull The net energy of the entire Universe is constantbull The best we can do is scrape up some useful

crumbs

Examplesbull Unit conversion

ndash 100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Calndash 100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 Jndash 100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWhndash 10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWhndash How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86Calorieshour About what average person eats

ndash Gasoline is $3gal Electricity if $015kWh Which is moreexpensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh)= $008kWh for gasoline Gasoline is cheap in the USA

37

Examplesbull Power vs Energy (P=Etime E = P t t = EP)

ndash Car goes 60 miles in one hour and uses 3 gal of gas What wastotal power in Watts P=Et Power = (3 gal1 hour) = 3galhr(366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W[Alternative method 3 galhr (132000000 J1 gal) (1 hr3600sec) = 110000 Jsec = 110000 W

ndash 1000 W space heater is on for 3 hours How much does it cost ifelectricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr(1kW1000W) = 3kWh ($15kWh) = $45 [Alternative methodE = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000J (1 kWh3600000J) = 3 kWh Again 45 cents

ndash AAA Battery contains 33 Calories of chemical energy How longcan it run a 2 Watt light bulb time = EP time = 33 Calories2W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1hr3600 sec) = 19 hours

QuestionThe US uses about 7 Gbarrels of oil each year This couldbe converted into which of the following units

A Joules B Watts C QBtus D Dollars $ E Any of the above

38

QuestionIf one barrel of oil contains 1700 kWh of energy how manyWatts is 7 Gbarrelyear

A 1400 GW (Giga Watts)

B 14 GW

C 11900 W

D 119 MW

E 1 x 1011 W

QuestionIf the total yearly oil use in the US is about 1400 GW howmany 1000 MW nuclear reactors will need to be built toreplace all oil use with electricity

A Only one will be needed

B Around 14

C Around 140

D Around 1400

E Cant convert Watts to reactors power vs energy

39

More Power Examplesbull How much power does it take to lift 10 kg up 2 meters in 2

secondsmgh = (10 kg)times(10 ms2)times(2 m) = 200J

200 J in 2 seconds rarr 100 Wattsbull If you want to heat the 3 m cubic room by 10ordmC with a

1000 W space heater how long will it takeWe know from before that the room needs to have 360000 J addedto it so at 1000 W = 1000 Js this will take 360 seconds or sixminutes

But the walls need to be warmed up too so it will actually takelonger (and depends on quality of insulation etc)

A note on arithmetic of unitsbull You should carry units in your calculations and multiply and divide them

as if they were numbersbull Example the force of air drag is given bybull Fdrag = frac12cDrAv2

bull cD is a dimensionless drag coefficientbull r is the density of air 13 kgm3

bull A is the cross-sectional area of the body in m2

bull v is the velocity in msbull units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) =

kgmiddotmiddotmm22middotmiddotmm22

m3middotmiddotss22kgmiddotmiddotmm44

m3middotmiddotss22= = kgmiddotmiddotmsms22 = = NewtonsNewtons

9

We live in a special time and placehellipbull We use almost 100 times the amount used by the rest of the

world (by population)bull This phase has only lasted for the last century or sobull Most of our resources come from fossil fuels presently and

this has a short finite lifetimebull Fossil fuels formed from solar energy over 300 million

years will be used up in a few centuries

2000 2500 3000 3500 4000150010005000

year

ener

gy u

sage

10

Energy the capacity to do work

bull This notion makes sense even in acolloquial contextndash hard to get work done when yoursquore wiped out

(low on energy)ndash work makes you tired yoursquove used up energy

bull But we can make this definition of energymuch more precise by specifying exactlywhat we mean by work

Work =Energy more than justunpleasant tasks

bull In physics the definition of work is the application of aforce through a distance Energy is needed to do it

W = Fd

bull W is the work done = energy usedbull F is the force appliedbull d is the distance through which the force actsbull Only the force that acts in the direction of motion counts

towards work

11

Okay what is Force thenbull Force is a pushingpulling agentbull Examples

ndash gravity exerts a downward force on youndash the floor exerts an upward force on a ball during its bouncendash a car seat exerts a forward force on your body when you accelerate forward from

a stopndash the seat yoursquore sitting in now is exerting an upward force on you (can you feel it)ndash you exert a sideways force on a couch that you slide across the floorndash a string exerts a centrally-directed (centripetal) force on a rock at the end of a

string that yoursquore twirling over your headndash the expanding gas in your carrsquos cylinder exerts a force against the piston

Forces have Directionbull In all the previous examples force had a

direction associated with itbull If multiple forces act on an object they

could potentially add or cancel dependingon direction

Force 1Force 2

Total Force Force 1

Force 2

Total Force = 0

12

When net force is not zero

bull When an object experiences a non-zero net force it mustaccelerate

bull Newtonrsquos second lawF = ma Force = mass times acceleration

bull The same force makes a small object accelerate more thanit would a more massive objectndash hit a golf ball and a bowling ball with a golf club and see what

happens

QuestionA 150 lb person is standing still on the edge of a cliff Whatis the total force on the person

A zeroB 150 lbC Canrsquot say from this info

13

QuestionA 150 lb person jumps (or was he pushed) off a cliff and isfalling to their death What is the total force on the person

A zeroB 150 lbC Canrsquot say from this info

But what is acceleration

bull This is getting to be like the ldquohole in thebucketrdquo song but wersquore almost therehellip

bull Acceleration is any change in velocity(speed andor direction of motion)

bull Measured as rate of change of velocityndash velocity is expressed in meters per second (ms)ndash acceleration is meters per second per secondndash expressed as ms2 (meters per second-squared)

14

Putting it back together Units ofEnergy

bull Force is a mass times an accelerationndash mass has units of kilogramsndash acceleration is ms2

ndash force is then kgms2 which we call Newtons (N)

bull Work is a force times a distancendash units are then (kgms2)m = kg m2s2 = Nm = Joules (J)ndash One joule is one Newton of force acting through one meterndash Imperial units of force and distance are pounds and feet so unit of

energy is foot-pound which equals 136 J

bull Energy has the same units as work Joules

A Zoo of Unitsbull The main metric unit of energy is the Joule and most of

the world uses this but many others existbull The calorie is 4184 Joules

ndash raise 1 gram (cc) of water one degree Celsiusbull The Calorie (kilocalorie) is 4184 J (used for food energy)

ndash raise 1 kg (1 liter) of water one degree Celsiusbull The Btu (British thermal unit) is 1055 J (roughly 1 kJ) or

about 14 Calorie or chemical energy of one matchndash raise 1 pound of water one degree Fahrenheit

bull The kilowatt-hour (kWh) is 3600000 J = 3600 kJ or 860Calories (used for electrical energy)ndash one Watt (W) is one Joule per secondndash a kWh is 1000 W for one hour (3600 seconds)

bull Can also use ldquobarrel of oilrdquo ldquoton of coalrdquo 1000 cubic feetof natural gas gram of Uranium or amount of any energycontaining source etc

15

The Physics of Energy Formula List

bull Lots of forms of energy coming fast and furious but to putit in perspective herersquos a list of formulas

P = ΔEΔtPower (rate of energy use)

F = σT4 (temperature to the fourthpower times a constant)

Radiative energy flux

E = mc2 (mass times speed of lightsquared)

Mass energy

ΔE = cpmΔT (mass times change intemperature times heat capacity)

Heat Energy

E = mgh (mass times height times10ms2)

(Grav) Potential Energy

KE = frac12mv2 (mass times velocitysquared)

Kinetic Energy

W = Fd (Force times distance)Work

Energy FormulaEnergy Form

Kinetic Energybull Kinetic Energy the energy of motionbull Moving things carry energy in the amount

KE = frac12mv2

bull Note the v2 dependencemdashthis is whyndash a car at 60 mph is 4 times more dangerous than a car at 30 mphndash hurricane-force winds at 100 mph are much more destructive (4

times) than 50 mph gale-force windsndash a bullet shot from a gun is at least 100 times as destructive as a

thrown bullet even if you can throw it a tenth as fast as you couldshoot it

16

Numerical examples of kineticenergy

bull A baseball (mass is 0145 kg = 145 g) moving at 30 ms(67 mph) has kinetic energy

KE = frac12times(0145 kg)times(30 ms)2

= 6525 kgm2s2 asymp 65 J

bull A quarter (mass = 000567 kg = 567 g) flipped about fourfeet into the air has a speed on reaching your hand of about5 ms The kinetic energy is

KE = frac12times(000567 kg)times(5 ms)2

= 007 kgm2s2 = 007 J

More numerical examples

bull A 1500 kg car moves down the freeway at30 ms (67 mph)

KE = frac12times(1500 kg)times(30 ms)2

= 675000 kgm2s2 = 675 kJConvert to Calories 4184 kJ = 1 Calorie675 kJ (1 Calorie4184 kJ) = 161 Calorie

bull A 2 kg (~44 lb) fish jumps out of the waterwith a speed of 1 ms (22 mph)

KE = frac12times(2 kg)times(1 ms)2

= 1 kgm2s2 = 1 J

17

QuestionKinetic energy is E = 12 m v2 Which has more energy

A 10 kg object going 100 ms

B 100 kg object going 10 ms

C 1 kg object going 1000 ms

D 1000 kg object going 1 ms

1 ms = 22 mph

Gravitational Potential Energybull It takes work to lift a mass against the pull (force) of

gravitybull The force of gravity is mg where m is the mass and g is

the gravitational accelerationF = mg (note similarity to F = ma)

ndash g = 98 ms2 on the surface of the earth or 32 fts2

bull Lifting a height h against the gravitational forcerequires an energy input (work) of

ΔE = W = F h = mghbull Rolling a boulder up a hill and perching it on the edge of a

cliff gives it gravitational potential energy that can be laterreleased when the roadrunner is down below

bull Water in river or hydroelectric plant is using potentialenergy that it got from being lifted up when Sun (solarenergy) evaporated the water

18

QuestionPotential energy is E = 10 m h (metric units) Which hasmore energy

A 1 ton of water at a height of 100 ft

B 100 tons of water at a height of 1 ft

C 200 lb (110 ton) of water at 1000 ft

D All of the above have same energy

1 ms = 22 mph

First Example of Energy Exchangebull When the boulder falls off the cliff it picks up

speed and therefore gains kinetic energybull Where does this energy come from

rArr from the gravitational potential energybull The higher the cliff the more kinetic energy the

boulder will have when it reaches the ground

mgh

becomes

frac12mv2

Energy is conserved sofrac12mv2 = mgh

Can even figure out v since v2 = 2gh

h

19

Examples of GravitationalPotential Energy

bull How much gravitational potential energy does a70 kg high-diver have on the 10 meter platform

mgh = (70 kg)times(10 ms2)times(10 m)= 7000 kgm2s2 = 7 kJ

7 kJ (1 Calorie4182kJ) = 16 CaloriesThis is amount of energy the diver used in climbing the

stairs (actually more than this since some energy waswasted) They got that energy from the food they ate

The Energy of Heatbull Hot things have more energy than their cold

counterpartsbull Heat is really just kinetic energy on microscopic

scales the vibration or otherwise fast motion ofindividual atomsmoleculesndash Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are randombull Heat is frequently quantified by calories (or Btu)

ndash One calorie (4184 J) raises one gram of H2O 1ordmCndash One Calorie (4184 J) raises one kilogram of H2O 1ordmCndash One Btu (1055 J) raises one pound of H2O 1ordmF

20

Energy of Heat continuedbull Food Calories are with the ldquobigrdquo C or kilocalories (kcal)bull Since water has a density of one gram per cubic centimeter 1

cal heats 1 cc of water 1ordmC and likewise 1 kcal (Calorie) heatsone liter of water 1ordmC In British Units 1 Btu heats 1 pound ofwater 1 degree Fahrenheitndash these are useful numbers to hang onto

bull Example to heat a 2-liter bottle of Coke from the 5ordmCrefrigerator temperature to 20ordmC room temperature requires 30Calories or 1225 kJ

bull Drink a pint (16 oz) of ice cold water (or coke) It weighs about1 pound To heat it to body temperature (986 degrees minus 32degrees or change of 666 degrees Takes about 67 BtuConvert to Calories 1 Calorie = 1kJ = 4 Btu so

67 Btu (1 Calorie 4 Btu) = 1675 Calories Since 16 oz ofcoke has 210 Calories and about 17 Calories are used justheating to your body temp you get less calories drinking it cold(or drinking quart of cold water ldquoburnsrdquo 17 Calories)

The Physics of Energy Formula List

P = ΔEΔtPower (rate of energy use)

F = σT4 (temperature to the fourthpower times a constant)

Radiative energy flux

E = mc2 (mass times speed oflight squared)

Mass energy

ΔE = cpmΔT (mass times changein temperature times heatcapacity)

Heat Energy

E = mgh (mass times height times10ms2)

(Grav) Potential Energy

KE = frac12mv2 (mass times velocitysquared)

Kinetic Energy

W = Fd (Force times distance)Work

Energy FormulaEnergy Form

21

Heat Capacitybull Different materials have different capacities to

hold heatndash Add the same energy to different materials and yoursquoll

get different temperature risesndash Quantified as heat capacityndash Water is exceptional with 4184 JkgordmCndash Most materials are about 1000 JkgordmC (including

wood air metals)bull Example to add 10ordmC to a room 3 meters on a side

(cubic) how much energy do we needair density is 13 kgm3 and we have 27 m3 so 35 kg ofair and we need 1000 J per kg per ordmC so we end upneeding 350000 J (= 836 Cal)

Important in designing solar heated houses Also reasonit is cooler near the coast than inland

Powerbull Power is simply energy exchanged

per unit time or how fast you getwork done (Watts = Joulessec)

bull One horsepower = 745 Wbull Perform 100 J of work in 1 s and

call it 100 Wbull Run upstairs raising your 70 kg

(700 N) mass 3 m (2100 J) in 3seconds rarr 700 W output

bull Shuttle puts out a few GW(gigawatts or 109 W) of power

bull A big electrical power plant putsout around a GW That is 1 BillionJoules per second House takes afew kW (kilowatt)

22

QuestionPower is Energy used per second P= energytime Whichhighest power

A Using 100 Calories in 10 minutes

B Using 1000 Calories in 100 minutes

C Using 10 Calories in 1 minute

D Using 1 Calorie in 6 seconds

E All of the above are the same power usage

1 Calorieminute = Watts

Wind Energy

bull Wind can be used as a source of energy (windmills sailingships etc)

bull Really just kinetic energybull Example wind passing through a square meter at 8 meters

per secondndash Each second we have 8 cubic metersndash Air has density of 13 kgm3 so (8 m3)times(13 kgm3) = 104 kg of

air each secondndash frac12mv2 = frac12times(104 kg)times(8 ms)2 = 333 Jndash 333 J every second rarr 333 Watts of available power per square

meter (but to get all of it yoursquod have to stop the wind)bull Stronger winds rarr more power (like v2)

23

Chemical Energy

bull Electrostatic energy (associated with chargedparticles like electrons) is stored in the chemicalbonds of substances

bull Rearranging these bonds can release energy (somereactions require energy to be put in)

bull Typical numbers are 100ndash200 kJ per molendash a mole is 6022times1023 moleculesparticlesndash typical molecules are tens of grams per molerarrworks

out to typical numbers like several thousand Joules pergram or a few Calories per gram (remember 1 Cal = 1kcal = 4187 J)

Chemical Energy Examples

bull Burning a wooden match releases about oneBtu or 1055 Joules (a match is about 03grams) so this is gt3000 Jg nearly 1 Calg

bull Burning coal releases about 20 kJ per gramof chemical energy or roughly 5 Calg

bull Burning gasoline yields about 39 kJ pergram or just over 9 Calg

bull Very few substances over about 11 Calg

24

Energy from Food

bull We get the energy to do the things we do out of food(stored solar energy in the form of chemical energy)

bull Energy sources recognized by our digestive systemsndash Carbohydrates 4 Calories per gramndash Proteins 4 Calories per gramndash Fats 9 Calories per gram (like gasoline) (9 is more than

4 so gain more weight eating same amount of fat thancarbs or protein)

ndash Roughly 3500 Caloriespound in your body fat Less inyour protein (muscle skin etc)

Our Human Energy Budget

bull A 2000 Calorie per daydiet means 2000times4184 J =8368000 J per day

bull 837 MJ in (24 hrday) times(60 minhr)times(60 secmin)= 86400 sec correspondsto 97 Watts of power

bull Even a couch-potato at1500 Calday burns 75 W

bull More active lifestylesrequire greater Caloricintake (more energy)

25

Nutrition Labelsbull Nutrition labels tell you about the

energy content of foodbull Note they use Calories with capitol Cbull Conversions Fat 9 Calg

Carbs 4 CalgProtein 4 Calg

bull This product has 72 Cal from fat 48Cal from carbohydrates and 32 Calfrom proteinndash sum is 152 Calories compare to label

bull 152 Cal = 636 kJ enough to climbabout 1000 meters (64 kg person)

bull 1kwh = 860 Cal or about 14 lb bodyfat

bull 1 gal of gas has 31000 Calories

Mass-energy

bull Einsteinrsquos famous relationE = mc2

relates mass to energybull In effect they are the same thing

ndash one can be transformed into the otherndash physicists speak generally of mass-energy

bull Seldom experienced in daily life directlyndash Happens at large scale in the center of the sun and in

nuclear bombs and reactorsndash Actually does happen at barely detectable level in all

energy transactions but the effect is tiny

26

E = mc2 Examples

bull The energy equivalent of one gram of material(any composition) is (0001 kg)times(30times108 ms)2

= 90times1013 J = 90000000000000 J = 90 TJndash Man thatrsquos bigndash Our global energy budget is equivalent to 1000 kgyr

(thatrsquos about 1 ton per year)bull If one gram of material undergoes a chemical

reaction losing about 9000 J of energy howmuch mass does it lose

9000 J = Δmc2 so Δm = 9000c2 = 9times1039times1016

= 10-13 kg (would we ever notice)

Solar Energy is Nuclear Using E= mc2

bull Thermonuclear fusion reactions in the sunrsquos centerndash Sun is 16 million degrees Celsius in its centerndash Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then heliumndash Reaction per atom 20 million times more energetic than chemical

reactions in general

4 protonsmass = 4029

4He nucleusmass = 40015

2 neutrinos photons (light)

27

E = mc2 in Sun

bull Helium nucleus is lighter than the four protonsbull Mass difference is 4029 - 40015 = 00276 amu

ndash 1 amu (atomic mass unit) is 16605times10-27 kgndash difference of 458times10-29 kgndash multiply by c2 to get 412times10-12 Jndash 1 mole (6022times1023 particles) of protons rarr 25times1012 Jndash typical chemical reactions are 100-200 kJmolendash nuclear fusion is ~20 million times more potent stuffndash Nuclear fusion is energy source of hydrogen bomb

Energy from Lightbull The tremendous energy from the sun is released as light So light

carries energybull Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiationbull Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequencybull Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellipbull All objects emit ldquolightrdquobull The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter moreradiation and color is ldquobluerrdquo

28

Emitted Radiationrsquos Color andIntensity depend on Temperature

Object

YouHeat LampCandle FlameBulb FilamentSunrsquos SurfaceNeutron StarMolecules in deep space

Temperature

~ 30 C~ 500 C~ 1700 C~ 2700 C~ 5500 C~ millions C

lt -272C

Color

Infrared (invisible)Dull redDim orangeYellowBrilliant whiteX-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted lightThe hotter it gets the more intense the radiation (more energy)

ldquoBlackbodyrdquo or Planck Spectrum

29

Same thing on logarithmic scale

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm(note 0degC = 273degK 300degK = 27degC = 81degF)

Okay but how much energybull The power given off of a surface in the form of light is

proportional to the fourth power of temperatureF = σT4 in Watts per square meter

ndash the constant σ is numerically 567times10-8 WordmK4m2

ndash easy to remember constant 5678ndash temperature must be in Kelvin

bull ordmK = ordmC + 273bull ordmC = (59)times(ordmF ndash32)

bull Example radiation from your body(567 times10-8) times(310)4 = 523 Watts per square meter(if naked in the cold of space donrsquot let this happen to you)

30

Radiant Energy continued

bull Example The sun is 5800ordmK on its surface soF = σT4 = (567times10-8)times(5800)4 = 64times107 Wm2

Summing over entire surface area of sun gives39times1026 W

bull Compare to total capacity of energy production onearth 33times1012 Wndash Single power plant typically 05ndash10 GW (109 W)

bull In earthly situations radiated power out partiallybalanced by radiated power in from other sourcesndash Not 523 Wm2 in 70ordmF room more like 100 Wm2

bull goes like σTh4 ndash σTc

4

Electrical Energybull Opposite charges attract so electrons are attracted to

protons This holds atoms togetherbull It takes energy to pull electrons off their atomsbull Electrons want to get back home to their protons They can

only travel through conductors like wires not throughinsulators like plastic paper or wood They will gothrough miles of wire to get home to their protons

bull This is how electricity works The electronrsquos energy canbe stolen as it goes home Can be used in many manyways

bull Note electricity is not a primary source of energy Energy(from burning coal nat gas from hydro wind nuke orsolar) is used to pull of electrons and that energy can bemoved through wires and got back at will

31

And those are the majorplayershellip

bull Wersquove now seen most of the major energyplayersndash work as force times distancendash kinetic energy (wind ocean currents)ndash gravitational potential energy (hydroelectric tidal)ndash chemical energy (fossil fuels batteries food biomass)ndash heat energy (power plants space heating)ndash mass-energy (nuclear sources sunrsquos energy)ndash radiant energy (solar energy)ndash electrical energy (energy of electrons separated from

their atoms)

Conservation and Exchange ofEnergy

Nothing Comes for Free

32

Energy is Conservedbull Conservation of Energy is different from Energy

Conservation the latter being about using energywisely

bull Conservation of Energy means energy is neithercreated nor destroyed The amount of energy inthe Universe is constant

bull Donrsquot we create energy at a power plantndash Oh that this were truemdashno we simply transform

energy at our power plantsbull Doesnrsquot the sun create energy

ndash Nopemdashit exchanges mass for energybull Donrsquot batteries give us new energy

ndash Nope just convert stored chemical energy to electricalenergy Someone had to put that energy in there

height referenceh

Energy Exchangebull Though the total energy of a system is constant

the form of the energy can changebull A simple example is that of a simple pendulum in

which a continual exchange goes on betweenkinetic and potential energy

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

33

Perpetual Motion

bull Why wonrsquot the pendulum swing foreverbull Itrsquos hard to design a system free of energy pathsbull The pendulum slows down by several mechanisms

ndash Friction at the contact point requires force to opposeforce acts through distance rarr work is done

ndash Air resistance must push through air with a force(through a distance) rarr work is done

ndash Gets some air swirling puts kinetic energy into air (notreally fair to separate these last two)

bull Perpetual motion means no loss of energyndash solar system orbits come very close

Some Energy Chains

bull A coffee mug with some gravitational potentialenergy is dropped

bull potential energy turns into kinetic energybull kinetic energy of the mug goes into

ndash ripping the mug apart (chemical breaking bonds)ndash sending the pieces flying (kinetic)ndash into soundndash into heating the floor and pieces through friction as the

pieces slide to a stopbull In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored inthe potential energy)

34

Gasoline Examplebull Put gas in your car containing 9 Calgbull Combust gas turning 9 Calg into kinetic energy of

explosionbull Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a wholebull That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water andsurrounding air) and friction of transmission system(heat) and noise of engine (heating the air) etc

bull Much of energy goes into stirring the air (ends up as heat)bull Apply the brakes and convert kinetic energy into heatbull It all ends up as waste heat ultimately

Bouncing Ballbull Superball has gravitational potential energybull Drop the ball and this becomes kinetic energybull Ball hits ground and compresses (force times

distance) storing energy in the springbull Ball releases this mechanically stored energy

and it goes back into kinetic form (bouncesup)

bull Inefficiencies in ldquospringrdquo end up heating theball and the floor and stirring the air a bit

bull In the end all is heat

35

Why donrsquot we get hotter andhotter

bull If all these processes end up as heat why arenrsquotwe continually getting hotter

bull If earth retained all its heat we would get hotterbull All of earthrsquos heat is radiated away

F = σT4

bull If we dump more power the temperature goes upthe radiated power increases dramaticallyndash comes to equilibrium power dumped = power radiatedndash stable against perturbation T tracks power budget

Rough numbers

bull How much power does the earth radiatebull F = σT4 for T = 288ordmK = 15ordmC is 390 Wm2

bull Summed over entire surface area (4πR2 where R= 6378000 meters) is 20times1017 W

bull Global production is 3times1012 Wbull Solar radiation incident on earth is 18times1017 W

ndash just solar luminosity of 39times1026 W divided bygeometrical fraction that points at earth

bull Amazing coincidence of numbers (or is ithellip)

36

No Energy for Free

bull No matter what you canrsquot create energy out ofnothing it has to come from somewhere

bull We can transform energy from one form toanother we can store energy we can utilizeenergy being conveyed from natural sources

bull The net energy of the entire Universe is constantbull The best we can do is scrape up some useful

crumbs

Examplesbull Unit conversion

ndash 100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Calndash 100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 Jndash 100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWhndash 10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWhndash How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86Calorieshour About what average person eats

ndash Gasoline is $3gal Electricity if $015kWh Which is moreexpensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh)= $008kWh for gasoline Gasoline is cheap in the USA

37

Examplesbull Power vs Energy (P=Etime E = P t t = EP)

ndash Car goes 60 miles in one hour and uses 3 gal of gas What wastotal power in Watts P=Et Power = (3 gal1 hour) = 3galhr(366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W[Alternative method 3 galhr (132000000 J1 gal) (1 hr3600sec) = 110000 Jsec = 110000 W

ndash 1000 W space heater is on for 3 hours How much does it cost ifelectricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr(1kW1000W) = 3kWh ($15kWh) = $45 [Alternative methodE = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000J (1 kWh3600000J) = 3 kWh Again 45 cents

ndash AAA Battery contains 33 Calories of chemical energy How longcan it run a 2 Watt light bulb time = EP time = 33 Calories2W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1hr3600 sec) = 19 hours

QuestionThe US uses about 7 Gbarrels of oil each year This couldbe converted into which of the following units

A Joules B Watts C QBtus D Dollars $ E Any of the above

38

QuestionIf one barrel of oil contains 1700 kWh of energy how manyWatts is 7 Gbarrelyear

A 1400 GW (Giga Watts)

B 14 GW

C 11900 W

D 119 MW

E 1 x 1011 W

QuestionIf the total yearly oil use in the US is about 1400 GW howmany 1000 MW nuclear reactors will need to be built toreplace all oil use with electricity

A Only one will be needed

B Around 14

C Around 140

D Around 1400

E Cant convert Watts to reactors power vs energy

39

More Power Examplesbull How much power does it take to lift 10 kg up 2 meters in 2

secondsmgh = (10 kg)times(10 ms2)times(2 m) = 200J

200 J in 2 seconds rarr 100 Wattsbull If you want to heat the 3 m cubic room by 10ordmC with a

1000 W space heater how long will it takeWe know from before that the room needs to have 360000 J addedto it so at 1000 W = 1000 Js this will take 360 seconds or sixminutes

But the walls need to be warmed up too so it will actually takelonger (and depends on quality of insulation etc)

A note on arithmetic of unitsbull You should carry units in your calculations and multiply and divide them

as if they were numbersbull Example the force of air drag is given bybull Fdrag = frac12cDrAv2

bull cD is a dimensionless drag coefficientbull r is the density of air 13 kgm3

bull A is the cross-sectional area of the body in m2

bull v is the velocity in msbull units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) =

kgmiddotmiddotmm22middotmiddotmm22

m3middotmiddotss22kgmiddotmiddotmm44

m3middotmiddotss22= = kgmiddotmiddotmsms22 = = NewtonsNewtons

10

Energy the capacity to do work

bull This notion makes sense even in acolloquial contextndash hard to get work done when yoursquore wiped out

(low on energy)ndash work makes you tired yoursquove used up energy

bull But we can make this definition of energymuch more precise by specifying exactlywhat we mean by work

Work =Energy more than justunpleasant tasks

bull In physics the definition of work is the application of aforce through a distance Energy is needed to do it

W = Fd

bull W is the work done = energy usedbull F is the force appliedbull d is the distance through which the force actsbull Only the force that acts in the direction of motion counts

towards work

11

Okay what is Force thenbull Force is a pushingpulling agentbull Examples

ndash gravity exerts a downward force on youndash the floor exerts an upward force on a ball during its bouncendash a car seat exerts a forward force on your body when you accelerate forward from

a stopndash the seat yoursquore sitting in now is exerting an upward force on you (can you feel it)ndash you exert a sideways force on a couch that you slide across the floorndash a string exerts a centrally-directed (centripetal) force on a rock at the end of a

string that yoursquore twirling over your headndash the expanding gas in your carrsquos cylinder exerts a force against the piston

Forces have Directionbull In all the previous examples force had a

direction associated with itbull If multiple forces act on an object they

could potentially add or cancel dependingon direction

Force 1Force 2

Total Force Force 1

Force 2

Total Force = 0

12

When net force is not zero

bull When an object experiences a non-zero net force it mustaccelerate

bull Newtonrsquos second lawF = ma Force = mass times acceleration

bull The same force makes a small object accelerate more thanit would a more massive objectndash hit a golf ball and a bowling ball with a golf club and see what

happens

QuestionA 150 lb person is standing still on the edge of a cliff Whatis the total force on the person

A zeroB 150 lbC Canrsquot say from this info

13

QuestionA 150 lb person jumps (or was he pushed) off a cliff and isfalling to their death What is the total force on the person

A zeroB 150 lbC Canrsquot say from this info

But what is acceleration

bull This is getting to be like the ldquohole in thebucketrdquo song but wersquore almost therehellip

bull Acceleration is any change in velocity(speed andor direction of motion)

bull Measured as rate of change of velocityndash velocity is expressed in meters per second (ms)ndash acceleration is meters per second per secondndash expressed as ms2 (meters per second-squared)

14

Putting it back together Units ofEnergy

bull Force is a mass times an accelerationndash mass has units of kilogramsndash acceleration is ms2

ndash force is then kgms2 which we call Newtons (N)

bull Work is a force times a distancendash units are then (kgms2)m = kg m2s2 = Nm = Joules (J)ndash One joule is one Newton of force acting through one meterndash Imperial units of force and distance are pounds and feet so unit of

energy is foot-pound which equals 136 J

bull Energy has the same units as work Joules

A Zoo of Unitsbull The main metric unit of energy is the Joule and most of

the world uses this but many others existbull The calorie is 4184 Joules

ndash raise 1 gram (cc) of water one degree Celsiusbull The Calorie (kilocalorie) is 4184 J (used for food energy)

ndash raise 1 kg (1 liter) of water one degree Celsiusbull The Btu (British thermal unit) is 1055 J (roughly 1 kJ) or

about 14 Calorie or chemical energy of one matchndash raise 1 pound of water one degree Fahrenheit

bull The kilowatt-hour (kWh) is 3600000 J = 3600 kJ or 860Calories (used for electrical energy)ndash one Watt (W) is one Joule per secondndash a kWh is 1000 W for one hour (3600 seconds)

bull Can also use ldquobarrel of oilrdquo ldquoton of coalrdquo 1000 cubic feetof natural gas gram of Uranium or amount of any energycontaining source etc

15

The Physics of Energy Formula List

bull Lots of forms of energy coming fast and furious but to putit in perspective herersquos a list of formulas

P = ΔEΔtPower (rate of energy use)

F = σT4 (temperature to the fourthpower times a constant)

Radiative energy flux

E = mc2 (mass times speed of lightsquared)

Mass energy

ΔE = cpmΔT (mass times change intemperature times heat capacity)

Heat Energy

E = mgh (mass times height times10ms2)

(Grav) Potential Energy

KE = frac12mv2 (mass times velocitysquared)

Kinetic Energy

W = Fd (Force times distance)Work

Energy FormulaEnergy Form

Kinetic Energybull Kinetic Energy the energy of motionbull Moving things carry energy in the amount

KE = frac12mv2

bull Note the v2 dependencemdashthis is whyndash a car at 60 mph is 4 times more dangerous than a car at 30 mphndash hurricane-force winds at 100 mph are much more destructive (4

times) than 50 mph gale-force windsndash a bullet shot from a gun is at least 100 times as destructive as a

thrown bullet even if you can throw it a tenth as fast as you couldshoot it

16

Numerical examples of kineticenergy

bull A baseball (mass is 0145 kg = 145 g) moving at 30 ms(67 mph) has kinetic energy

KE = frac12times(0145 kg)times(30 ms)2

= 6525 kgm2s2 asymp 65 J

bull A quarter (mass = 000567 kg = 567 g) flipped about fourfeet into the air has a speed on reaching your hand of about5 ms The kinetic energy is

KE = frac12times(000567 kg)times(5 ms)2

= 007 kgm2s2 = 007 J

More numerical examples

bull A 1500 kg car moves down the freeway at30 ms (67 mph)

KE = frac12times(1500 kg)times(30 ms)2

= 675000 kgm2s2 = 675 kJConvert to Calories 4184 kJ = 1 Calorie675 kJ (1 Calorie4184 kJ) = 161 Calorie

bull A 2 kg (~44 lb) fish jumps out of the waterwith a speed of 1 ms (22 mph)

KE = frac12times(2 kg)times(1 ms)2

= 1 kgm2s2 = 1 J

17

QuestionKinetic energy is E = 12 m v2 Which has more energy

A 10 kg object going 100 ms

B 100 kg object going 10 ms

C 1 kg object going 1000 ms

D 1000 kg object going 1 ms

1 ms = 22 mph

Gravitational Potential Energybull It takes work to lift a mass against the pull (force) of

gravitybull The force of gravity is mg where m is the mass and g is

the gravitational accelerationF = mg (note similarity to F = ma)

ndash g = 98 ms2 on the surface of the earth or 32 fts2

bull Lifting a height h against the gravitational forcerequires an energy input (work) of

ΔE = W = F h = mghbull Rolling a boulder up a hill and perching it on the edge of a

cliff gives it gravitational potential energy that can be laterreleased when the roadrunner is down below

bull Water in river or hydroelectric plant is using potentialenergy that it got from being lifted up when Sun (solarenergy) evaporated the water

18

QuestionPotential energy is E = 10 m h (metric units) Which hasmore energy

A 1 ton of water at a height of 100 ft

B 100 tons of water at a height of 1 ft

C 200 lb (110 ton) of water at 1000 ft

D All of the above have same energy

1 ms = 22 mph

First Example of Energy Exchangebull When the boulder falls off the cliff it picks up

speed and therefore gains kinetic energybull Where does this energy come from

rArr from the gravitational potential energybull The higher the cliff the more kinetic energy the

boulder will have when it reaches the ground

mgh

becomes

frac12mv2

Energy is conserved sofrac12mv2 = mgh

Can even figure out v since v2 = 2gh

h

19

Examples of GravitationalPotential Energy

bull How much gravitational potential energy does a70 kg high-diver have on the 10 meter platform

mgh = (70 kg)times(10 ms2)times(10 m)= 7000 kgm2s2 = 7 kJ

7 kJ (1 Calorie4182kJ) = 16 CaloriesThis is amount of energy the diver used in climbing the

stairs (actually more than this since some energy waswasted) They got that energy from the food they ate

The Energy of Heatbull Hot things have more energy than their cold

counterpartsbull Heat is really just kinetic energy on microscopic

scales the vibration or otherwise fast motion ofindividual atomsmoleculesndash Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are randombull Heat is frequently quantified by calories (or Btu)

ndash One calorie (4184 J) raises one gram of H2O 1ordmCndash One Calorie (4184 J) raises one kilogram of H2O 1ordmCndash One Btu (1055 J) raises one pound of H2O 1ordmF

20

Energy of Heat continuedbull Food Calories are with the ldquobigrdquo C or kilocalories (kcal)bull Since water has a density of one gram per cubic centimeter 1

cal heats 1 cc of water 1ordmC and likewise 1 kcal (Calorie) heatsone liter of water 1ordmC In British Units 1 Btu heats 1 pound ofwater 1 degree Fahrenheitndash these are useful numbers to hang onto

bull Example to heat a 2-liter bottle of Coke from the 5ordmCrefrigerator temperature to 20ordmC room temperature requires 30Calories or 1225 kJ

bull Drink a pint (16 oz) of ice cold water (or coke) It weighs about1 pound To heat it to body temperature (986 degrees minus 32degrees or change of 666 degrees Takes about 67 BtuConvert to Calories 1 Calorie = 1kJ = 4 Btu so

67 Btu (1 Calorie 4 Btu) = 1675 Calories Since 16 oz ofcoke has 210 Calories and about 17 Calories are used justheating to your body temp you get less calories drinking it cold(or drinking quart of cold water ldquoburnsrdquo 17 Calories)

The Physics of Energy Formula List

P = ΔEΔtPower (rate of energy use)

F = σT4 (temperature to the fourthpower times a constant)

Radiative energy flux

E = mc2 (mass times speed oflight squared)

Mass energy

ΔE = cpmΔT (mass times changein temperature times heatcapacity)

Heat Energy

E = mgh (mass times height times10ms2)

(Grav) Potential Energy

KE = frac12mv2 (mass times velocitysquared)

Kinetic Energy

W = Fd (Force times distance)Work

Energy FormulaEnergy Form

21

Heat Capacitybull Different materials have different capacities to

hold heatndash Add the same energy to different materials and yoursquoll

get different temperature risesndash Quantified as heat capacityndash Water is exceptional with 4184 JkgordmCndash Most materials are about 1000 JkgordmC (including

wood air metals)bull Example to add 10ordmC to a room 3 meters on a side

(cubic) how much energy do we needair density is 13 kgm3 and we have 27 m3 so 35 kg ofair and we need 1000 J per kg per ordmC so we end upneeding 350000 J (= 836 Cal)

Important in designing solar heated houses Also reasonit is cooler near the coast than inland

Powerbull Power is simply energy exchanged

per unit time or how fast you getwork done (Watts = Joulessec)

bull One horsepower = 745 Wbull Perform 100 J of work in 1 s and

call it 100 Wbull Run upstairs raising your 70 kg

(700 N) mass 3 m (2100 J) in 3seconds rarr 700 W output

bull Shuttle puts out a few GW(gigawatts or 109 W) of power

bull A big electrical power plant putsout around a GW That is 1 BillionJoules per second House takes afew kW (kilowatt)

22

QuestionPower is Energy used per second P= energytime Whichhighest power

A Using 100 Calories in 10 minutes

B Using 1000 Calories in 100 minutes

C Using 10 Calories in 1 minute

D Using 1 Calorie in 6 seconds

E All of the above are the same power usage

1 Calorieminute = Watts

Wind Energy

bull Wind can be used as a source of energy (windmills sailingships etc)

bull Really just kinetic energybull Example wind passing through a square meter at 8 meters

per secondndash Each second we have 8 cubic metersndash Air has density of 13 kgm3 so (8 m3)times(13 kgm3) = 104 kg of

air each secondndash frac12mv2 = frac12times(104 kg)times(8 ms)2 = 333 Jndash 333 J every second rarr 333 Watts of available power per square

meter (but to get all of it yoursquod have to stop the wind)bull Stronger winds rarr more power (like v2)

23

Chemical Energy

bull Electrostatic energy (associated with chargedparticles like electrons) is stored in the chemicalbonds of substances

bull Rearranging these bonds can release energy (somereactions require energy to be put in)

bull Typical numbers are 100ndash200 kJ per molendash a mole is 6022times1023 moleculesparticlesndash typical molecules are tens of grams per molerarrworks

out to typical numbers like several thousand Joules pergram or a few Calories per gram (remember 1 Cal = 1kcal = 4187 J)

Chemical Energy Examples

bull Burning a wooden match releases about oneBtu or 1055 Joules (a match is about 03grams) so this is gt3000 Jg nearly 1 Calg

bull Burning coal releases about 20 kJ per gramof chemical energy or roughly 5 Calg

bull Burning gasoline yields about 39 kJ pergram or just over 9 Calg

bull Very few substances over about 11 Calg

24

Energy from Food

bull We get the energy to do the things we do out of food(stored solar energy in the form of chemical energy)

bull Energy sources recognized by our digestive systemsndash Carbohydrates 4 Calories per gramndash Proteins 4 Calories per gramndash Fats 9 Calories per gram (like gasoline) (9 is more than

4 so gain more weight eating same amount of fat thancarbs or protein)

ndash Roughly 3500 Caloriespound in your body fat Less inyour protein (muscle skin etc)

Our Human Energy Budget

bull A 2000 Calorie per daydiet means 2000times4184 J =8368000 J per day

bull 837 MJ in (24 hrday) times(60 minhr)times(60 secmin)= 86400 sec correspondsto 97 Watts of power

bull Even a couch-potato at1500 Calday burns 75 W

bull More active lifestylesrequire greater Caloricintake (more energy)

25

Nutrition Labelsbull Nutrition labels tell you about the

energy content of foodbull Note they use Calories with capitol Cbull Conversions Fat 9 Calg

Carbs 4 CalgProtein 4 Calg

bull This product has 72 Cal from fat 48Cal from carbohydrates and 32 Calfrom proteinndash sum is 152 Calories compare to label

bull 152 Cal = 636 kJ enough to climbabout 1000 meters (64 kg person)

bull 1kwh = 860 Cal or about 14 lb bodyfat

bull 1 gal of gas has 31000 Calories

Mass-energy

bull Einsteinrsquos famous relationE = mc2

relates mass to energybull In effect they are the same thing

ndash one can be transformed into the otherndash physicists speak generally of mass-energy

bull Seldom experienced in daily life directlyndash Happens at large scale in the center of the sun and in

nuclear bombs and reactorsndash Actually does happen at barely detectable level in all

energy transactions but the effect is tiny

26

E = mc2 Examples

bull The energy equivalent of one gram of material(any composition) is (0001 kg)times(30times108 ms)2

= 90times1013 J = 90000000000000 J = 90 TJndash Man thatrsquos bigndash Our global energy budget is equivalent to 1000 kgyr

(thatrsquos about 1 ton per year)bull If one gram of material undergoes a chemical

reaction losing about 9000 J of energy howmuch mass does it lose

9000 J = Δmc2 so Δm = 9000c2 = 9times1039times1016

= 10-13 kg (would we ever notice)

Solar Energy is Nuclear Using E= mc2

bull Thermonuclear fusion reactions in the sunrsquos centerndash Sun is 16 million degrees Celsius in its centerndash Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then heliumndash Reaction per atom 20 million times more energetic than chemical

reactions in general

4 protonsmass = 4029

4He nucleusmass = 40015

2 neutrinos photons (light)

27

E = mc2 in Sun

bull Helium nucleus is lighter than the four protonsbull Mass difference is 4029 - 40015 = 00276 amu

ndash 1 amu (atomic mass unit) is 16605times10-27 kgndash difference of 458times10-29 kgndash multiply by c2 to get 412times10-12 Jndash 1 mole (6022times1023 particles) of protons rarr 25times1012 Jndash typical chemical reactions are 100-200 kJmolendash nuclear fusion is ~20 million times more potent stuffndash Nuclear fusion is energy source of hydrogen bomb

Energy from Lightbull The tremendous energy from the sun is released as light So light

carries energybull Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiationbull Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequencybull Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellipbull All objects emit ldquolightrdquobull The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter moreradiation and color is ldquobluerrdquo

28

Emitted Radiationrsquos Color andIntensity depend on Temperature

Object

YouHeat LampCandle FlameBulb FilamentSunrsquos SurfaceNeutron StarMolecules in deep space

Temperature

~ 30 C~ 500 C~ 1700 C~ 2700 C~ 5500 C~ millions C

lt -272C

Color

Infrared (invisible)Dull redDim orangeYellowBrilliant whiteX-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted lightThe hotter it gets the more intense the radiation (more energy)

ldquoBlackbodyrdquo or Planck Spectrum

29

Same thing on logarithmic scale

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm(note 0degC = 273degK 300degK = 27degC = 81degF)

Okay but how much energybull The power given off of a surface in the form of light is

proportional to the fourth power of temperatureF = σT4 in Watts per square meter

ndash the constant σ is numerically 567times10-8 WordmK4m2

ndash easy to remember constant 5678ndash temperature must be in Kelvin

bull ordmK = ordmC + 273bull ordmC = (59)times(ordmF ndash32)

bull Example radiation from your body(567 times10-8) times(310)4 = 523 Watts per square meter(if naked in the cold of space donrsquot let this happen to you)

30

Radiant Energy continued

bull Example The sun is 5800ordmK on its surface soF = σT4 = (567times10-8)times(5800)4 = 64times107 Wm2

Summing over entire surface area of sun gives39times1026 W

bull Compare to total capacity of energy production onearth 33times1012 Wndash Single power plant typically 05ndash10 GW (109 W)

bull In earthly situations radiated power out partiallybalanced by radiated power in from other sourcesndash Not 523 Wm2 in 70ordmF room more like 100 Wm2

bull goes like σTh4 ndash σTc

4

Electrical Energybull Opposite charges attract so electrons are attracted to

protons This holds atoms togetherbull It takes energy to pull electrons off their atomsbull Electrons want to get back home to their protons They can

only travel through conductors like wires not throughinsulators like plastic paper or wood They will gothrough miles of wire to get home to their protons

bull This is how electricity works The electronrsquos energy canbe stolen as it goes home Can be used in many manyways

bull Note electricity is not a primary source of energy Energy(from burning coal nat gas from hydro wind nuke orsolar) is used to pull of electrons and that energy can bemoved through wires and got back at will

31

And those are the majorplayershellip

bull Wersquove now seen most of the major energyplayersndash work as force times distancendash kinetic energy (wind ocean currents)ndash gravitational potential energy (hydroelectric tidal)ndash chemical energy (fossil fuels batteries food biomass)ndash heat energy (power plants space heating)ndash mass-energy (nuclear sources sunrsquos energy)ndash radiant energy (solar energy)ndash electrical energy (energy of electrons separated from

their atoms)

Conservation and Exchange ofEnergy

Nothing Comes for Free

32

Energy is Conservedbull Conservation of Energy is different from Energy

Conservation the latter being about using energywisely

bull Conservation of Energy means energy is neithercreated nor destroyed The amount of energy inthe Universe is constant

bull Donrsquot we create energy at a power plantndash Oh that this were truemdashno we simply transform

energy at our power plantsbull Doesnrsquot the sun create energy

ndash Nopemdashit exchanges mass for energybull Donrsquot batteries give us new energy

ndash Nope just convert stored chemical energy to electricalenergy Someone had to put that energy in there

height referenceh

Energy Exchangebull Though the total energy of a system is constant

the form of the energy can changebull A simple example is that of a simple pendulum in

which a continual exchange goes on betweenkinetic and potential energy

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

33

Perpetual Motion

bull Why wonrsquot the pendulum swing foreverbull Itrsquos hard to design a system free of energy pathsbull The pendulum slows down by several mechanisms

ndash Friction at the contact point requires force to opposeforce acts through distance rarr work is done

ndash Air resistance must push through air with a force(through a distance) rarr work is done

ndash Gets some air swirling puts kinetic energy into air (notreally fair to separate these last two)

bull Perpetual motion means no loss of energyndash solar system orbits come very close

Some Energy Chains

bull A coffee mug with some gravitational potentialenergy is dropped

bull potential energy turns into kinetic energybull kinetic energy of the mug goes into

ndash ripping the mug apart (chemical breaking bonds)ndash sending the pieces flying (kinetic)ndash into soundndash into heating the floor and pieces through friction as the

pieces slide to a stopbull In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored inthe potential energy)

34

Gasoline Examplebull Put gas in your car containing 9 Calgbull Combust gas turning 9 Calg into kinetic energy of

explosionbull Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a wholebull That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water andsurrounding air) and friction of transmission system(heat) and noise of engine (heating the air) etc

bull Much of energy goes into stirring the air (ends up as heat)bull Apply the brakes and convert kinetic energy into heatbull It all ends up as waste heat ultimately

Bouncing Ballbull Superball has gravitational potential energybull Drop the ball and this becomes kinetic energybull Ball hits ground and compresses (force times

distance) storing energy in the springbull Ball releases this mechanically stored energy

and it goes back into kinetic form (bouncesup)

bull Inefficiencies in ldquospringrdquo end up heating theball and the floor and stirring the air a bit

bull In the end all is heat

35

Why donrsquot we get hotter andhotter

bull If all these processes end up as heat why arenrsquotwe continually getting hotter

bull If earth retained all its heat we would get hotterbull All of earthrsquos heat is radiated away

F = σT4

bull If we dump more power the temperature goes upthe radiated power increases dramaticallyndash comes to equilibrium power dumped = power radiatedndash stable against perturbation T tracks power budget

Rough numbers

bull How much power does the earth radiatebull F = σT4 for T = 288ordmK = 15ordmC is 390 Wm2

bull Summed over entire surface area (4πR2 where R= 6378000 meters) is 20times1017 W

bull Global production is 3times1012 Wbull Solar radiation incident on earth is 18times1017 W

ndash just solar luminosity of 39times1026 W divided bygeometrical fraction that points at earth

bull Amazing coincidence of numbers (or is ithellip)

36

No Energy for Free

bull No matter what you canrsquot create energy out ofnothing it has to come from somewhere

bull We can transform energy from one form toanother we can store energy we can utilizeenergy being conveyed from natural sources

bull The net energy of the entire Universe is constantbull The best we can do is scrape up some useful

crumbs

Examplesbull Unit conversion

ndash 100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Calndash 100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 Jndash 100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWhndash 10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWhndash How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86Calorieshour About what average person eats

ndash Gasoline is $3gal Electricity if $015kWh Which is moreexpensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh)= $008kWh for gasoline Gasoline is cheap in the USA

37

Examplesbull Power vs Energy (P=Etime E = P t t = EP)

ndash Car goes 60 miles in one hour and uses 3 gal of gas What wastotal power in Watts P=Et Power = (3 gal1 hour) = 3galhr(366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W[Alternative method 3 galhr (132000000 J1 gal) (1 hr3600sec) = 110000 Jsec = 110000 W

ndash 1000 W space heater is on for 3 hours How much does it cost ifelectricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr(1kW1000W) = 3kWh ($15kWh) = $45 [Alternative methodE = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000J (1 kWh3600000J) = 3 kWh Again 45 cents

ndash AAA Battery contains 33 Calories of chemical energy How longcan it run a 2 Watt light bulb time = EP time = 33 Calories2W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1hr3600 sec) = 19 hours

QuestionThe US uses about 7 Gbarrels of oil each year This couldbe converted into which of the following units

A Joules B Watts C QBtus D Dollars $ E Any of the above

38

QuestionIf one barrel of oil contains 1700 kWh of energy how manyWatts is 7 Gbarrelyear

A 1400 GW (Giga Watts)

B 14 GW

C 11900 W

D 119 MW

E 1 x 1011 W

QuestionIf the total yearly oil use in the US is about 1400 GW howmany 1000 MW nuclear reactors will need to be built toreplace all oil use with electricity

A Only one will be needed

B Around 14

C Around 140

D Around 1400

E Cant convert Watts to reactors power vs energy

39

More Power Examplesbull How much power does it take to lift 10 kg up 2 meters in 2

secondsmgh = (10 kg)times(10 ms2)times(2 m) = 200J

200 J in 2 seconds rarr 100 Wattsbull If you want to heat the 3 m cubic room by 10ordmC with a

1000 W space heater how long will it takeWe know from before that the room needs to have 360000 J addedto it so at 1000 W = 1000 Js this will take 360 seconds or sixminutes

But the walls need to be warmed up too so it will actually takelonger (and depends on quality of insulation etc)

A note on arithmetic of unitsbull You should carry units in your calculations and multiply and divide them

as if they were numbersbull Example the force of air drag is given bybull Fdrag = frac12cDrAv2

bull cD is a dimensionless drag coefficientbull r is the density of air 13 kgm3

bull A is the cross-sectional area of the body in m2

bull v is the velocity in msbull units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) =

kgmiddotmiddotmm22middotmiddotmm22

m3middotmiddotss22kgmiddotmiddotmm44

m3middotmiddotss22= = kgmiddotmiddotmsms22 = = NewtonsNewtons

11

Okay what is Force thenbull Force is a pushingpulling agentbull Examples

ndash gravity exerts a downward force on youndash the floor exerts an upward force on a ball during its bouncendash a car seat exerts a forward force on your body when you accelerate forward from

a stopndash the seat yoursquore sitting in now is exerting an upward force on you (can you feel it)ndash you exert a sideways force on a couch that you slide across the floorndash a string exerts a centrally-directed (centripetal) force on a rock at the end of a

string that yoursquore twirling over your headndash the expanding gas in your carrsquos cylinder exerts a force against the piston

Forces have Directionbull In all the previous examples force had a

direction associated with itbull If multiple forces act on an object they

could potentially add or cancel dependingon direction

Force 1Force 2

Total Force Force 1

Force 2

Total Force = 0

12

When net force is not zero

bull When an object experiences a non-zero net force it mustaccelerate

bull Newtonrsquos second lawF = ma Force = mass times acceleration

bull The same force makes a small object accelerate more thanit would a more massive objectndash hit a golf ball and a bowling ball with a golf club and see what

happens

QuestionA 150 lb person is standing still on the edge of a cliff Whatis the total force on the person

A zeroB 150 lbC Canrsquot say from this info

13

QuestionA 150 lb person jumps (or was he pushed) off a cliff and isfalling to their death What is the total force on the person

A zeroB 150 lbC Canrsquot say from this info

But what is acceleration

bull This is getting to be like the ldquohole in thebucketrdquo song but wersquore almost therehellip

bull Acceleration is any change in velocity(speed andor direction of motion)

bull Measured as rate of change of velocityndash velocity is expressed in meters per second (ms)ndash acceleration is meters per second per secondndash expressed as ms2 (meters per second-squared)

14

Putting it back together Units ofEnergy

bull Force is a mass times an accelerationndash mass has units of kilogramsndash acceleration is ms2

ndash force is then kgms2 which we call Newtons (N)

bull Work is a force times a distancendash units are then (kgms2)m = kg m2s2 = Nm = Joules (J)ndash One joule is one Newton of force acting through one meterndash Imperial units of force and distance are pounds and feet so unit of

energy is foot-pound which equals 136 J

bull Energy has the same units as work Joules

A Zoo of Unitsbull The main metric unit of energy is the Joule and most of

the world uses this but many others existbull The calorie is 4184 Joules

ndash raise 1 gram (cc) of water one degree Celsiusbull The Calorie (kilocalorie) is 4184 J (used for food energy)

ndash raise 1 kg (1 liter) of water one degree Celsiusbull The Btu (British thermal unit) is 1055 J (roughly 1 kJ) or

about 14 Calorie or chemical energy of one matchndash raise 1 pound of water one degree Fahrenheit

bull The kilowatt-hour (kWh) is 3600000 J = 3600 kJ or 860Calories (used for electrical energy)ndash one Watt (W) is one Joule per secondndash a kWh is 1000 W for one hour (3600 seconds)

bull Can also use ldquobarrel of oilrdquo ldquoton of coalrdquo 1000 cubic feetof natural gas gram of Uranium or amount of any energycontaining source etc

15

The Physics of Energy Formula List

bull Lots of forms of energy coming fast and furious but to putit in perspective herersquos a list of formulas

P = ΔEΔtPower (rate of energy use)

F = σT4 (temperature to the fourthpower times a constant)

Radiative energy flux

E = mc2 (mass times speed of lightsquared)

Mass energy

ΔE = cpmΔT (mass times change intemperature times heat capacity)

Heat Energy

E = mgh (mass times height times10ms2)

(Grav) Potential Energy

KE = frac12mv2 (mass times velocitysquared)

Kinetic Energy

W = Fd (Force times distance)Work

Energy FormulaEnergy Form

Kinetic Energybull Kinetic Energy the energy of motionbull Moving things carry energy in the amount

KE = frac12mv2

bull Note the v2 dependencemdashthis is whyndash a car at 60 mph is 4 times more dangerous than a car at 30 mphndash hurricane-force winds at 100 mph are much more destructive (4

times) than 50 mph gale-force windsndash a bullet shot from a gun is at least 100 times as destructive as a

thrown bullet even if you can throw it a tenth as fast as you couldshoot it

16

Numerical examples of kineticenergy

bull A baseball (mass is 0145 kg = 145 g) moving at 30 ms(67 mph) has kinetic energy

KE = frac12times(0145 kg)times(30 ms)2

= 6525 kgm2s2 asymp 65 J

bull A quarter (mass = 000567 kg = 567 g) flipped about fourfeet into the air has a speed on reaching your hand of about5 ms The kinetic energy is

KE = frac12times(000567 kg)times(5 ms)2

= 007 kgm2s2 = 007 J

More numerical examples

bull A 1500 kg car moves down the freeway at30 ms (67 mph)

KE = frac12times(1500 kg)times(30 ms)2

= 675000 kgm2s2 = 675 kJConvert to Calories 4184 kJ = 1 Calorie675 kJ (1 Calorie4184 kJ) = 161 Calorie

bull A 2 kg (~44 lb) fish jumps out of the waterwith a speed of 1 ms (22 mph)

KE = frac12times(2 kg)times(1 ms)2

= 1 kgm2s2 = 1 J

17

QuestionKinetic energy is E = 12 m v2 Which has more energy

A 10 kg object going 100 ms

B 100 kg object going 10 ms

C 1 kg object going 1000 ms

D 1000 kg object going 1 ms

1 ms = 22 mph

Gravitational Potential Energybull It takes work to lift a mass against the pull (force) of

gravitybull The force of gravity is mg where m is the mass and g is

the gravitational accelerationF = mg (note similarity to F = ma)

ndash g = 98 ms2 on the surface of the earth or 32 fts2

bull Lifting a height h against the gravitational forcerequires an energy input (work) of

ΔE = W = F h = mghbull Rolling a boulder up a hill and perching it on the edge of a

cliff gives it gravitational potential energy that can be laterreleased when the roadrunner is down below

bull Water in river or hydroelectric plant is using potentialenergy that it got from being lifted up when Sun (solarenergy) evaporated the water

18

QuestionPotential energy is E = 10 m h (metric units) Which hasmore energy

A 1 ton of water at a height of 100 ft

B 100 tons of water at a height of 1 ft

C 200 lb (110 ton) of water at 1000 ft

D All of the above have same energy

1 ms = 22 mph

First Example of Energy Exchangebull When the boulder falls off the cliff it picks up

speed and therefore gains kinetic energybull Where does this energy come from

rArr from the gravitational potential energybull The higher the cliff the more kinetic energy the

boulder will have when it reaches the ground

mgh

becomes

frac12mv2

Energy is conserved sofrac12mv2 = mgh

Can even figure out v since v2 = 2gh

h

19

Examples of GravitationalPotential Energy

bull How much gravitational potential energy does a70 kg high-diver have on the 10 meter platform

mgh = (70 kg)times(10 ms2)times(10 m)= 7000 kgm2s2 = 7 kJ

7 kJ (1 Calorie4182kJ) = 16 CaloriesThis is amount of energy the diver used in climbing the

stairs (actually more than this since some energy waswasted) They got that energy from the food they ate

The Energy of Heatbull Hot things have more energy than their cold

counterpartsbull Heat is really just kinetic energy on microscopic

scales the vibration or otherwise fast motion ofindividual atomsmoleculesndash Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are randombull Heat is frequently quantified by calories (or Btu)

ndash One calorie (4184 J) raises one gram of H2O 1ordmCndash One Calorie (4184 J) raises one kilogram of H2O 1ordmCndash One Btu (1055 J) raises one pound of H2O 1ordmF

20

Energy of Heat continuedbull Food Calories are with the ldquobigrdquo C or kilocalories (kcal)bull Since water has a density of one gram per cubic centimeter 1

cal heats 1 cc of water 1ordmC and likewise 1 kcal (Calorie) heatsone liter of water 1ordmC In British Units 1 Btu heats 1 pound ofwater 1 degree Fahrenheitndash these are useful numbers to hang onto

bull Example to heat a 2-liter bottle of Coke from the 5ordmCrefrigerator temperature to 20ordmC room temperature requires 30Calories or 1225 kJ

bull Drink a pint (16 oz) of ice cold water (or coke) It weighs about1 pound To heat it to body temperature (986 degrees minus 32degrees or change of 666 degrees Takes about 67 BtuConvert to Calories 1 Calorie = 1kJ = 4 Btu so

67 Btu (1 Calorie 4 Btu) = 1675 Calories Since 16 oz ofcoke has 210 Calories and about 17 Calories are used justheating to your body temp you get less calories drinking it cold(or drinking quart of cold water ldquoburnsrdquo 17 Calories)

The Physics of Energy Formula List

P = ΔEΔtPower (rate of energy use)

F = σT4 (temperature to the fourthpower times a constant)

Radiative energy flux

E = mc2 (mass times speed oflight squared)

Mass energy

ΔE = cpmΔT (mass times changein temperature times heatcapacity)

Heat Energy

E = mgh (mass times height times10ms2)

(Grav) Potential Energy

KE = frac12mv2 (mass times velocitysquared)

Kinetic Energy

W = Fd (Force times distance)Work

Energy FormulaEnergy Form

21

Heat Capacitybull Different materials have different capacities to

hold heatndash Add the same energy to different materials and yoursquoll

get different temperature risesndash Quantified as heat capacityndash Water is exceptional with 4184 JkgordmCndash Most materials are about 1000 JkgordmC (including

wood air metals)bull Example to add 10ordmC to a room 3 meters on a side

(cubic) how much energy do we needair density is 13 kgm3 and we have 27 m3 so 35 kg ofair and we need 1000 J per kg per ordmC so we end upneeding 350000 J (= 836 Cal)

Important in designing solar heated houses Also reasonit is cooler near the coast than inland

Powerbull Power is simply energy exchanged

per unit time or how fast you getwork done (Watts = Joulessec)

bull One horsepower = 745 Wbull Perform 100 J of work in 1 s and

call it 100 Wbull Run upstairs raising your 70 kg

(700 N) mass 3 m (2100 J) in 3seconds rarr 700 W output

bull Shuttle puts out a few GW(gigawatts or 109 W) of power

bull A big electrical power plant putsout around a GW That is 1 BillionJoules per second House takes afew kW (kilowatt)

22

QuestionPower is Energy used per second P= energytime Whichhighest power

A Using 100 Calories in 10 minutes

B Using 1000 Calories in 100 minutes

C Using 10 Calories in 1 minute

D Using 1 Calorie in 6 seconds

E All of the above are the same power usage

1 Calorieminute = Watts

Wind Energy

bull Wind can be used as a source of energy (windmills sailingships etc)

bull Really just kinetic energybull Example wind passing through a square meter at 8 meters

per secondndash Each second we have 8 cubic metersndash Air has density of 13 kgm3 so (8 m3)times(13 kgm3) = 104 kg of

air each secondndash frac12mv2 = frac12times(104 kg)times(8 ms)2 = 333 Jndash 333 J every second rarr 333 Watts of available power per square

meter (but to get all of it yoursquod have to stop the wind)bull Stronger winds rarr more power (like v2)

23

Chemical Energy

bull Electrostatic energy (associated with chargedparticles like electrons) is stored in the chemicalbonds of substances

bull Rearranging these bonds can release energy (somereactions require energy to be put in)

bull Typical numbers are 100ndash200 kJ per molendash a mole is 6022times1023 moleculesparticlesndash typical molecules are tens of grams per molerarrworks

out to typical numbers like several thousand Joules pergram or a few Calories per gram (remember 1 Cal = 1kcal = 4187 J)

Chemical Energy Examples

bull Burning a wooden match releases about oneBtu or 1055 Joules (a match is about 03grams) so this is gt3000 Jg nearly 1 Calg

bull Burning coal releases about 20 kJ per gramof chemical energy or roughly 5 Calg

bull Burning gasoline yields about 39 kJ pergram or just over 9 Calg

bull Very few substances over about 11 Calg

24

Energy from Food

bull We get the energy to do the things we do out of food(stored solar energy in the form of chemical energy)

bull Energy sources recognized by our digestive systemsndash Carbohydrates 4 Calories per gramndash Proteins 4 Calories per gramndash Fats 9 Calories per gram (like gasoline) (9 is more than

4 so gain more weight eating same amount of fat thancarbs or protein)

ndash Roughly 3500 Caloriespound in your body fat Less inyour protein (muscle skin etc)

Our Human Energy Budget

bull A 2000 Calorie per daydiet means 2000times4184 J =8368000 J per day

bull 837 MJ in (24 hrday) times(60 minhr)times(60 secmin)= 86400 sec correspondsto 97 Watts of power

bull Even a couch-potato at1500 Calday burns 75 W

bull More active lifestylesrequire greater Caloricintake (more energy)

25

Nutrition Labelsbull Nutrition labels tell you about the

energy content of foodbull Note they use Calories with capitol Cbull Conversions Fat 9 Calg

Carbs 4 CalgProtein 4 Calg

bull This product has 72 Cal from fat 48Cal from carbohydrates and 32 Calfrom proteinndash sum is 152 Calories compare to label

bull 152 Cal = 636 kJ enough to climbabout 1000 meters (64 kg person)

bull 1kwh = 860 Cal or about 14 lb bodyfat

bull 1 gal of gas has 31000 Calories

Mass-energy

bull Einsteinrsquos famous relationE = mc2

relates mass to energybull In effect they are the same thing

ndash one can be transformed into the otherndash physicists speak generally of mass-energy

bull Seldom experienced in daily life directlyndash Happens at large scale in the center of the sun and in

nuclear bombs and reactorsndash Actually does happen at barely detectable level in all

energy transactions but the effect is tiny

26

E = mc2 Examples

bull The energy equivalent of one gram of material(any composition) is (0001 kg)times(30times108 ms)2

= 90times1013 J = 90000000000000 J = 90 TJndash Man thatrsquos bigndash Our global energy budget is equivalent to 1000 kgyr

(thatrsquos about 1 ton per year)bull If one gram of material undergoes a chemical

reaction losing about 9000 J of energy howmuch mass does it lose

9000 J = Δmc2 so Δm = 9000c2 = 9times1039times1016

= 10-13 kg (would we ever notice)

Solar Energy is Nuclear Using E= mc2

bull Thermonuclear fusion reactions in the sunrsquos centerndash Sun is 16 million degrees Celsius in its centerndash Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then heliumndash Reaction per atom 20 million times more energetic than chemical

reactions in general

4 protonsmass = 4029

4He nucleusmass = 40015

2 neutrinos photons (light)

27

E = mc2 in Sun

bull Helium nucleus is lighter than the four protonsbull Mass difference is 4029 - 40015 = 00276 amu

ndash 1 amu (atomic mass unit) is 16605times10-27 kgndash difference of 458times10-29 kgndash multiply by c2 to get 412times10-12 Jndash 1 mole (6022times1023 particles) of protons rarr 25times1012 Jndash typical chemical reactions are 100-200 kJmolendash nuclear fusion is ~20 million times more potent stuffndash Nuclear fusion is energy source of hydrogen bomb

Energy from Lightbull The tremendous energy from the sun is released as light So light

carries energybull Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiationbull Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequencybull Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellipbull All objects emit ldquolightrdquobull The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter moreradiation and color is ldquobluerrdquo

28

Emitted Radiationrsquos Color andIntensity depend on Temperature

Object

YouHeat LampCandle FlameBulb FilamentSunrsquos SurfaceNeutron StarMolecules in deep space

Temperature

~ 30 C~ 500 C~ 1700 C~ 2700 C~ 5500 C~ millions C

lt -272C

Color

Infrared (invisible)Dull redDim orangeYellowBrilliant whiteX-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted lightThe hotter it gets the more intense the radiation (more energy)

ldquoBlackbodyrdquo or Planck Spectrum

29

Same thing on logarithmic scale

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm(note 0degC = 273degK 300degK = 27degC = 81degF)

Okay but how much energybull The power given off of a surface in the form of light is

proportional to the fourth power of temperatureF = σT4 in Watts per square meter

ndash the constant σ is numerically 567times10-8 WordmK4m2

ndash easy to remember constant 5678ndash temperature must be in Kelvin

bull ordmK = ordmC + 273bull ordmC = (59)times(ordmF ndash32)

bull Example radiation from your body(567 times10-8) times(310)4 = 523 Watts per square meter(if naked in the cold of space donrsquot let this happen to you)

30

Radiant Energy continued

bull Example The sun is 5800ordmK on its surface soF = σT4 = (567times10-8)times(5800)4 = 64times107 Wm2

Summing over entire surface area of sun gives39times1026 W

bull Compare to total capacity of energy production onearth 33times1012 Wndash Single power plant typically 05ndash10 GW (109 W)

bull In earthly situations radiated power out partiallybalanced by radiated power in from other sourcesndash Not 523 Wm2 in 70ordmF room more like 100 Wm2

bull goes like σTh4 ndash σTc

4

Electrical Energybull Opposite charges attract so electrons are attracted to

protons This holds atoms togetherbull It takes energy to pull electrons off their atomsbull Electrons want to get back home to their protons They can

only travel through conductors like wires not throughinsulators like plastic paper or wood They will gothrough miles of wire to get home to their protons

bull This is how electricity works The electronrsquos energy canbe stolen as it goes home Can be used in many manyways

bull Note electricity is not a primary source of energy Energy(from burning coal nat gas from hydro wind nuke orsolar) is used to pull of electrons and that energy can bemoved through wires and got back at will

31

And those are the majorplayershellip

bull Wersquove now seen most of the major energyplayersndash work as force times distancendash kinetic energy (wind ocean currents)ndash gravitational potential energy (hydroelectric tidal)ndash chemical energy (fossil fuels batteries food biomass)ndash heat energy (power plants space heating)ndash mass-energy (nuclear sources sunrsquos energy)ndash radiant energy (solar energy)ndash electrical energy (energy of electrons separated from

their atoms)

Conservation and Exchange ofEnergy

Nothing Comes for Free

32

Energy is Conservedbull Conservation of Energy is different from Energy

Conservation the latter being about using energywisely

bull Conservation of Energy means energy is neithercreated nor destroyed The amount of energy inthe Universe is constant

bull Donrsquot we create energy at a power plantndash Oh that this were truemdashno we simply transform

energy at our power plantsbull Doesnrsquot the sun create energy

ndash Nopemdashit exchanges mass for energybull Donrsquot batteries give us new energy

ndash Nope just convert stored chemical energy to electricalenergy Someone had to put that energy in there

height referenceh

Energy Exchangebull Though the total energy of a system is constant

the form of the energy can changebull A simple example is that of a simple pendulum in

which a continual exchange goes on betweenkinetic and potential energy

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

33

Perpetual Motion

bull Why wonrsquot the pendulum swing foreverbull Itrsquos hard to design a system free of energy pathsbull The pendulum slows down by several mechanisms

ndash Friction at the contact point requires force to opposeforce acts through distance rarr work is done

ndash Air resistance must push through air with a force(through a distance) rarr work is done

ndash Gets some air swirling puts kinetic energy into air (notreally fair to separate these last two)

bull Perpetual motion means no loss of energyndash solar system orbits come very close

Some Energy Chains

bull A coffee mug with some gravitational potentialenergy is dropped

bull potential energy turns into kinetic energybull kinetic energy of the mug goes into

ndash ripping the mug apart (chemical breaking bonds)ndash sending the pieces flying (kinetic)ndash into soundndash into heating the floor and pieces through friction as the

pieces slide to a stopbull In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored inthe potential energy)

34

Gasoline Examplebull Put gas in your car containing 9 Calgbull Combust gas turning 9 Calg into kinetic energy of

explosionbull Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a wholebull That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water andsurrounding air) and friction of transmission system(heat) and noise of engine (heating the air) etc

bull Much of energy goes into stirring the air (ends up as heat)bull Apply the brakes and convert kinetic energy into heatbull It all ends up as waste heat ultimately

Bouncing Ballbull Superball has gravitational potential energybull Drop the ball and this becomes kinetic energybull Ball hits ground and compresses (force times

distance) storing energy in the springbull Ball releases this mechanically stored energy

and it goes back into kinetic form (bouncesup)

bull Inefficiencies in ldquospringrdquo end up heating theball and the floor and stirring the air a bit

bull In the end all is heat

35

Why donrsquot we get hotter andhotter

bull If all these processes end up as heat why arenrsquotwe continually getting hotter

bull If earth retained all its heat we would get hotterbull All of earthrsquos heat is radiated away

F = σT4

bull If we dump more power the temperature goes upthe radiated power increases dramaticallyndash comes to equilibrium power dumped = power radiatedndash stable against perturbation T tracks power budget

Rough numbers

bull How much power does the earth radiatebull F = σT4 for T = 288ordmK = 15ordmC is 390 Wm2

bull Summed over entire surface area (4πR2 where R= 6378000 meters) is 20times1017 W

bull Global production is 3times1012 Wbull Solar radiation incident on earth is 18times1017 W

ndash just solar luminosity of 39times1026 W divided bygeometrical fraction that points at earth

bull Amazing coincidence of numbers (or is ithellip)

36

No Energy for Free

bull No matter what you canrsquot create energy out ofnothing it has to come from somewhere

bull We can transform energy from one form toanother we can store energy we can utilizeenergy being conveyed from natural sources

bull The net energy of the entire Universe is constantbull The best we can do is scrape up some useful

crumbs

Examplesbull Unit conversion

ndash 100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Calndash 100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 Jndash 100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWhndash 10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWhndash How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86Calorieshour About what average person eats

ndash Gasoline is $3gal Electricity if $015kWh Which is moreexpensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh)= $008kWh for gasoline Gasoline is cheap in the USA

37

Examplesbull Power vs Energy (P=Etime E = P t t = EP)

ndash Car goes 60 miles in one hour and uses 3 gal of gas What wastotal power in Watts P=Et Power = (3 gal1 hour) = 3galhr(366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W[Alternative method 3 galhr (132000000 J1 gal) (1 hr3600sec) = 110000 Jsec = 110000 W

ndash 1000 W space heater is on for 3 hours How much does it cost ifelectricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr(1kW1000W) = 3kWh ($15kWh) = $45 [Alternative methodE = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000J (1 kWh3600000J) = 3 kWh Again 45 cents

ndash AAA Battery contains 33 Calories of chemical energy How longcan it run a 2 Watt light bulb time = EP time = 33 Calories2W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1hr3600 sec) = 19 hours

QuestionThe US uses about 7 Gbarrels of oil each year This couldbe converted into which of the following units

A Joules B Watts C QBtus D Dollars $ E Any of the above

38

QuestionIf one barrel of oil contains 1700 kWh of energy how manyWatts is 7 Gbarrelyear

A 1400 GW (Giga Watts)

B 14 GW

C 11900 W

D 119 MW

E 1 x 1011 W

QuestionIf the total yearly oil use in the US is about 1400 GW howmany 1000 MW nuclear reactors will need to be built toreplace all oil use with electricity

A Only one will be needed

B Around 14

C Around 140

D Around 1400

E Cant convert Watts to reactors power vs energy

39

More Power Examplesbull How much power does it take to lift 10 kg up 2 meters in 2

secondsmgh = (10 kg)times(10 ms2)times(2 m) = 200J

200 J in 2 seconds rarr 100 Wattsbull If you want to heat the 3 m cubic room by 10ordmC with a

1000 W space heater how long will it takeWe know from before that the room needs to have 360000 J addedto it so at 1000 W = 1000 Js this will take 360 seconds or sixminutes

But the walls need to be warmed up too so it will actually takelonger (and depends on quality of insulation etc)

A note on arithmetic of unitsbull You should carry units in your calculations and multiply and divide them

as if they were numbersbull Example the force of air drag is given bybull Fdrag = frac12cDrAv2

bull cD is a dimensionless drag coefficientbull r is the density of air 13 kgm3

bull A is the cross-sectional area of the body in m2

bull v is the velocity in msbull units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) =

kgmiddotmiddotmm22middotmiddotmm22

m3middotmiddotss22kgmiddotmiddotmm44

m3middotmiddotss22= = kgmiddotmiddotmsms22 = = NewtonsNewtons

12

When net force is not zero

bull When an object experiences a non-zero net force it mustaccelerate

bull Newtonrsquos second lawF = ma Force = mass times acceleration

bull The same force makes a small object accelerate more thanit would a more massive objectndash hit a golf ball and a bowling ball with a golf club and see what

happens

QuestionA 150 lb person is standing still on the edge of a cliff Whatis the total force on the person

A zeroB 150 lbC Canrsquot say from this info

13

QuestionA 150 lb person jumps (or was he pushed) off a cliff and isfalling to their death What is the total force on the person

A zeroB 150 lbC Canrsquot say from this info

But what is acceleration

bull This is getting to be like the ldquohole in thebucketrdquo song but wersquore almost therehellip

bull Acceleration is any change in velocity(speed andor direction of motion)

bull Measured as rate of change of velocityndash velocity is expressed in meters per second (ms)ndash acceleration is meters per second per secondndash expressed as ms2 (meters per second-squared)

14

Putting it back together Units ofEnergy

bull Force is a mass times an accelerationndash mass has units of kilogramsndash acceleration is ms2

ndash force is then kgms2 which we call Newtons (N)

bull Work is a force times a distancendash units are then (kgms2)m = kg m2s2 = Nm = Joules (J)ndash One joule is one Newton of force acting through one meterndash Imperial units of force and distance are pounds and feet so unit of

energy is foot-pound which equals 136 J

bull Energy has the same units as work Joules

A Zoo of Unitsbull The main metric unit of energy is the Joule and most of

the world uses this but many others existbull The calorie is 4184 Joules

ndash raise 1 gram (cc) of water one degree Celsiusbull The Calorie (kilocalorie) is 4184 J (used for food energy)

ndash raise 1 kg (1 liter) of water one degree Celsiusbull The Btu (British thermal unit) is 1055 J (roughly 1 kJ) or

about 14 Calorie or chemical energy of one matchndash raise 1 pound of water one degree Fahrenheit

bull The kilowatt-hour (kWh) is 3600000 J = 3600 kJ or 860Calories (used for electrical energy)ndash one Watt (W) is one Joule per secondndash a kWh is 1000 W for one hour (3600 seconds)

bull Can also use ldquobarrel of oilrdquo ldquoton of coalrdquo 1000 cubic feetof natural gas gram of Uranium or amount of any energycontaining source etc

15

The Physics of Energy Formula List

bull Lots of forms of energy coming fast and furious but to putit in perspective herersquos a list of formulas

P = ΔEΔtPower (rate of energy use)

F = σT4 (temperature to the fourthpower times a constant)

Radiative energy flux

E = mc2 (mass times speed of lightsquared)

Mass energy

ΔE = cpmΔT (mass times change intemperature times heat capacity)

Heat Energy

E = mgh (mass times height times10ms2)

(Grav) Potential Energy

KE = frac12mv2 (mass times velocitysquared)

Kinetic Energy

W = Fd (Force times distance)Work

Energy FormulaEnergy Form

Kinetic Energybull Kinetic Energy the energy of motionbull Moving things carry energy in the amount

KE = frac12mv2

bull Note the v2 dependencemdashthis is whyndash a car at 60 mph is 4 times more dangerous than a car at 30 mphndash hurricane-force winds at 100 mph are much more destructive (4

times) than 50 mph gale-force windsndash a bullet shot from a gun is at least 100 times as destructive as a

thrown bullet even if you can throw it a tenth as fast as you couldshoot it

16

Numerical examples of kineticenergy

bull A baseball (mass is 0145 kg = 145 g) moving at 30 ms(67 mph) has kinetic energy

KE = frac12times(0145 kg)times(30 ms)2

= 6525 kgm2s2 asymp 65 J

bull A quarter (mass = 000567 kg = 567 g) flipped about fourfeet into the air has a speed on reaching your hand of about5 ms The kinetic energy is

KE = frac12times(000567 kg)times(5 ms)2

= 007 kgm2s2 = 007 J

More numerical examples

bull A 1500 kg car moves down the freeway at30 ms (67 mph)

KE = frac12times(1500 kg)times(30 ms)2

= 675000 kgm2s2 = 675 kJConvert to Calories 4184 kJ = 1 Calorie675 kJ (1 Calorie4184 kJ) = 161 Calorie

bull A 2 kg (~44 lb) fish jumps out of the waterwith a speed of 1 ms (22 mph)

KE = frac12times(2 kg)times(1 ms)2

= 1 kgm2s2 = 1 J

17

QuestionKinetic energy is E = 12 m v2 Which has more energy

A 10 kg object going 100 ms

B 100 kg object going 10 ms

C 1 kg object going 1000 ms

D 1000 kg object going 1 ms

1 ms = 22 mph

Gravitational Potential Energybull It takes work to lift a mass against the pull (force) of

gravitybull The force of gravity is mg where m is the mass and g is

the gravitational accelerationF = mg (note similarity to F = ma)

ndash g = 98 ms2 on the surface of the earth or 32 fts2

bull Lifting a height h against the gravitational forcerequires an energy input (work) of

ΔE = W = F h = mghbull Rolling a boulder up a hill and perching it on the edge of a

cliff gives it gravitational potential energy that can be laterreleased when the roadrunner is down below

bull Water in river or hydroelectric plant is using potentialenergy that it got from being lifted up when Sun (solarenergy) evaporated the water

18

QuestionPotential energy is E = 10 m h (metric units) Which hasmore energy

A 1 ton of water at a height of 100 ft

B 100 tons of water at a height of 1 ft

C 200 lb (110 ton) of water at 1000 ft

D All of the above have same energy

1 ms = 22 mph

First Example of Energy Exchangebull When the boulder falls off the cliff it picks up

speed and therefore gains kinetic energybull Where does this energy come from

rArr from the gravitational potential energybull The higher the cliff the more kinetic energy the

boulder will have when it reaches the ground

mgh

becomes

frac12mv2

Energy is conserved sofrac12mv2 = mgh

Can even figure out v since v2 = 2gh

h

19

Examples of GravitationalPotential Energy

bull How much gravitational potential energy does a70 kg high-diver have on the 10 meter platform

mgh = (70 kg)times(10 ms2)times(10 m)= 7000 kgm2s2 = 7 kJ

7 kJ (1 Calorie4182kJ) = 16 CaloriesThis is amount of energy the diver used in climbing the

stairs (actually more than this since some energy waswasted) They got that energy from the food they ate

The Energy of Heatbull Hot things have more energy than their cold

counterpartsbull Heat is really just kinetic energy on microscopic

scales the vibration or otherwise fast motion ofindividual atomsmoleculesndash Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are randombull Heat is frequently quantified by calories (or Btu)

ndash One calorie (4184 J) raises one gram of H2O 1ordmCndash One Calorie (4184 J) raises one kilogram of H2O 1ordmCndash One Btu (1055 J) raises one pound of H2O 1ordmF

20

Energy of Heat continuedbull Food Calories are with the ldquobigrdquo C or kilocalories (kcal)bull Since water has a density of one gram per cubic centimeter 1

cal heats 1 cc of water 1ordmC and likewise 1 kcal (Calorie) heatsone liter of water 1ordmC In British Units 1 Btu heats 1 pound ofwater 1 degree Fahrenheitndash these are useful numbers to hang onto

bull Example to heat a 2-liter bottle of Coke from the 5ordmCrefrigerator temperature to 20ordmC room temperature requires 30Calories or 1225 kJ

bull Drink a pint (16 oz) of ice cold water (or coke) It weighs about1 pound To heat it to body temperature (986 degrees minus 32degrees or change of 666 degrees Takes about 67 BtuConvert to Calories 1 Calorie = 1kJ = 4 Btu so

67 Btu (1 Calorie 4 Btu) = 1675 Calories Since 16 oz ofcoke has 210 Calories and about 17 Calories are used justheating to your body temp you get less calories drinking it cold(or drinking quart of cold water ldquoburnsrdquo 17 Calories)

The Physics of Energy Formula List

P = ΔEΔtPower (rate of energy use)

F = σT4 (temperature to the fourthpower times a constant)

Radiative energy flux

E = mc2 (mass times speed oflight squared)

Mass energy

ΔE = cpmΔT (mass times changein temperature times heatcapacity)

Heat Energy

E = mgh (mass times height times10ms2)

(Grav) Potential Energy

KE = frac12mv2 (mass times velocitysquared)

Kinetic Energy

W = Fd (Force times distance)Work

Energy FormulaEnergy Form

21

Heat Capacitybull Different materials have different capacities to

hold heatndash Add the same energy to different materials and yoursquoll

get different temperature risesndash Quantified as heat capacityndash Water is exceptional with 4184 JkgordmCndash Most materials are about 1000 JkgordmC (including

wood air metals)bull Example to add 10ordmC to a room 3 meters on a side

(cubic) how much energy do we needair density is 13 kgm3 and we have 27 m3 so 35 kg ofair and we need 1000 J per kg per ordmC so we end upneeding 350000 J (= 836 Cal)

Important in designing solar heated houses Also reasonit is cooler near the coast than inland

Powerbull Power is simply energy exchanged

per unit time or how fast you getwork done (Watts = Joulessec)

bull One horsepower = 745 Wbull Perform 100 J of work in 1 s and

call it 100 Wbull Run upstairs raising your 70 kg

(700 N) mass 3 m (2100 J) in 3seconds rarr 700 W output

bull Shuttle puts out a few GW(gigawatts or 109 W) of power

bull A big electrical power plant putsout around a GW That is 1 BillionJoules per second House takes afew kW (kilowatt)

22

QuestionPower is Energy used per second P= energytime Whichhighest power

A Using 100 Calories in 10 minutes

B Using 1000 Calories in 100 minutes

C Using 10 Calories in 1 minute

D Using 1 Calorie in 6 seconds

E All of the above are the same power usage

1 Calorieminute = Watts

Wind Energy

bull Wind can be used as a source of energy (windmills sailingships etc)

bull Really just kinetic energybull Example wind passing through a square meter at 8 meters

per secondndash Each second we have 8 cubic metersndash Air has density of 13 kgm3 so (8 m3)times(13 kgm3) = 104 kg of

air each secondndash frac12mv2 = frac12times(104 kg)times(8 ms)2 = 333 Jndash 333 J every second rarr 333 Watts of available power per square

meter (but to get all of it yoursquod have to stop the wind)bull Stronger winds rarr more power (like v2)

23

Chemical Energy

bull Electrostatic energy (associated with chargedparticles like electrons) is stored in the chemicalbonds of substances

bull Rearranging these bonds can release energy (somereactions require energy to be put in)

bull Typical numbers are 100ndash200 kJ per molendash a mole is 6022times1023 moleculesparticlesndash typical molecules are tens of grams per molerarrworks

out to typical numbers like several thousand Joules pergram or a few Calories per gram (remember 1 Cal = 1kcal = 4187 J)

Chemical Energy Examples

bull Burning a wooden match releases about oneBtu or 1055 Joules (a match is about 03grams) so this is gt3000 Jg nearly 1 Calg

bull Burning coal releases about 20 kJ per gramof chemical energy or roughly 5 Calg

bull Burning gasoline yields about 39 kJ pergram or just over 9 Calg

bull Very few substances over about 11 Calg

24

Energy from Food

bull We get the energy to do the things we do out of food(stored solar energy in the form of chemical energy)

bull Energy sources recognized by our digestive systemsndash Carbohydrates 4 Calories per gramndash Proteins 4 Calories per gramndash Fats 9 Calories per gram (like gasoline) (9 is more than

4 so gain more weight eating same amount of fat thancarbs or protein)

ndash Roughly 3500 Caloriespound in your body fat Less inyour protein (muscle skin etc)

Our Human Energy Budget

bull A 2000 Calorie per daydiet means 2000times4184 J =8368000 J per day

bull 837 MJ in (24 hrday) times(60 minhr)times(60 secmin)= 86400 sec correspondsto 97 Watts of power

bull Even a couch-potato at1500 Calday burns 75 W

bull More active lifestylesrequire greater Caloricintake (more energy)

25

Nutrition Labelsbull Nutrition labels tell you about the

energy content of foodbull Note they use Calories with capitol Cbull Conversions Fat 9 Calg

Carbs 4 CalgProtein 4 Calg

bull This product has 72 Cal from fat 48Cal from carbohydrates and 32 Calfrom proteinndash sum is 152 Calories compare to label

bull 152 Cal = 636 kJ enough to climbabout 1000 meters (64 kg person)

bull 1kwh = 860 Cal or about 14 lb bodyfat

bull 1 gal of gas has 31000 Calories

Mass-energy

bull Einsteinrsquos famous relationE = mc2

relates mass to energybull In effect they are the same thing

ndash one can be transformed into the otherndash physicists speak generally of mass-energy

bull Seldom experienced in daily life directlyndash Happens at large scale in the center of the sun and in

nuclear bombs and reactorsndash Actually does happen at barely detectable level in all

energy transactions but the effect is tiny

26

E = mc2 Examples

bull The energy equivalent of one gram of material(any composition) is (0001 kg)times(30times108 ms)2

= 90times1013 J = 90000000000000 J = 90 TJndash Man thatrsquos bigndash Our global energy budget is equivalent to 1000 kgyr

(thatrsquos about 1 ton per year)bull If one gram of material undergoes a chemical

reaction losing about 9000 J of energy howmuch mass does it lose

9000 J = Δmc2 so Δm = 9000c2 = 9times1039times1016

= 10-13 kg (would we ever notice)

Solar Energy is Nuclear Using E= mc2

bull Thermonuclear fusion reactions in the sunrsquos centerndash Sun is 16 million degrees Celsius in its centerndash Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then heliumndash Reaction per atom 20 million times more energetic than chemical

reactions in general

4 protonsmass = 4029

4He nucleusmass = 40015

2 neutrinos photons (light)

27

E = mc2 in Sun

bull Helium nucleus is lighter than the four protonsbull Mass difference is 4029 - 40015 = 00276 amu

ndash 1 amu (atomic mass unit) is 16605times10-27 kgndash difference of 458times10-29 kgndash multiply by c2 to get 412times10-12 Jndash 1 mole (6022times1023 particles) of protons rarr 25times1012 Jndash typical chemical reactions are 100-200 kJmolendash nuclear fusion is ~20 million times more potent stuffndash Nuclear fusion is energy source of hydrogen bomb

Energy from Lightbull The tremendous energy from the sun is released as light So light

carries energybull Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiationbull Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequencybull Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellipbull All objects emit ldquolightrdquobull The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter moreradiation and color is ldquobluerrdquo

28

Emitted Radiationrsquos Color andIntensity depend on Temperature

Object

YouHeat LampCandle FlameBulb FilamentSunrsquos SurfaceNeutron StarMolecules in deep space

Temperature

~ 30 C~ 500 C~ 1700 C~ 2700 C~ 5500 C~ millions C

lt -272C

Color

Infrared (invisible)Dull redDim orangeYellowBrilliant whiteX-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted lightThe hotter it gets the more intense the radiation (more energy)

ldquoBlackbodyrdquo or Planck Spectrum

29

Same thing on logarithmic scale

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm(note 0degC = 273degK 300degK = 27degC = 81degF)

Okay but how much energybull The power given off of a surface in the form of light is

proportional to the fourth power of temperatureF = σT4 in Watts per square meter

ndash the constant σ is numerically 567times10-8 WordmK4m2

ndash easy to remember constant 5678ndash temperature must be in Kelvin

bull ordmK = ordmC + 273bull ordmC = (59)times(ordmF ndash32)

bull Example radiation from your body(567 times10-8) times(310)4 = 523 Watts per square meter(if naked in the cold of space donrsquot let this happen to you)

30

Radiant Energy continued

bull Example The sun is 5800ordmK on its surface soF = σT4 = (567times10-8)times(5800)4 = 64times107 Wm2

Summing over entire surface area of sun gives39times1026 W

bull Compare to total capacity of energy production onearth 33times1012 Wndash Single power plant typically 05ndash10 GW (109 W)

bull In earthly situations radiated power out partiallybalanced by radiated power in from other sourcesndash Not 523 Wm2 in 70ordmF room more like 100 Wm2

bull goes like σTh4 ndash σTc

4

Electrical Energybull Opposite charges attract so electrons are attracted to

protons This holds atoms togetherbull It takes energy to pull electrons off their atomsbull Electrons want to get back home to their protons They can

only travel through conductors like wires not throughinsulators like plastic paper or wood They will gothrough miles of wire to get home to their protons

bull This is how electricity works The electronrsquos energy canbe stolen as it goes home Can be used in many manyways

bull Note electricity is not a primary source of energy Energy(from burning coal nat gas from hydro wind nuke orsolar) is used to pull of electrons and that energy can bemoved through wires and got back at will

31

And those are the majorplayershellip

bull Wersquove now seen most of the major energyplayersndash work as force times distancendash kinetic energy (wind ocean currents)ndash gravitational potential energy (hydroelectric tidal)ndash chemical energy (fossil fuels batteries food biomass)ndash heat energy (power plants space heating)ndash mass-energy (nuclear sources sunrsquos energy)ndash radiant energy (solar energy)ndash electrical energy (energy of electrons separated from

their atoms)

Conservation and Exchange ofEnergy

Nothing Comes for Free

32

Energy is Conservedbull Conservation of Energy is different from Energy

Conservation the latter being about using energywisely

bull Conservation of Energy means energy is neithercreated nor destroyed The amount of energy inthe Universe is constant

bull Donrsquot we create energy at a power plantndash Oh that this were truemdashno we simply transform

energy at our power plantsbull Doesnrsquot the sun create energy

ndash Nopemdashit exchanges mass for energybull Donrsquot batteries give us new energy

ndash Nope just convert stored chemical energy to electricalenergy Someone had to put that energy in there

height referenceh

Energy Exchangebull Though the total energy of a system is constant

the form of the energy can changebull A simple example is that of a simple pendulum in

which a continual exchange goes on betweenkinetic and potential energy

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

33

Perpetual Motion

bull Why wonrsquot the pendulum swing foreverbull Itrsquos hard to design a system free of energy pathsbull The pendulum slows down by several mechanisms

ndash Friction at the contact point requires force to opposeforce acts through distance rarr work is done

ndash Air resistance must push through air with a force(through a distance) rarr work is done

ndash Gets some air swirling puts kinetic energy into air (notreally fair to separate these last two)

bull Perpetual motion means no loss of energyndash solar system orbits come very close

Some Energy Chains

bull A coffee mug with some gravitational potentialenergy is dropped

bull potential energy turns into kinetic energybull kinetic energy of the mug goes into

ndash ripping the mug apart (chemical breaking bonds)ndash sending the pieces flying (kinetic)ndash into soundndash into heating the floor and pieces through friction as the

pieces slide to a stopbull In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored inthe potential energy)

34

Gasoline Examplebull Put gas in your car containing 9 Calgbull Combust gas turning 9 Calg into kinetic energy of

explosionbull Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a wholebull That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water andsurrounding air) and friction of transmission system(heat) and noise of engine (heating the air) etc

bull Much of energy goes into stirring the air (ends up as heat)bull Apply the brakes and convert kinetic energy into heatbull It all ends up as waste heat ultimately

Bouncing Ballbull Superball has gravitational potential energybull Drop the ball and this becomes kinetic energybull Ball hits ground and compresses (force times

distance) storing energy in the springbull Ball releases this mechanically stored energy

and it goes back into kinetic form (bouncesup)

bull Inefficiencies in ldquospringrdquo end up heating theball and the floor and stirring the air a bit

bull In the end all is heat

35

Why donrsquot we get hotter andhotter

bull If all these processes end up as heat why arenrsquotwe continually getting hotter

bull If earth retained all its heat we would get hotterbull All of earthrsquos heat is radiated away

F = σT4

bull If we dump more power the temperature goes upthe radiated power increases dramaticallyndash comes to equilibrium power dumped = power radiatedndash stable against perturbation T tracks power budget

Rough numbers

bull How much power does the earth radiatebull F = σT4 for T = 288ordmK = 15ordmC is 390 Wm2

bull Summed over entire surface area (4πR2 where R= 6378000 meters) is 20times1017 W

bull Global production is 3times1012 Wbull Solar radiation incident on earth is 18times1017 W

ndash just solar luminosity of 39times1026 W divided bygeometrical fraction that points at earth

bull Amazing coincidence of numbers (or is ithellip)

36

No Energy for Free

bull No matter what you canrsquot create energy out ofnothing it has to come from somewhere

bull We can transform energy from one form toanother we can store energy we can utilizeenergy being conveyed from natural sources

bull The net energy of the entire Universe is constantbull The best we can do is scrape up some useful

crumbs

Examplesbull Unit conversion

ndash 100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Calndash 100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 Jndash 100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWhndash 10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWhndash How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86Calorieshour About what average person eats

ndash Gasoline is $3gal Electricity if $015kWh Which is moreexpensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh)= $008kWh for gasoline Gasoline is cheap in the USA

37

Examplesbull Power vs Energy (P=Etime E = P t t = EP)

ndash Car goes 60 miles in one hour and uses 3 gal of gas What wastotal power in Watts P=Et Power = (3 gal1 hour) = 3galhr(366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W[Alternative method 3 galhr (132000000 J1 gal) (1 hr3600sec) = 110000 Jsec = 110000 W

ndash 1000 W space heater is on for 3 hours How much does it cost ifelectricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr(1kW1000W) = 3kWh ($15kWh) = $45 [Alternative methodE = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000J (1 kWh3600000J) = 3 kWh Again 45 cents

ndash AAA Battery contains 33 Calories of chemical energy How longcan it run a 2 Watt light bulb time = EP time = 33 Calories2W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1hr3600 sec) = 19 hours

QuestionThe US uses about 7 Gbarrels of oil each year This couldbe converted into which of the following units

A Joules B Watts C QBtus D Dollars $ E Any of the above

38

QuestionIf one barrel of oil contains 1700 kWh of energy how manyWatts is 7 Gbarrelyear

A 1400 GW (Giga Watts)

B 14 GW

C 11900 W

D 119 MW

E 1 x 1011 W

QuestionIf the total yearly oil use in the US is about 1400 GW howmany 1000 MW nuclear reactors will need to be built toreplace all oil use with electricity

A Only one will be needed

B Around 14

C Around 140

D Around 1400

E Cant convert Watts to reactors power vs energy

39

More Power Examplesbull How much power does it take to lift 10 kg up 2 meters in 2

secondsmgh = (10 kg)times(10 ms2)times(2 m) = 200J

200 J in 2 seconds rarr 100 Wattsbull If you want to heat the 3 m cubic room by 10ordmC with a

1000 W space heater how long will it takeWe know from before that the room needs to have 360000 J addedto it so at 1000 W = 1000 Js this will take 360 seconds or sixminutes

But the walls need to be warmed up too so it will actually takelonger (and depends on quality of insulation etc)

A note on arithmetic of unitsbull You should carry units in your calculations and multiply and divide them

as if they were numbersbull Example the force of air drag is given bybull Fdrag = frac12cDrAv2

bull cD is a dimensionless drag coefficientbull r is the density of air 13 kgm3

bull A is the cross-sectional area of the body in m2

bull v is the velocity in msbull units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) =

kgmiddotmiddotmm22middotmiddotmm22

m3middotmiddotss22kgmiddotmiddotmm44

m3middotmiddotss22= = kgmiddotmiddotmsms22 = = NewtonsNewtons

13

QuestionA 150 lb person jumps (or was he pushed) off a cliff and isfalling to their death What is the total force on the person

A zeroB 150 lbC Canrsquot say from this info

But what is acceleration

bull This is getting to be like the ldquohole in thebucketrdquo song but wersquore almost therehellip

bull Acceleration is any change in velocity(speed andor direction of motion)

bull Measured as rate of change of velocityndash velocity is expressed in meters per second (ms)ndash acceleration is meters per second per secondndash expressed as ms2 (meters per second-squared)

14

Putting it back together Units ofEnergy

bull Force is a mass times an accelerationndash mass has units of kilogramsndash acceleration is ms2

ndash force is then kgms2 which we call Newtons (N)

bull Work is a force times a distancendash units are then (kgms2)m = kg m2s2 = Nm = Joules (J)ndash One joule is one Newton of force acting through one meterndash Imperial units of force and distance are pounds and feet so unit of

energy is foot-pound which equals 136 J

bull Energy has the same units as work Joules

A Zoo of Unitsbull The main metric unit of energy is the Joule and most of

the world uses this but many others existbull The calorie is 4184 Joules

ndash raise 1 gram (cc) of water one degree Celsiusbull The Calorie (kilocalorie) is 4184 J (used for food energy)

ndash raise 1 kg (1 liter) of water one degree Celsiusbull The Btu (British thermal unit) is 1055 J (roughly 1 kJ) or

about 14 Calorie or chemical energy of one matchndash raise 1 pound of water one degree Fahrenheit

bull The kilowatt-hour (kWh) is 3600000 J = 3600 kJ or 860Calories (used for electrical energy)ndash one Watt (W) is one Joule per secondndash a kWh is 1000 W for one hour (3600 seconds)

bull Can also use ldquobarrel of oilrdquo ldquoton of coalrdquo 1000 cubic feetof natural gas gram of Uranium or amount of any energycontaining source etc

15

The Physics of Energy Formula List

bull Lots of forms of energy coming fast and furious but to putit in perspective herersquos a list of formulas

P = ΔEΔtPower (rate of energy use)

F = σT4 (temperature to the fourthpower times a constant)

Radiative energy flux

E = mc2 (mass times speed of lightsquared)

Mass energy

ΔE = cpmΔT (mass times change intemperature times heat capacity)

Heat Energy

E = mgh (mass times height times10ms2)

(Grav) Potential Energy

KE = frac12mv2 (mass times velocitysquared)

Kinetic Energy

W = Fd (Force times distance)Work

Energy FormulaEnergy Form

Kinetic Energybull Kinetic Energy the energy of motionbull Moving things carry energy in the amount

KE = frac12mv2

bull Note the v2 dependencemdashthis is whyndash a car at 60 mph is 4 times more dangerous than a car at 30 mphndash hurricane-force winds at 100 mph are much more destructive (4

times) than 50 mph gale-force windsndash a bullet shot from a gun is at least 100 times as destructive as a

thrown bullet even if you can throw it a tenth as fast as you couldshoot it

16

Numerical examples of kineticenergy

bull A baseball (mass is 0145 kg = 145 g) moving at 30 ms(67 mph) has kinetic energy

KE = frac12times(0145 kg)times(30 ms)2

= 6525 kgm2s2 asymp 65 J

bull A quarter (mass = 000567 kg = 567 g) flipped about fourfeet into the air has a speed on reaching your hand of about5 ms The kinetic energy is

KE = frac12times(000567 kg)times(5 ms)2

= 007 kgm2s2 = 007 J

More numerical examples

bull A 1500 kg car moves down the freeway at30 ms (67 mph)

KE = frac12times(1500 kg)times(30 ms)2

= 675000 kgm2s2 = 675 kJConvert to Calories 4184 kJ = 1 Calorie675 kJ (1 Calorie4184 kJ) = 161 Calorie

bull A 2 kg (~44 lb) fish jumps out of the waterwith a speed of 1 ms (22 mph)

KE = frac12times(2 kg)times(1 ms)2

= 1 kgm2s2 = 1 J

17

QuestionKinetic energy is E = 12 m v2 Which has more energy

A 10 kg object going 100 ms

B 100 kg object going 10 ms

C 1 kg object going 1000 ms

D 1000 kg object going 1 ms

1 ms = 22 mph

Gravitational Potential Energybull It takes work to lift a mass against the pull (force) of

gravitybull The force of gravity is mg where m is the mass and g is

the gravitational accelerationF = mg (note similarity to F = ma)

ndash g = 98 ms2 on the surface of the earth or 32 fts2

bull Lifting a height h against the gravitational forcerequires an energy input (work) of

ΔE = W = F h = mghbull Rolling a boulder up a hill and perching it on the edge of a

cliff gives it gravitational potential energy that can be laterreleased when the roadrunner is down below

bull Water in river or hydroelectric plant is using potentialenergy that it got from being lifted up when Sun (solarenergy) evaporated the water

18

QuestionPotential energy is E = 10 m h (metric units) Which hasmore energy

A 1 ton of water at a height of 100 ft

B 100 tons of water at a height of 1 ft

C 200 lb (110 ton) of water at 1000 ft

D All of the above have same energy

1 ms = 22 mph

First Example of Energy Exchangebull When the boulder falls off the cliff it picks up

speed and therefore gains kinetic energybull Where does this energy come from

rArr from the gravitational potential energybull The higher the cliff the more kinetic energy the

boulder will have when it reaches the ground

mgh

becomes

frac12mv2

Energy is conserved sofrac12mv2 = mgh

Can even figure out v since v2 = 2gh

h

19

Examples of GravitationalPotential Energy

bull How much gravitational potential energy does a70 kg high-diver have on the 10 meter platform

mgh = (70 kg)times(10 ms2)times(10 m)= 7000 kgm2s2 = 7 kJ

7 kJ (1 Calorie4182kJ) = 16 CaloriesThis is amount of energy the diver used in climbing the

stairs (actually more than this since some energy waswasted) They got that energy from the food they ate

The Energy of Heatbull Hot things have more energy than their cold

counterpartsbull Heat is really just kinetic energy on microscopic

scales the vibration or otherwise fast motion ofindividual atomsmoleculesndash Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are randombull Heat is frequently quantified by calories (or Btu)

ndash One calorie (4184 J) raises one gram of H2O 1ordmCndash One Calorie (4184 J) raises one kilogram of H2O 1ordmCndash One Btu (1055 J) raises one pound of H2O 1ordmF

20

Energy of Heat continuedbull Food Calories are with the ldquobigrdquo C or kilocalories (kcal)bull Since water has a density of one gram per cubic centimeter 1

cal heats 1 cc of water 1ordmC and likewise 1 kcal (Calorie) heatsone liter of water 1ordmC In British Units 1 Btu heats 1 pound ofwater 1 degree Fahrenheitndash these are useful numbers to hang onto

bull Example to heat a 2-liter bottle of Coke from the 5ordmCrefrigerator temperature to 20ordmC room temperature requires 30Calories or 1225 kJ

bull Drink a pint (16 oz) of ice cold water (or coke) It weighs about1 pound To heat it to body temperature (986 degrees minus 32degrees or change of 666 degrees Takes about 67 BtuConvert to Calories 1 Calorie = 1kJ = 4 Btu so

67 Btu (1 Calorie 4 Btu) = 1675 Calories Since 16 oz ofcoke has 210 Calories and about 17 Calories are used justheating to your body temp you get less calories drinking it cold(or drinking quart of cold water ldquoburnsrdquo 17 Calories)

The Physics of Energy Formula List

P = ΔEΔtPower (rate of energy use)

F = σT4 (temperature to the fourthpower times a constant)

Radiative energy flux

E = mc2 (mass times speed oflight squared)

Mass energy

ΔE = cpmΔT (mass times changein temperature times heatcapacity)

Heat Energy

E = mgh (mass times height times10ms2)

(Grav) Potential Energy

KE = frac12mv2 (mass times velocitysquared)

Kinetic Energy

W = Fd (Force times distance)Work

Energy FormulaEnergy Form

21

Heat Capacitybull Different materials have different capacities to

hold heatndash Add the same energy to different materials and yoursquoll

get different temperature risesndash Quantified as heat capacityndash Water is exceptional with 4184 JkgordmCndash Most materials are about 1000 JkgordmC (including

wood air metals)bull Example to add 10ordmC to a room 3 meters on a side

(cubic) how much energy do we needair density is 13 kgm3 and we have 27 m3 so 35 kg ofair and we need 1000 J per kg per ordmC so we end upneeding 350000 J (= 836 Cal)

Important in designing solar heated houses Also reasonit is cooler near the coast than inland

Powerbull Power is simply energy exchanged

per unit time or how fast you getwork done (Watts = Joulessec)

bull One horsepower = 745 Wbull Perform 100 J of work in 1 s and

call it 100 Wbull Run upstairs raising your 70 kg

(700 N) mass 3 m (2100 J) in 3seconds rarr 700 W output

bull Shuttle puts out a few GW(gigawatts or 109 W) of power

bull A big electrical power plant putsout around a GW That is 1 BillionJoules per second House takes afew kW (kilowatt)

22

QuestionPower is Energy used per second P= energytime Whichhighest power

A Using 100 Calories in 10 minutes

B Using 1000 Calories in 100 minutes

C Using 10 Calories in 1 minute

D Using 1 Calorie in 6 seconds

E All of the above are the same power usage

1 Calorieminute = Watts

Wind Energy

bull Wind can be used as a source of energy (windmills sailingships etc)

bull Really just kinetic energybull Example wind passing through a square meter at 8 meters

per secondndash Each second we have 8 cubic metersndash Air has density of 13 kgm3 so (8 m3)times(13 kgm3) = 104 kg of

air each secondndash frac12mv2 = frac12times(104 kg)times(8 ms)2 = 333 Jndash 333 J every second rarr 333 Watts of available power per square

meter (but to get all of it yoursquod have to stop the wind)bull Stronger winds rarr more power (like v2)

23

Chemical Energy

bull Electrostatic energy (associated with chargedparticles like electrons) is stored in the chemicalbonds of substances

bull Rearranging these bonds can release energy (somereactions require energy to be put in)

bull Typical numbers are 100ndash200 kJ per molendash a mole is 6022times1023 moleculesparticlesndash typical molecules are tens of grams per molerarrworks

out to typical numbers like several thousand Joules pergram or a few Calories per gram (remember 1 Cal = 1kcal = 4187 J)

Chemical Energy Examples

bull Burning a wooden match releases about oneBtu or 1055 Joules (a match is about 03grams) so this is gt3000 Jg nearly 1 Calg

bull Burning coal releases about 20 kJ per gramof chemical energy or roughly 5 Calg

bull Burning gasoline yields about 39 kJ pergram or just over 9 Calg

bull Very few substances over about 11 Calg

24

Energy from Food

bull We get the energy to do the things we do out of food(stored solar energy in the form of chemical energy)

bull Energy sources recognized by our digestive systemsndash Carbohydrates 4 Calories per gramndash Proteins 4 Calories per gramndash Fats 9 Calories per gram (like gasoline) (9 is more than

4 so gain more weight eating same amount of fat thancarbs or protein)

ndash Roughly 3500 Caloriespound in your body fat Less inyour protein (muscle skin etc)

Our Human Energy Budget

bull A 2000 Calorie per daydiet means 2000times4184 J =8368000 J per day

bull 837 MJ in (24 hrday) times(60 minhr)times(60 secmin)= 86400 sec correspondsto 97 Watts of power

bull Even a couch-potato at1500 Calday burns 75 W

bull More active lifestylesrequire greater Caloricintake (more energy)

25

Nutrition Labelsbull Nutrition labels tell you about the

energy content of foodbull Note they use Calories with capitol Cbull Conversions Fat 9 Calg

Carbs 4 CalgProtein 4 Calg

bull This product has 72 Cal from fat 48Cal from carbohydrates and 32 Calfrom proteinndash sum is 152 Calories compare to label

bull 152 Cal = 636 kJ enough to climbabout 1000 meters (64 kg person)

bull 1kwh = 860 Cal or about 14 lb bodyfat

bull 1 gal of gas has 31000 Calories

Mass-energy

bull Einsteinrsquos famous relationE = mc2

relates mass to energybull In effect they are the same thing

ndash one can be transformed into the otherndash physicists speak generally of mass-energy

bull Seldom experienced in daily life directlyndash Happens at large scale in the center of the sun and in

nuclear bombs and reactorsndash Actually does happen at barely detectable level in all

energy transactions but the effect is tiny

26

E = mc2 Examples

bull The energy equivalent of one gram of material(any composition) is (0001 kg)times(30times108 ms)2

= 90times1013 J = 90000000000000 J = 90 TJndash Man thatrsquos bigndash Our global energy budget is equivalent to 1000 kgyr

(thatrsquos about 1 ton per year)bull If one gram of material undergoes a chemical

reaction losing about 9000 J of energy howmuch mass does it lose

9000 J = Δmc2 so Δm = 9000c2 = 9times1039times1016

= 10-13 kg (would we ever notice)

Solar Energy is Nuclear Using E= mc2

bull Thermonuclear fusion reactions in the sunrsquos centerndash Sun is 16 million degrees Celsius in its centerndash Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then heliumndash Reaction per atom 20 million times more energetic than chemical

reactions in general

4 protonsmass = 4029

4He nucleusmass = 40015

2 neutrinos photons (light)

27

E = mc2 in Sun

bull Helium nucleus is lighter than the four protonsbull Mass difference is 4029 - 40015 = 00276 amu

ndash 1 amu (atomic mass unit) is 16605times10-27 kgndash difference of 458times10-29 kgndash multiply by c2 to get 412times10-12 Jndash 1 mole (6022times1023 particles) of protons rarr 25times1012 Jndash typical chemical reactions are 100-200 kJmolendash nuclear fusion is ~20 million times more potent stuffndash Nuclear fusion is energy source of hydrogen bomb

Energy from Lightbull The tremendous energy from the sun is released as light So light

carries energybull Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiationbull Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequencybull Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellipbull All objects emit ldquolightrdquobull The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter moreradiation and color is ldquobluerrdquo

28

Emitted Radiationrsquos Color andIntensity depend on Temperature

Object

YouHeat LampCandle FlameBulb FilamentSunrsquos SurfaceNeutron StarMolecules in deep space

Temperature

~ 30 C~ 500 C~ 1700 C~ 2700 C~ 5500 C~ millions C

lt -272C

Color

Infrared (invisible)Dull redDim orangeYellowBrilliant whiteX-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted lightThe hotter it gets the more intense the radiation (more energy)

ldquoBlackbodyrdquo or Planck Spectrum

29

Same thing on logarithmic scale

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm(note 0degC = 273degK 300degK = 27degC = 81degF)

Okay but how much energybull The power given off of a surface in the form of light is

proportional to the fourth power of temperatureF = σT4 in Watts per square meter

ndash the constant σ is numerically 567times10-8 WordmK4m2

ndash easy to remember constant 5678ndash temperature must be in Kelvin

bull ordmK = ordmC + 273bull ordmC = (59)times(ordmF ndash32)

bull Example radiation from your body(567 times10-8) times(310)4 = 523 Watts per square meter(if naked in the cold of space donrsquot let this happen to you)

30

Radiant Energy continued

bull Example The sun is 5800ordmK on its surface soF = σT4 = (567times10-8)times(5800)4 = 64times107 Wm2

Summing over entire surface area of sun gives39times1026 W

bull Compare to total capacity of energy production onearth 33times1012 Wndash Single power plant typically 05ndash10 GW (109 W)

bull In earthly situations radiated power out partiallybalanced by radiated power in from other sourcesndash Not 523 Wm2 in 70ordmF room more like 100 Wm2

bull goes like σTh4 ndash σTc

4

Electrical Energybull Opposite charges attract so electrons are attracted to

protons This holds atoms togetherbull It takes energy to pull electrons off their atomsbull Electrons want to get back home to their protons They can

only travel through conductors like wires not throughinsulators like plastic paper or wood They will gothrough miles of wire to get home to their protons

bull This is how electricity works The electronrsquos energy canbe stolen as it goes home Can be used in many manyways

bull Note electricity is not a primary source of energy Energy(from burning coal nat gas from hydro wind nuke orsolar) is used to pull of electrons and that energy can bemoved through wires and got back at will

31

And those are the majorplayershellip

bull Wersquove now seen most of the major energyplayersndash work as force times distancendash kinetic energy (wind ocean currents)ndash gravitational potential energy (hydroelectric tidal)ndash chemical energy (fossil fuels batteries food biomass)ndash heat energy (power plants space heating)ndash mass-energy (nuclear sources sunrsquos energy)ndash radiant energy (solar energy)ndash electrical energy (energy of electrons separated from

their atoms)

Conservation and Exchange ofEnergy

Nothing Comes for Free

32

Energy is Conservedbull Conservation of Energy is different from Energy

Conservation the latter being about using energywisely

bull Conservation of Energy means energy is neithercreated nor destroyed The amount of energy inthe Universe is constant

bull Donrsquot we create energy at a power plantndash Oh that this were truemdashno we simply transform

energy at our power plantsbull Doesnrsquot the sun create energy

ndash Nopemdashit exchanges mass for energybull Donrsquot batteries give us new energy

ndash Nope just convert stored chemical energy to electricalenergy Someone had to put that energy in there

height referenceh

Energy Exchangebull Though the total energy of a system is constant

the form of the energy can changebull A simple example is that of a simple pendulum in

which a continual exchange goes on betweenkinetic and potential energy

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

33

Perpetual Motion

bull Why wonrsquot the pendulum swing foreverbull Itrsquos hard to design a system free of energy pathsbull The pendulum slows down by several mechanisms

ndash Friction at the contact point requires force to opposeforce acts through distance rarr work is done

ndash Air resistance must push through air with a force(through a distance) rarr work is done

ndash Gets some air swirling puts kinetic energy into air (notreally fair to separate these last two)

bull Perpetual motion means no loss of energyndash solar system orbits come very close

Some Energy Chains

bull A coffee mug with some gravitational potentialenergy is dropped

bull potential energy turns into kinetic energybull kinetic energy of the mug goes into

ndash ripping the mug apart (chemical breaking bonds)ndash sending the pieces flying (kinetic)ndash into soundndash into heating the floor and pieces through friction as the

pieces slide to a stopbull In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored inthe potential energy)

34

Gasoline Examplebull Put gas in your car containing 9 Calgbull Combust gas turning 9 Calg into kinetic energy of

explosionbull Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a wholebull That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water andsurrounding air) and friction of transmission system(heat) and noise of engine (heating the air) etc

bull Much of energy goes into stirring the air (ends up as heat)bull Apply the brakes and convert kinetic energy into heatbull It all ends up as waste heat ultimately

Bouncing Ballbull Superball has gravitational potential energybull Drop the ball and this becomes kinetic energybull Ball hits ground and compresses (force times

distance) storing energy in the springbull Ball releases this mechanically stored energy

and it goes back into kinetic form (bouncesup)

bull Inefficiencies in ldquospringrdquo end up heating theball and the floor and stirring the air a bit

bull In the end all is heat

35

Why donrsquot we get hotter andhotter

bull If all these processes end up as heat why arenrsquotwe continually getting hotter

bull If earth retained all its heat we would get hotterbull All of earthrsquos heat is radiated away

F = σT4

bull If we dump more power the temperature goes upthe radiated power increases dramaticallyndash comes to equilibrium power dumped = power radiatedndash stable against perturbation T tracks power budget

Rough numbers

bull How much power does the earth radiatebull F = σT4 for T = 288ordmK = 15ordmC is 390 Wm2

bull Summed over entire surface area (4πR2 where R= 6378000 meters) is 20times1017 W

bull Global production is 3times1012 Wbull Solar radiation incident on earth is 18times1017 W

ndash just solar luminosity of 39times1026 W divided bygeometrical fraction that points at earth

bull Amazing coincidence of numbers (or is ithellip)

36

No Energy for Free

bull No matter what you canrsquot create energy out ofnothing it has to come from somewhere

bull We can transform energy from one form toanother we can store energy we can utilizeenergy being conveyed from natural sources

bull The net energy of the entire Universe is constantbull The best we can do is scrape up some useful

crumbs

Examplesbull Unit conversion

ndash 100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Calndash 100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 Jndash 100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWhndash 10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWhndash How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86Calorieshour About what average person eats

ndash Gasoline is $3gal Electricity if $015kWh Which is moreexpensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh)= $008kWh for gasoline Gasoline is cheap in the USA

37

Examplesbull Power vs Energy (P=Etime E = P t t = EP)

ndash Car goes 60 miles in one hour and uses 3 gal of gas What wastotal power in Watts P=Et Power = (3 gal1 hour) = 3galhr(366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W[Alternative method 3 galhr (132000000 J1 gal) (1 hr3600sec) = 110000 Jsec = 110000 W

ndash 1000 W space heater is on for 3 hours How much does it cost ifelectricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr(1kW1000W) = 3kWh ($15kWh) = $45 [Alternative methodE = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000J (1 kWh3600000J) = 3 kWh Again 45 cents

ndash AAA Battery contains 33 Calories of chemical energy How longcan it run a 2 Watt light bulb time = EP time = 33 Calories2W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1hr3600 sec) = 19 hours

QuestionThe US uses about 7 Gbarrels of oil each year This couldbe converted into which of the following units

A Joules B Watts C QBtus D Dollars $ E Any of the above

38

QuestionIf one barrel of oil contains 1700 kWh of energy how manyWatts is 7 Gbarrelyear

A 1400 GW (Giga Watts)

B 14 GW

C 11900 W

D 119 MW

E 1 x 1011 W

QuestionIf the total yearly oil use in the US is about 1400 GW howmany 1000 MW nuclear reactors will need to be built toreplace all oil use with electricity

A Only one will be needed

B Around 14

C Around 140

D Around 1400

E Cant convert Watts to reactors power vs energy

39

More Power Examplesbull How much power does it take to lift 10 kg up 2 meters in 2

secondsmgh = (10 kg)times(10 ms2)times(2 m) = 200J

200 J in 2 seconds rarr 100 Wattsbull If you want to heat the 3 m cubic room by 10ordmC with a

1000 W space heater how long will it takeWe know from before that the room needs to have 360000 J addedto it so at 1000 W = 1000 Js this will take 360 seconds or sixminutes

But the walls need to be warmed up too so it will actually takelonger (and depends on quality of insulation etc)

A note on arithmetic of unitsbull You should carry units in your calculations and multiply and divide them

as if they were numbersbull Example the force of air drag is given bybull Fdrag = frac12cDrAv2

bull cD is a dimensionless drag coefficientbull r is the density of air 13 kgm3

bull A is the cross-sectional area of the body in m2

bull v is the velocity in msbull units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) =

kgmiddotmiddotmm22middotmiddotmm22

m3middotmiddotss22kgmiddotmiddotmm44

m3middotmiddotss22= = kgmiddotmiddotmsms22 = = NewtonsNewtons

14

Putting it back together Units ofEnergy

bull Force is a mass times an accelerationndash mass has units of kilogramsndash acceleration is ms2

ndash force is then kgms2 which we call Newtons (N)

bull Work is a force times a distancendash units are then (kgms2)m = kg m2s2 = Nm = Joules (J)ndash One joule is one Newton of force acting through one meterndash Imperial units of force and distance are pounds and feet so unit of

energy is foot-pound which equals 136 J

bull Energy has the same units as work Joules

A Zoo of Unitsbull The main metric unit of energy is the Joule and most of

the world uses this but many others existbull The calorie is 4184 Joules

ndash raise 1 gram (cc) of water one degree Celsiusbull The Calorie (kilocalorie) is 4184 J (used for food energy)

ndash raise 1 kg (1 liter) of water one degree Celsiusbull The Btu (British thermal unit) is 1055 J (roughly 1 kJ) or

about 14 Calorie or chemical energy of one matchndash raise 1 pound of water one degree Fahrenheit

bull The kilowatt-hour (kWh) is 3600000 J = 3600 kJ or 860Calories (used for electrical energy)ndash one Watt (W) is one Joule per secondndash a kWh is 1000 W for one hour (3600 seconds)

bull Can also use ldquobarrel of oilrdquo ldquoton of coalrdquo 1000 cubic feetof natural gas gram of Uranium or amount of any energycontaining source etc

15

The Physics of Energy Formula List

bull Lots of forms of energy coming fast and furious but to putit in perspective herersquos a list of formulas

P = ΔEΔtPower (rate of energy use)

F = σT4 (temperature to the fourthpower times a constant)

Radiative energy flux

E = mc2 (mass times speed of lightsquared)

Mass energy

ΔE = cpmΔT (mass times change intemperature times heat capacity)

Heat Energy

E = mgh (mass times height times10ms2)

(Grav) Potential Energy

KE = frac12mv2 (mass times velocitysquared)

Kinetic Energy

W = Fd (Force times distance)Work

Energy FormulaEnergy Form

Kinetic Energybull Kinetic Energy the energy of motionbull Moving things carry energy in the amount

KE = frac12mv2

bull Note the v2 dependencemdashthis is whyndash a car at 60 mph is 4 times more dangerous than a car at 30 mphndash hurricane-force winds at 100 mph are much more destructive (4

times) than 50 mph gale-force windsndash a bullet shot from a gun is at least 100 times as destructive as a

thrown bullet even if you can throw it a tenth as fast as you couldshoot it

16

Numerical examples of kineticenergy

bull A baseball (mass is 0145 kg = 145 g) moving at 30 ms(67 mph) has kinetic energy

KE = frac12times(0145 kg)times(30 ms)2

= 6525 kgm2s2 asymp 65 J

bull A quarter (mass = 000567 kg = 567 g) flipped about fourfeet into the air has a speed on reaching your hand of about5 ms The kinetic energy is

KE = frac12times(000567 kg)times(5 ms)2

= 007 kgm2s2 = 007 J

More numerical examples

bull A 1500 kg car moves down the freeway at30 ms (67 mph)

KE = frac12times(1500 kg)times(30 ms)2

= 675000 kgm2s2 = 675 kJConvert to Calories 4184 kJ = 1 Calorie675 kJ (1 Calorie4184 kJ) = 161 Calorie

bull A 2 kg (~44 lb) fish jumps out of the waterwith a speed of 1 ms (22 mph)

KE = frac12times(2 kg)times(1 ms)2

= 1 kgm2s2 = 1 J

17

QuestionKinetic energy is E = 12 m v2 Which has more energy

A 10 kg object going 100 ms

B 100 kg object going 10 ms

C 1 kg object going 1000 ms

D 1000 kg object going 1 ms

1 ms = 22 mph

Gravitational Potential Energybull It takes work to lift a mass against the pull (force) of

gravitybull The force of gravity is mg where m is the mass and g is

the gravitational accelerationF = mg (note similarity to F = ma)

ndash g = 98 ms2 on the surface of the earth or 32 fts2

bull Lifting a height h against the gravitational forcerequires an energy input (work) of

ΔE = W = F h = mghbull Rolling a boulder up a hill and perching it on the edge of a

cliff gives it gravitational potential energy that can be laterreleased when the roadrunner is down below

bull Water in river or hydroelectric plant is using potentialenergy that it got from being lifted up when Sun (solarenergy) evaporated the water

18

QuestionPotential energy is E = 10 m h (metric units) Which hasmore energy

A 1 ton of water at a height of 100 ft

B 100 tons of water at a height of 1 ft

C 200 lb (110 ton) of water at 1000 ft

D All of the above have same energy

1 ms = 22 mph

First Example of Energy Exchangebull When the boulder falls off the cliff it picks up

speed and therefore gains kinetic energybull Where does this energy come from

rArr from the gravitational potential energybull The higher the cliff the more kinetic energy the

boulder will have when it reaches the ground

mgh

becomes

frac12mv2

Energy is conserved sofrac12mv2 = mgh

Can even figure out v since v2 = 2gh

h

19

Examples of GravitationalPotential Energy

bull How much gravitational potential energy does a70 kg high-diver have on the 10 meter platform

mgh = (70 kg)times(10 ms2)times(10 m)= 7000 kgm2s2 = 7 kJ

7 kJ (1 Calorie4182kJ) = 16 CaloriesThis is amount of energy the diver used in climbing the

stairs (actually more than this since some energy waswasted) They got that energy from the food they ate

The Energy of Heatbull Hot things have more energy than their cold

counterpartsbull Heat is really just kinetic energy on microscopic

scales the vibration or otherwise fast motion ofindividual atomsmoleculesndash Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are randombull Heat is frequently quantified by calories (or Btu)

ndash One calorie (4184 J) raises one gram of H2O 1ordmCndash One Calorie (4184 J) raises one kilogram of H2O 1ordmCndash One Btu (1055 J) raises one pound of H2O 1ordmF

20

Energy of Heat continuedbull Food Calories are with the ldquobigrdquo C or kilocalories (kcal)bull Since water has a density of one gram per cubic centimeter 1

cal heats 1 cc of water 1ordmC and likewise 1 kcal (Calorie) heatsone liter of water 1ordmC In British Units 1 Btu heats 1 pound ofwater 1 degree Fahrenheitndash these are useful numbers to hang onto

bull Example to heat a 2-liter bottle of Coke from the 5ordmCrefrigerator temperature to 20ordmC room temperature requires 30Calories or 1225 kJ

bull Drink a pint (16 oz) of ice cold water (or coke) It weighs about1 pound To heat it to body temperature (986 degrees minus 32degrees or change of 666 degrees Takes about 67 BtuConvert to Calories 1 Calorie = 1kJ = 4 Btu so

67 Btu (1 Calorie 4 Btu) = 1675 Calories Since 16 oz ofcoke has 210 Calories and about 17 Calories are used justheating to your body temp you get less calories drinking it cold(or drinking quart of cold water ldquoburnsrdquo 17 Calories)

The Physics of Energy Formula List

P = ΔEΔtPower (rate of energy use)

F = σT4 (temperature to the fourthpower times a constant)

Radiative energy flux

E = mc2 (mass times speed oflight squared)

Mass energy

ΔE = cpmΔT (mass times changein temperature times heatcapacity)

Heat Energy

E = mgh (mass times height times10ms2)

(Grav) Potential Energy

KE = frac12mv2 (mass times velocitysquared)

Kinetic Energy

W = Fd (Force times distance)Work

Energy FormulaEnergy Form

21

Heat Capacitybull Different materials have different capacities to

hold heatndash Add the same energy to different materials and yoursquoll

get different temperature risesndash Quantified as heat capacityndash Water is exceptional with 4184 JkgordmCndash Most materials are about 1000 JkgordmC (including

wood air metals)bull Example to add 10ordmC to a room 3 meters on a side

(cubic) how much energy do we needair density is 13 kgm3 and we have 27 m3 so 35 kg ofair and we need 1000 J per kg per ordmC so we end upneeding 350000 J (= 836 Cal)

Important in designing solar heated houses Also reasonit is cooler near the coast than inland

Powerbull Power is simply energy exchanged

per unit time or how fast you getwork done (Watts = Joulessec)

bull One horsepower = 745 Wbull Perform 100 J of work in 1 s and

call it 100 Wbull Run upstairs raising your 70 kg

(700 N) mass 3 m (2100 J) in 3seconds rarr 700 W output

bull Shuttle puts out a few GW(gigawatts or 109 W) of power

bull A big electrical power plant putsout around a GW That is 1 BillionJoules per second House takes afew kW (kilowatt)

22

QuestionPower is Energy used per second P= energytime Whichhighest power

A Using 100 Calories in 10 minutes

B Using 1000 Calories in 100 minutes

C Using 10 Calories in 1 minute

D Using 1 Calorie in 6 seconds

E All of the above are the same power usage

1 Calorieminute = Watts

Wind Energy

bull Wind can be used as a source of energy (windmills sailingships etc)

bull Really just kinetic energybull Example wind passing through a square meter at 8 meters

per secondndash Each second we have 8 cubic metersndash Air has density of 13 kgm3 so (8 m3)times(13 kgm3) = 104 kg of

air each secondndash frac12mv2 = frac12times(104 kg)times(8 ms)2 = 333 Jndash 333 J every second rarr 333 Watts of available power per square

meter (but to get all of it yoursquod have to stop the wind)bull Stronger winds rarr more power (like v2)

23

Chemical Energy

bull Electrostatic energy (associated with chargedparticles like electrons) is stored in the chemicalbonds of substances

bull Rearranging these bonds can release energy (somereactions require energy to be put in)

bull Typical numbers are 100ndash200 kJ per molendash a mole is 6022times1023 moleculesparticlesndash typical molecules are tens of grams per molerarrworks

out to typical numbers like several thousand Joules pergram or a few Calories per gram (remember 1 Cal = 1kcal = 4187 J)

Chemical Energy Examples

bull Burning a wooden match releases about oneBtu or 1055 Joules (a match is about 03grams) so this is gt3000 Jg nearly 1 Calg

bull Burning coal releases about 20 kJ per gramof chemical energy or roughly 5 Calg

bull Burning gasoline yields about 39 kJ pergram or just over 9 Calg

bull Very few substances over about 11 Calg

24

Energy from Food

bull We get the energy to do the things we do out of food(stored solar energy in the form of chemical energy)

bull Energy sources recognized by our digestive systemsndash Carbohydrates 4 Calories per gramndash Proteins 4 Calories per gramndash Fats 9 Calories per gram (like gasoline) (9 is more than

4 so gain more weight eating same amount of fat thancarbs or protein)

ndash Roughly 3500 Caloriespound in your body fat Less inyour protein (muscle skin etc)

Our Human Energy Budget

bull A 2000 Calorie per daydiet means 2000times4184 J =8368000 J per day

bull 837 MJ in (24 hrday) times(60 minhr)times(60 secmin)= 86400 sec correspondsto 97 Watts of power

bull Even a couch-potato at1500 Calday burns 75 W

bull More active lifestylesrequire greater Caloricintake (more energy)

25

Nutrition Labelsbull Nutrition labels tell you about the

energy content of foodbull Note they use Calories with capitol Cbull Conversions Fat 9 Calg

Carbs 4 CalgProtein 4 Calg

bull This product has 72 Cal from fat 48Cal from carbohydrates and 32 Calfrom proteinndash sum is 152 Calories compare to label

bull 152 Cal = 636 kJ enough to climbabout 1000 meters (64 kg person)

bull 1kwh = 860 Cal or about 14 lb bodyfat

bull 1 gal of gas has 31000 Calories

Mass-energy

bull Einsteinrsquos famous relationE = mc2

relates mass to energybull In effect they are the same thing

ndash one can be transformed into the otherndash physicists speak generally of mass-energy

bull Seldom experienced in daily life directlyndash Happens at large scale in the center of the sun and in

nuclear bombs and reactorsndash Actually does happen at barely detectable level in all

energy transactions but the effect is tiny

26

E = mc2 Examples

bull The energy equivalent of one gram of material(any composition) is (0001 kg)times(30times108 ms)2

= 90times1013 J = 90000000000000 J = 90 TJndash Man thatrsquos bigndash Our global energy budget is equivalent to 1000 kgyr

(thatrsquos about 1 ton per year)bull If one gram of material undergoes a chemical

reaction losing about 9000 J of energy howmuch mass does it lose

9000 J = Δmc2 so Δm = 9000c2 = 9times1039times1016

= 10-13 kg (would we ever notice)

Solar Energy is Nuclear Using E= mc2

bull Thermonuclear fusion reactions in the sunrsquos centerndash Sun is 16 million degrees Celsius in its centerndash Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then heliumndash Reaction per atom 20 million times more energetic than chemical

reactions in general

4 protonsmass = 4029

4He nucleusmass = 40015

2 neutrinos photons (light)

27

E = mc2 in Sun

bull Helium nucleus is lighter than the four protonsbull Mass difference is 4029 - 40015 = 00276 amu

ndash 1 amu (atomic mass unit) is 16605times10-27 kgndash difference of 458times10-29 kgndash multiply by c2 to get 412times10-12 Jndash 1 mole (6022times1023 particles) of protons rarr 25times1012 Jndash typical chemical reactions are 100-200 kJmolendash nuclear fusion is ~20 million times more potent stuffndash Nuclear fusion is energy source of hydrogen bomb

Energy from Lightbull The tremendous energy from the sun is released as light So light

carries energybull Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiationbull Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequencybull Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellipbull All objects emit ldquolightrdquobull The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter moreradiation and color is ldquobluerrdquo

28

Emitted Radiationrsquos Color andIntensity depend on Temperature

Object

YouHeat LampCandle FlameBulb FilamentSunrsquos SurfaceNeutron StarMolecules in deep space

Temperature

~ 30 C~ 500 C~ 1700 C~ 2700 C~ 5500 C~ millions C

lt -272C

Color

Infrared (invisible)Dull redDim orangeYellowBrilliant whiteX-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted lightThe hotter it gets the more intense the radiation (more energy)

ldquoBlackbodyrdquo or Planck Spectrum

29

Same thing on logarithmic scale

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm(note 0degC = 273degK 300degK = 27degC = 81degF)

Okay but how much energybull The power given off of a surface in the form of light is

proportional to the fourth power of temperatureF = σT4 in Watts per square meter

ndash the constant σ is numerically 567times10-8 WordmK4m2

ndash easy to remember constant 5678ndash temperature must be in Kelvin

bull ordmK = ordmC + 273bull ordmC = (59)times(ordmF ndash32)

bull Example radiation from your body(567 times10-8) times(310)4 = 523 Watts per square meter(if naked in the cold of space donrsquot let this happen to you)

30

Radiant Energy continued

bull Example The sun is 5800ordmK on its surface soF = σT4 = (567times10-8)times(5800)4 = 64times107 Wm2

Summing over entire surface area of sun gives39times1026 W

bull Compare to total capacity of energy production onearth 33times1012 Wndash Single power plant typically 05ndash10 GW (109 W)

bull In earthly situations radiated power out partiallybalanced by radiated power in from other sourcesndash Not 523 Wm2 in 70ordmF room more like 100 Wm2

bull goes like σTh4 ndash σTc

4

Electrical Energybull Opposite charges attract so electrons are attracted to

protons This holds atoms togetherbull It takes energy to pull electrons off their atomsbull Electrons want to get back home to their protons They can

only travel through conductors like wires not throughinsulators like plastic paper or wood They will gothrough miles of wire to get home to their protons

bull This is how electricity works The electronrsquos energy canbe stolen as it goes home Can be used in many manyways

bull Note electricity is not a primary source of energy Energy(from burning coal nat gas from hydro wind nuke orsolar) is used to pull of electrons and that energy can bemoved through wires and got back at will

31

And those are the majorplayershellip

bull Wersquove now seen most of the major energyplayersndash work as force times distancendash kinetic energy (wind ocean currents)ndash gravitational potential energy (hydroelectric tidal)ndash chemical energy (fossil fuels batteries food biomass)ndash heat energy (power plants space heating)ndash mass-energy (nuclear sources sunrsquos energy)ndash radiant energy (solar energy)ndash electrical energy (energy of electrons separated from

their atoms)

Conservation and Exchange ofEnergy

Nothing Comes for Free

32

Energy is Conservedbull Conservation of Energy is different from Energy

Conservation the latter being about using energywisely

bull Conservation of Energy means energy is neithercreated nor destroyed The amount of energy inthe Universe is constant

bull Donrsquot we create energy at a power plantndash Oh that this were truemdashno we simply transform

energy at our power plantsbull Doesnrsquot the sun create energy

ndash Nopemdashit exchanges mass for energybull Donrsquot batteries give us new energy

ndash Nope just convert stored chemical energy to electricalenergy Someone had to put that energy in there

height referenceh

Energy Exchangebull Though the total energy of a system is constant

the form of the energy can changebull A simple example is that of a simple pendulum in

which a continual exchange goes on betweenkinetic and potential energy

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

33

Perpetual Motion

bull Why wonrsquot the pendulum swing foreverbull Itrsquos hard to design a system free of energy pathsbull The pendulum slows down by several mechanisms

ndash Friction at the contact point requires force to opposeforce acts through distance rarr work is done

ndash Air resistance must push through air with a force(through a distance) rarr work is done

ndash Gets some air swirling puts kinetic energy into air (notreally fair to separate these last two)

bull Perpetual motion means no loss of energyndash solar system orbits come very close

Some Energy Chains

bull A coffee mug with some gravitational potentialenergy is dropped

bull potential energy turns into kinetic energybull kinetic energy of the mug goes into

ndash ripping the mug apart (chemical breaking bonds)ndash sending the pieces flying (kinetic)ndash into soundndash into heating the floor and pieces through friction as the

pieces slide to a stopbull In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored inthe potential energy)

34

Gasoline Examplebull Put gas in your car containing 9 Calgbull Combust gas turning 9 Calg into kinetic energy of

explosionbull Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a wholebull That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water andsurrounding air) and friction of transmission system(heat) and noise of engine (heating the air) etc

bull Much of energy goes into stirring the air (ends up as heat)bull Apply the brakes and convert kinetic energy into heatbull It all ends up as waste heat ultimately

Bouncing Ballbull Superball has gravitational potential energybull Drop the ball and this becomes kinetic energybull Ball hits ground and compresses (force times

distance) storing energy in the springbull Ball releases this mechanically stored energy

and it goes back into kinetic form (bouncesup)

bull Inefficiencies in ldquospringrdquo end up heating theball and the floor and stirring the air a bit

bull In the end all is heat

35

Why donrsquot we get hotter andhotter

bull If all these processes end up as heat why arenrsquotwe continually getting hotter

bull If earth retained all its heat we would get hotterbull All of earthrsquos heat is radiated away

F = σT4

bull If we dump more power the temperature goes upthe radiated power increases dramaticallyndash comes to equilibrium power dumped = power radiatedndash stable against perturbation T tracks power budget

Rough numbers

bull How much power does the earth radiatebull F = σT4 for T = 288ordmK = 15ordmC is 390 Wm2

bull Summed over entire surface area (4πR2 where R= 6378000 meters) is 20times1017 W

bull Global production is 3times1012 Wbull Solar radiation incident on earth is 18times1017 W

ndash just solar luminosity of 39times1026 W divided bygeometrical fraction that points at earth

bull Amazing coincidence of numbers (or is ithellip)

36

No Energy for Free

bull No matter what you canrsquot create energy out ofnothing it has to come from somewhere

bull We can transform energy from one form toanother we can store energy we can utilizeenergy being conveyed from natural sources

bull The net energy of the entire Universe is constantbull The best we can do is scrape up some useful

crumbs

Examplesbull Unit conversion

ndash 100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Calndash 100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 Jndash 100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWhndash 10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWhndash How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86Calorieshour About what average person eats

ndash Gasoline is $3gal Electricity if $015kWh Which is moreexpensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh)= $008kWh for gasoline Gasoline is cheap in the USA

37

Examplesbull Power vs Energy (P=Etime E = P t t = EP)

ndash Car goes 60 miles in one hour and uses 3 gal of gas What wastotal power in Watts P=Et Power = (3 gal1 hour) = 3galhr(366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W[Alternative method 3 galhr (132000000 J1 gal) (1 hr3600sec) = 110000 Jsec = 110000 W

ndash 1000 W space heater is on for 3 hours How much does it cost ifelectricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr(1kW1000W) = 3kWh ($15kWh) = $45 [Alternative methodE = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000J (1 kWh3600000J) = 3 kWh Again 45 cents

ndash AAA Battery contains 33 Calories of chemical energy How longcan it run a 2 Watt light bulb time = EP time = 33 Calories2W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1hr3600 sec) = 19 hours

QuestionThe US uses about 7 Gbarrels of oil each year This couldbe converted into which of the following units

A Joules B Watts C QBtus D Dollars $ E Any of the above

38

QuestionIf one barrel of oil contains 1700 kWh of energy how manyWatts is 7 Gbarrelyear

A 1400 GW (Giga Watts)

B 14 GW

C 11900 W

D 119 MW

E 1 x 1011 W

QuestionIf the total yearly oil use in the US is about 1400 GW howmany 1000 MW nuclear reactors will need to be built toreplace all oil use with electricity

A Only one will be needed

B Around 14

C Around 140

D Around 1400

E Cant convert Watts to reactors power vs energy

39

More Power Examplesbull How much power does it take to lift 10 kg up 2 meters in 2

secondsmgh = (10 kg)times(10 ms2)times(2 m) = 200J

200 J in 2 seconds rarr 100 Wattsbull If you want to heat the 3 m cubic room by 10ordmC with a

1000 W space heater how long will it takeWe know from before that the room needs to have 360000 J addedto it so at 1000 W = 1000 Js this will take 360 seconds or sixminutes

But the walls need to be warmed up too so it will actually takelonger (and depends on quality of insulation etc)

A note on arithmetic of unitsbull You should carry units in your calculations and multiply and divide them

as if they were numbersbull Example the force of air drag is given bybull Fdrag = frac12cDrAv2

bull cD is a dimensionless drag coefficientbull r is the density of air 13 kgm3

bull A is the cross-sectional area of the body in m2

bull v is the velocity in msbull units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) =

kgmiddotmiddotmm22middotmiddotmm22

m3middotmiddotss22kgmiddotmiddotmm44

m3middotmiddotss22= = kgmiddotmiddotmsms22 = = NewtonsNewtons

15

The Physics of Energy Formula List

bull Lots of forms of energy coming fast and furious but to putit in perspective herersquos a list of formulas

P = ΔEΔtPower (rate of energy use)

F = σT4 (temperature to the fourthpower times a constant)

Radiative energy flux

E = mc2 (mass times speed of lightsquared)

Mass energy

ΔE = cpmΔT (mass times change intemperature times heat capacity)

Heat Energy

E = mgh (mass times height times10ms2)

(Grav) Potential Energy

KE = frac12mv2 (mass times velocitysquared)

Kinetic Energy

W = Fd (Force times distance)Work

Energy FormulaEnergy Form

Kinetic Energybull Kinetic Energy the energy of motionbull Moving things carry energy in the amount

KE = frac12mv2

bull Note the v2 dependencemdashthis is whyndash a car at 60 mph is 4 times more dangerous than a car at 30 mphndash hurricane-force winds at 100 mph are much more destructive (4

times) than 50 mph gale-force windsndash a bullet shot from a gun is at least 100 times as destructive as a

thrown bullet even if you can throw it a tenth as fast as you couldshoot it

16

Numerical examples of kineticenergy

bull A baseball (mass is 0145 kg = 145 g) moving at 30 ms(67 mph) has kinetic energy

KE = frac12times(0145 kg)times(30 ms)2

= 6525 kgm2s2 asymp 65 J

bull A quarter (mass = 000567 kg = 567 g) flipped about fourfeet into the air has a speed on reaching your hand of about5 ms The kinetic energy is

KE = frac12times(000567 kg)times(5 ms)2

= 007 kgm2s2 = 007 J

More numerical examples

bull A 1500 kg car moves down the freeway at30 ms (67 mph)

KE = frac12times(1500 kg)times(30 ms)2

= 675000 kgm2s2 = 675 kJConvert to Calories 4184 kJ = 1 Calorie675 kJ (1 Calorie4184 kJ) = 161 Calorie

bull A 2 kg (~44 lb) fish jumps out of the waterwith a speed of 1 ms (22 mph)

KE = frac12times(2 kg)times(1 ms)2

= 1 kgm2s2 = 1 J

17

QuestionKinetic energy is E = 12 m v2 Which has more energy

A 10 kg object going 100 ms

B 100 kg object going 10 ms

C 1 kg object going 1000 ms

D 1000 kg object going 1 ms

1 ms = 22 mph

Gravitational Potential Energybull It takes work to lift a mass against the pull (force) of

gravitybull The force of gravity is mg where m is the mass and g is

the gravitational accelerationF = mg (note similarity to F = ma)

ndash g = 98 ms2 on the surface of the earth or 32 fts2

bull Lifting a height h against the gravitational forcerequires an energy input (work) of

ΔE = W = F h = mghbull Rolling a boulder up a hill and perching it on the edge of a

cliff gives it gravitational potential energy that can be laterreleased when the roadrunner is down below

bull Water in river or hydroelectric plant is using potentialenergy that it got from being lifted up when Sun (solarenergy) evaporated the water

18

QuestionPotential energy is E = 10 m h (metric units) Which hasmore energy

A 1 ton of water at a height of 100 ft

B 100 tons of water at a height of 1 ft

C 200 lb (110 ton) of water at 1000 ft

D All of the above have same energy

1 ms = 22 mph

First Example of Energy Exchangebull When the boulder falls off the cliff it picks up

speed and therefore gains kinetic energybull Where does this energy come from

rArr from the gravitational potential energybull The higher the cliff the more kinetic energy the

boulder will have when it reaches the ground

mgh

becomes

frac12mv2

Energy is conserved sofrac12mv2 = mgh

Can even figure out v since v2 = 2gh

h

19

Examples of GravitationalPotential Energy

bull How much gravitational potential energy does a70 kg high-diver have on the 10 meter platform

mgh = (70 kg)times(10 ms2)times(10 m)= 7000 kgm2s2 = 7 kJ

7 kJ (1 Calorie4182kJ) = 16 CaloriesThis is amount of energy the diver used in climbing the

stairs (actually more than this since some energy waswasted) They got that energy from the food they ate

The Energy of Heatbull Hot things have more energy than their cold

counterpartsbull Heat is really just kinetic energy on microscopic

scales the vibration or otherwise fast motion ofindividual atomsmoleculesndash Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are randombull Heat is frequently quantified by calories (or Btu)

ndash One calorie (4184 J) raises one gram of H2O 1ordmCndash One Calorie (4184 J) raises one kilogram of H2O 1ordmCndash One Btu (1055 J) raises one pound of H2O 1ordmF

20

Energy of Heat continuedbull Food Calories are with the ldquobigrdquo C or kilocalories (kcal)bull Since water has a density of one gram per cubic centimeter 1

cal heats 1 cc of water 1ordmC and likewise 1 kcal (Calorie) heatsone liter of water 1ordmC In British Units 1 Btu heats 1 pound ofwater 1 degree Fahrenheitndash these are useful numbers to hang onto

bull Example to heat a 2-liter bottle of Coke from the 5ordmCrefrigerator temperature to 20ordmC room temperature requires 30Calories or 1225 kJ

bull Drink a pint (16 oz) of ice cold water (or coke) It weighs about1 pound To heat it to body temperature (986 degrees minus 32degrees or change of 666 degrees Takes about 67 BtuConvert to Calories 1 Calorie = 1kJ = 4 Btu so

67 Btu (1 Calorie 4 Btu) = 1675 Calories Since 16 oz ofcoke has 210 Calories and about 17 Calories are used justheating to your body temp you get less calories drinking it cold(or drinking quart of cold water ldquoburnsrdquo 17 Calories)

The Physics of Energy Formula List

P = ΔEΔtPower (rate of energy use)

F = σT4 (temperature to the fourthpower times a constant)

Radiative energy flux

E = mc2 (mass times speed oflight squared)

Mass energy

ΔE = cpmΔT (mass times changein temperature times heatcapacity)

Heat Energy

E = mgh (mass times height times10ms2)

(Grav) Potential Energy

KE = frac12mv2 (mass times velocitysquared)

Kinetic Energy

W = Fd (Force times distance)Work

Energy FormulaEnergy Form

21

Heat Capacitybull Different materials have different capacities to

hold heatndash Add the same energy to different materials and yoursquoll

get different temperature risesndash Quantified as heat capacityndash Water is exceptional with 4184 JkgordmCndash Most materials are about 1000 JkgordmC (including

wood air metals)bull Example to add 10ordmC to a room 3 meters on a side

(cubic) how much energy do we needair density is 13 kgm3 and we have 27 m3 so 35 kg ofair and we need 1000 J per kg per ordmC so we end upneeding 350000 J (= 836 Cal)

Important in designing solar heated houses Also reasonit is cooler near the coast than inland

Powerbull Power is simply energy exchanged

per unit time or how fast you getwork done (Watts = Joulessec)

bull One horsepower = 745 Wbull Perform 100 J of work in 1 s and

call it 100 Wbull Run upstairs raising your 70 kg

(700 N) mass 3 m (2100 J) in 3seconds rarr 700 W output

bull Shuttle puts out a few GW(gigawatts or 109 W) of power

bull A big electrical power plant putsout around a GW That is 1 BillionJoules per second House takes afew kW (kilowatt)

22

QuestionPower is Energy used per second P= energytime Whichhighest power

A Using 100 Calories in 10 minutes

B Using 1000 Calories in 100 minutes

C Using 10 Calories in 1 minute

D Using 1 Calorie in 6 seconds

E All of the above are the same power usage

1 Calorieminute = Watts

Wind Energy

bull Wind can be used as a source of energy (windmills sailingships etc)

bull Really just kinetic energybull Example wind passing through a square meter at 8 meters

per secondndash Each second we have 8 cubic metersndash Air has density of 13 kgm3 so (8 m3)times(13 kgm3) = 104 kg of

air each secondndash frac12mv2 = frac12times(104 kg)times(8 ms)2 = 333 Jndash 333 J every second rarr 333 Watts of available power per square

meter (but to get all of it yoursquod have to stop the wind)bull Stronger winds rarr more power (like v2)

23

Chemical Energy

bull Electrostatic energy (associated with chargedparticles like electrons) is stored in the chemicalbonds of substances

bull Rearranging these bonds can release energy (somereactions require energy to be put in)

bull Typical numbers are 100ndash200 kJ per molendash a mole is 6022times1023 moleculesparticlesndash typical molecules are tens of grams per molerarrworks

out to typical numbers like several thousand Joules pergram or a few Calories per gram (remember 1 Cal = 1kcal = 4187 J)

Chemical Energy Examples

bull Burning a wooden match releases about oneBtu or 1055 Joules (a match is about 03grams) so this is gt3000 Jg nearly 1 Calg

bull Burning coal releases about 20 kJ per gramof chemical energy or roughly 5 Calg

bull Burning gasoline yields about 39 kJ pergram or just over 9 Calg

bull Very few substances over about 11 Calg

24

Energy from Food

bull We get the energy to do the things we do out of food(stored solar energy in the form of chemical energy)

bull Energy sources recognized by our digestive systemsndash Carbohydrates 4 Calories per gramndash Proteins 4 Calories per gramndash Fats 9 Calories per gram (like gasoline) (9 is more than

4 so gain more weight eating same amount of fat thancarbs or protein)

ndash Roughly 3500 Caloriespound in your body fat Less inyour protein (muscle skin etc)

Our Human Energy Budget

bull A 2000 Calorie per daydiet means 2000times4184 J =8368000 J per day

bull 837 MJ in (24 hrday) times(60 minhr)times(60 secmin)= 86400 sec correspondsto 97 Watts of power

bull Even a couch-potato at1500 Calday burns 75 W

bull More active lifestylesrequire greater Caloricintake (more energy)

25

Nutrition Labelsbull Nutrition labels tell you about the

energy content of foodbull Note they use Calories with capitol Cbull Conversions Fat 9 Calg

Carbs 4 CalgProtein 4 Calg

bull This product has 72 Cal from fat 48Cal from carbohydrates and 32 Calfrom proteinndash sum is 152 Calories compare to label

bull 152 Cal = 636 kJ enough to climbabout 1000 meters (64 kg person)

bull 1kwh = 860 Cal or about 14 lb bodyfat

bull 1 gal of gas has 31000 Calories

Mass-energy

bull Einsteinrsquos famous relationE = mc2

relates mass to energybull In effect they are the same thing

ndash one can be transformed into the otherndash physicists speak generally of mass-energy

bull Seldom experienced in daily life directlyndash Happens at large scale in the center of the sun and in

nuclear bombs and reactorsndash Actually does happen at barely detectable level in all

energy transactions but the effect is tiny

26

E = mc2 Examples

bull The energy equivalent of one gram of material(any composition) is (0001 kg)times(30times108 ms)2

= 90times1013 J = 90000000000000 J = 90 TJndash Man thatrsquos bigndash Our global energy budget is equivalent to 1000 kgyr

(thatrsquos about 1 ton per year)bull If one gram of material undergoes a chemical

reaction losing about 9000 J of energy howmuch mass does it lose

9000 J = Δmc2 so Δm = 9000c2 = 9times1039times1016

= 10-13 kg (would we ever notice)

Solar Energy is Nuclear Using E= mc2

bull Thermonuclear fusion reactions in the sunrsquos centerndash Sun is 16 million degrees Celsius in its centerndash Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then heliumndash Reaction per atom 20 million times more energetic than chemical

reactions in general

4 protonsmass = 4029

4He nucleusmass = 40015

2 neutrinos photons (light)

27

E = mc2 in Sun

bull Helium nucleus is lighter than the four protonsbull Mass difference is 4029 - 40015 = 00276 amu

ndash 1 amu (atomic mass unit) is 16605times10-27 kgndash difference of 458times10-29 kgndash multiply by c2 to get 412times10-12 Jndash 1 mole (6022times1023 particles) of protons rarr 25times1012 Jndash typical chemical reactions are 100-200 kJmolendash nuclear fusion is ~20 million times more potent stuffndash Nuclear fusion is energy source of hydrogen bomb

Energy from Lightbull The tremendous energy from the sun is released as light So light

carries energybull Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiationbull Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequencybull Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellipbull All objects emit ldquolightrdquobull The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter moreradiation and color is ldquobluerrdquo

28

Emitted Radiationrsquos Color andIntensity depend on Temperature

Object

YouHeat LampCandle FlameBulb FilamentSunrsquos SurfaceNeutron StarMolecules in deep space

Temperature

~ 30 C~ 500 C~ 1700 C~ 2700 C~ 5500 C~ millions C

lt -272C

Color

Infrared (invisible)Dull redDim orangeYellowBrilliant whiteX-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted lightThe hotter it gets the more intense the radiation (more energy)

ldquoBlackbodyrdquo or Planck Spectrum

29

Same thing on logarithmic scale

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm(note 0degC = 273degK 300degK = 27degC = 81degF)

Okay but how much energybull The power given off of a surface in the form of light is

proportional to the fourth power of temperatureF = σT4 in Watts per square meter

ndash the constant σ is numerically 567times10-8 WordmK4m2

ndash easy to remember constant 5678ndash temperature must be in Kelvin

bull ordmK = ordmC + 273bull ordmC = (59)times(ordmF ndash32)

bull Example radiation from your body(567 times10-8) times(310)4 = 523 Watts per square meter(if naked in the cold of space donrsquot let this happen to you)

30

Radiant Energy continued

bull Example The sun is 5800ordmK on its surface soF = σT4 = (567times10-8)times(5800)4 = 64times107 Wm2

Summing over entire surface area of sun gives39times1026 W

bull Compare to total capacity of energy production onearth 33times1012 Wndash Single power plant typically 05ndash10 GW (109 W)

bull In earthly situations radiated power out partiallybalanced by radiated power in from other sourcesndash Not 523 Wm2 in 70ordmF room more like 100 Wm2

bull goes like σTh4 ndash σTc

4

Electrical Energybull Opposite charges attract so electrons are attracted to

protons This holds atoms togetherbull It takes energy to pull electrons off their atomsbull Electrons want to get back home to their protons They can

only travel through conductors like wires not throughinsulators like plastic paper or wood They will gothrough miles of wire to get home to their protons

bull This is how electricity works The electronrsquos energy canbe stolen as it goes home Can be used in many manyways

bull Note electricity is not a primary source of energy Energy(from burning coal nat gas from hydro wind nuke orsolar) is used to pull of electrons and that energy can bemoved through wires and got back at will

31

And those are the majorplayershellip

bull Wersquove now seen most of the major energyplayersndash work as force times distancendash kinetic energy (wind ocean currents)ndash gravitational potential energy (hydroelectric tidal)ndash chemical energy (fossil fuels batteries food biomass)ndash heat energy (power plants space heating)ndash mass-energy (nuclear sources sunrsquos energy)ndash radiant energy (solar energy)ndash electrical energy (energy of electrons separated from

their atoms)

Conservation and Exchange ofEnergy

Nothing Comes for Free

32

Energy is Conservedbull Conservation of Energy is different from Energy

Conservation the latter being about using energywisely

bull Conservation of Energy means energy is neithercreated nor destroyed The amount of energy inthe Universe is constant

bull Donrsquot we create energy at a power plantndash Oh that this were truemdashno we simply transform

energy at our power plantsbull Doesnrsquot the sun create energy

ndash Nopemdashit exchanges mass for energybull Donrsquot batteries give us new energy

ndash Nope just convert stored chemical energy to electricalenergy Someone had to put that energy in there

height referenceh

Energy Exchangebull Though the total energy of a system is constant

the form of the energy can changebull A simple example is that of a simple pendulum in

which a continual exchange goes on betweenkinetic and potential energy

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

33

Perpetual Motion

bull Why wonrsquot the pendulum swing foreverbull Itrsquos hard to design a system free of energy pathsbull The pendulum slows down by several mechanisms

ndash Friction at the contact point requires force to opposeforce acts through distance rarr work is done

ndash Air resistance must push through air with a force(through a distance) rarr work is done

ndash Gets some air swirling puts kinetic energy into air (notreally fair to separate these last two)

bull Perpetual motion means no loss of energyndash solar system orbits come very close

Some Energy Chains

bull A coffee mug with some gravitational potentialenergy is dropped

bull potential energy turns into kinetic energybull kinetic energy of the mug goes into

ndash ripping the mug apart (chemical breaking bonds)ndash sending the pieces flying (kinetic)ndash into soundndash into heating the floor and pieces through friction as the

pieces slide to a stopbull In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored inthe potential energy)

34

Gasoline Examplebull Put gas in your car containing 9 Calgbull Combust gas turning 9 Calg into kinetic energy of

explosionbull Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a wholebull That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water andsurrounding air) and friction of transmission system(heat) and noise of engine (heating the air) etc

bull Much of energy goes into stirring the air (ends up as heat)bull Apply the brakes and convert kinetic energy into heatbull It all ends up as waste heat ultimately

Bouncing Ballbull Superball has gravitational potential energybull Drop the ball and this becomes kinetic energybull Ball hits ground and compresses (force times

distance) storing energy in the springbull Ball releases this mechanically stored energy

and it goes back into kinetic form (bouncesup)

bull Inefficiencies in ldquospringrdquo end up heating theball and the floor and stirring the air a bit

bull In the end all is heat

35

Why donrsquot we get hotter andhotter

bull If all these processes end up as heat why arenrsquotwe continually getting hotter

bull If earth retained all its heat we would get hotterbull All of earthrsquos heat is radiated away

F = σT4

bull If we dump more power the temperature goes upthe radiated power increases dramaticallyndash comes to equilibrium power dumped = power radiatedndash stable against perturbation T tracks power budget

Rough numbers

bull How much power does the earth radiatebull F = σT4 for T = 288ordmK = 15ordmC is 390 Wm2

bull Summed over entire surface area (4πR2 where R= 6378000 meters) is 20times1017 W

bull Global production is 3times1012 Wbull Solar radiation incident on earth is 18times1017 W

ndash just solar luminosity of 39times1026 W divided bygeometrical fraction that points at earth

bull Amazing coincidence of numbers (or is ithellip)

36

No Energy for Free

bull No matter what you canrsquot create energy out ofnothing it has to come from somewhere

bull We can transform energy from one form toanother we can store energy we can utilizeenergy being conveyed from natural sources

bull The net energy of the entire Universe is constantbull The best we can do is scrape up some useful

crumbs

Examplesbull Unit conversion

ndash 100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Calndash 100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 Jndash 100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWhndash 10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWhndash How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86Calorieshour About what average person eats

ndash Gasoline is $3gal Electricity if $015kWh Which is moreexpensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh)= $008kWh for gasoline Gasoline is cheap in the USA

37

Examplesbull Power vs Energy (P=Etime E = P t t = EP)

ndash Car goes 60 miles in one hour and uses 3 gal of gas What wastotal power in Watts P=Et Power = (3 gal1 hour) = 3galhr(366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W[Alternative method 3 galhr (132000000 J1 gal) (1 hr3600sec) = 110000 Jsec = 110000 W

ndash 1000 W space heater is on for 3 hours How much does it cost ifelectricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr(1kW1000W) = 3kWh ($15kWh) = $45 [Alternative methodE = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000J (1 kWh3600000J) = 3 kWh Again 45 cents

ndash AAA Battery contains 33 Calories of chemical energy How longcan it run a 2 Watt light bulb time = EP time = 33 Calories2W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1hr3600 sec) = 19 hours

QuestionThe US uses about 7 Gbarrels of oil each year This couldbe converted into which of the following units

A Joules B Watts C QBtus D Dollars $ E Any of the above

38

QuestionIf one barrel of oil contains 1700 kWh of energy how manyWatts is 7 Gbarrelyear

A 1400 GW (Giga Watts)

B 14 GW

C 11900 W

D 119 MW

E 1 x 1011 W

QuestionIf the total yearly oil use in the US is about 1400 GW howmany 1000 MW nuclear reactors will need to be built toreplace all oil use with electricity

A Only one will be needed

B Around 14

C Around 140

D Around 1400

E Cant convert Watts to reactors power vs energy

39

More Power Examplesbull How much power does it take to lift 10 kg up 2 meters in 2

secondsmgh = (10 kg)times(10 ms2)times(2 m) = 200J

200 J in 2 seconds rarr 100 Wattsbull If you want to heat the 3 m cubic room by 10ordmC with a

1000 W space heater how long will it takeWe know from before that the room needs to have 360000 J addedto it so at 1000 W = 1000 Js this will take 360 seconds or sixminutes

But the walls need to be warmed up too so it will actually takelonger (and depends on quality of insulation etc)

A note on arithmetic of unitsbull You should carry units in your calculations and multiply and divide them

as if they were numbersbull Example the force of air drag is given bybull Fdrag = frac12cDrAv2

bull cD is a dimensionless drag coefficientbull r is the density of air 13 kgm3

bull A is the cross-sectional area of the body in m2

bull v is the velocity in msbull units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) =

kgmiddotmiddotmm22middotmiddotmm22

m3middotmiddotss22kgmiddotmiddotmm44

m3middotmiddotss22= = kgmiddotmiddotmsms22 = = NewtonsNewtons

16

Numerical examples of kineticenergy

bull A baseball (mass is 0145 kg = 145 g) moving at 30 ms(67 mph) has kinetic energy

KE = frac12times(0145 kg)times(30 ms)2

= 6525 kgm2s2 asymp 65 J

bull A quarter (mass = 000567 kg = 567 g) flipped about fourfeet into the air has a speed on reaching your hand of about5 ms The kinetic energy is

KE = frac12times(000567 kg)times(5 ms)2

= 007 kgm2s2 = 007 J

More numerical examples

bull A 1500 kg car moves down the freeway at30 ms (67 mph)

KE = frac12times(1500 kg)times(30 ms)2

= 675000 kgm2s2 = 675 kJConvert to Calories 4184 kJ = 1 Calorie675 kJ (1 Calorie4184 kJ) = 161 Calorie

bull A 2 kg (~44 lb) fish jumps out of the waterwith a speed of 1 ms (22 mph)

KE = frac12times(2 kg)times(1 ms)2

= 1 kgm2s2 = 1 J

17

QuestionKinetic energy is E = 12 m v2 Which has more energy

A 10 kg object going 100 ms

B 100 kg object going 10 ms

C 1 kg object going 1000 ms

D 1000 kg object going 1 ms

1 ms = 22 mph

Gravitational Potential Energybull It takes work to lift a mass against the pull (force) of

gravitybull The force of gravity is mg where m is the mass and g is

the gravitational accelerationF = mg (note similarity to F = ma)

ndash g = 98 ms2 on the surface of the earth or 32 fts2

bull Lifting a height h against the gravitational forcerequires an energy input (work) of

ΔE = W = F h = mghbull Rolling a boulder up a hill and perching it on the edge of a

cliff gives it gravitational potential energy that can be laterreleased when the roadrunner is down below

bull Water in river or hydroelectric plant is using potentialenergy that it got from being lifted up when Sun (solarenergy) evaporated the water

18

QuestionPotential energy is E = 10 m h (metric units) Which hasmore energy

A 1 ton of water at a height of 100 ft

B 100 tons of water at a height of 1 ft

C 200 lb (110 ton) of water at 1000 ft

D All of the above have same energy

1 ms = 22 mph

First Example of Energy Exchangebull When the boulder falls off the cliff it picks up

speed and therefore gains kinetic energybull Where does this energy come from

rArr from the gravitational potential energybull The higher the cliff the more kinetic energy the

boulder will have when it reaches the ground

mgh

becomes

frac12mv2

Energy is conserved sofrac12mv2 = mgh

Can even figure out v since v2 = 2gh

h

19

Examples of GravitationalPotential Energy

bull How much gravitational potential energy does a70 kg high-diver have on the 10 meter platform

mgh = (70 kg)times(10 ms2)times(10 m)= 7000 kgm2s2 = 7 kJ

7 kJ (1 Calorie4182kJ) = 16 CaloriesThis is amount of energy the diver used in climbing the

stairs (actually more than this since some energy waswasted) They got that energy from the food they ate

The Energy of Heatbull Hot things have more energy than their cold

counterpartsbull Heat is really just kinetic energy on microscopic

scales the vibration or otherwise fast motion ofindividual atomsmoleculesndash Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are randombull Heat is frequently quantified by calories (or Btu)

ndash One calorie (4184 J) raises one gram of H2O 1ordmCndash One Calorie (4184 J) raises one kilogram of H2O 1ordmCndash One Btu (1055 J) raises one pound of H2O 1ordmF

20

Energy of Heat continuedbull Food Calories are with the ldquobigrdquo C or kilocalories (kcal)bull Since water has a density of one gram per cubic centimeter 1

cal heats 1 cc of water 1ordmC and likewise 1 kcal (Calorie) heatsone liter of water 1ordmC In British Units 1 Btu heats 1 pound ofwater 1 degree Fahrenheitndash these are useful numbers to hang onto

bull Example to heat a 2-liter bottle of Coke from the 5ordmCrefrigerator temperature to 20ordmC room temperature requires 30Calories or 1225 kJ

bull Drink a pint (16 oz) of ice cold water (or coke) It weighs about1 pound To heat it to body temperature (986 degrees minus 32degrees or change of 666 degrees Takes about 67 BtuConvert to Calories 1 Calorie = 1kJ = 4 Btu so

67 Btu (1 Calorie 4 Btu) = 1675 Calories Since 16 oz ofcoke has 210 Calories and about 17 Calories are used justheating to your body temp you get less calories drinking it cold(or drinking quart of cold water ldquoburnsrdquo 17 Calories)

The Physics of Energy Formula List

P = ΔEΔtPower (rate of energy use)

F = σT4 (temperature to the fourthpower times a constant)

Radiative energy flux

E = mc2 (mass times speed oflight squared)

Mass energy

ΔE = cpmΔT (mass times changein temperature times heatcapacity)

Heat Energy

E = mgh (mass times height times10ms2)

(Grav) Potential Energy

KE = frac12mv2 (mass times velocitysquared)

Kinetic Energy

W = Fd (Force times distance)Work

Energy FormulaEnergy Form

21

Heat Capacitybull Different materials have different capacities to

hold heatndash Add the same energy to different materials and yoursquoll

get different temperature risesndash Quantified as heat capacityndash Water is exceptional with 4184 JkgordmCndash Most materials are about 1000 JkgordmC (including

wood air metals)bull Example to add 10ordmC to a room 3 meters on a side

(cubic) how much energy do we needair density is 13 kgm3 and we have 27 m3 so 35 kg ofair and we need 1000 J per kg per ordmC so we end upneeding 350000 J (= 836 Cal)

Important in designing solar heated houses Also reasonit is cooler near the coast than inland

Powerbull Power is simply energy exchanged

per unit time or how fast you getwork done (Watts = Joulessec)

bull One horsepower = 745 Wbull Perform 100 J of work in 1 s and

call it 100 Wbull Run upstairs raising your 70 kg

(700 N) mass 3 m (2100 J) in 3seconds rarr 700 W output

bull Shuttle puts out a few GW(gigawatts or 109 W) of power

bull A big electrical power plant putsout around a GW That is 1 BillionJoules per second House takes afew kW (kilowatt)

22

QuestionPower is Energy used per second P= energytime Whichhighest power

A Using 100 Calories in 10 minutes

B Using 1000 Calories in 100 minutes

C Using 10 Calories in 1 minute

D Using 1 Calorie in 6 seconds

E All of the above are the same power usage

1 Calorieminute = Watts

Wind Energy

bull Wind can be used as a source of energy (windmills sailingships etc)

bull Really just kinetic energybull Example wind passing through a square meter at 8 meters

per secondndash Each second we have 8 cubic metersndash Air has density of 13 kgm3 so (8 m3)times(13 kgm3) = 104 kg of

air each secondndash frac12mv2 = frac12times(104 kg)times(8 ms)2 = 333 Jndash 333 J every second rarr 333 Watts of available power per square

meter (but to get all of it yoursquod have to stop the wind)bull Stronger winds rarr more power (like v2)

23

Chemical Energy

bull Electrostatic energy (associated with chargedparticles like electrons) is stored in the chemicalbonds of substances

bull Rearranging these bonds can release energy (somereactions require energy to be put in)

bull Typical numbers are 100ndash200 kJ per molendash a mole is 6022times1023 moleculesparticlesndash typical molecules are tens of grams per molerarrworks

out to typical numbers like several thousand Joules pergram or a few Calories per gram (remember 1 Cal = 1kcal = 4187 J)

Chemical Energy Examples

bull Burning a wooden match releases about oneBtu or 1055 Joules (a match is about 03grams) so this is gt3000 Jg nearly 1 Calg

bull Burning coal releases about 20 kJ per gramof chemical energy or roughly 5 Calg

bull Burning gasoline yields about 39 kJ pergram or just over 9 Calg

bull Very few substances over about 11 Calg

24

Energy from Food

bull We get the energy to do the things we do out of food(stored solar energy in the form of chemical energy)

bull Energy sources recognized by our digestive systemsndash Carbohydrates 4 Calories per gramndash Proteins 4 Calories per gramndash Fats 9 Calories per gram (like gasoline) (9 is more than

4 so gain more weight eating same amount of fat thancarbs or protein)

ndash Roughly 3500 Caloriespound in your body fat Less inyour protein (muscle skin etc)

Our Human Energy Budget

bull A 2000 Calorie per daydiet means 2000times4184 J =8368000 J per day

bull 837 MJ in (24 hrday) times(60 minhr)times(60 secmin)= 86400 sec correspondsto 97 Watts of power

bull Even a couch-potato at1500 Calday burns 75 W

bull More active lifestylesrequire greater Caloricintake (more energy)

25

Nutrition Labelsbull Nutrition labels tell you about the

energy content of foodbull Note they use Calories with capitol Cbull Conversions Fat 9 Calg

Carbs 4 CalgProtein 4 Calg

bull This product has 72 Cal from fat 48Cal from carbohydrates and 32 Calfrom proteinndash sum is 152 Calories compare to label

bull 152 Cal = 636 kJ enough to climbabout 1000 meters (64 kg person)

bull 1kwh = 860 Cal or about 14 lb bodyfat

bull 1 gal of gas has 31000 Calories

Mass-energy

bull Einsteinrsquos famous relationE = mc2

relates mass to energybull In effect they are the same thing

ndash one can be transformed into the otherndash physicists speak generally of mass-energy

bull Seldom experienced in daily life directlyndash Happens at large scale in the center of the sun and in

nuclear bombs and reactorsndash Actually does happen at barely detectable level in all

energy transactions but the effect is tiny

26

E = mc2 Examples

bull The energy equivalent of one gram of material(any composition) is (0001 kg)times(30times108 ms)2

= 90times1013 J = 90000000000000 J = 90 TJndash Man thatrsquos bigndash Our global energy budget is equivalent to 1000 kgyr

(thatrsquos about 1 ton per year)bull If one gram of material undergoes a chemical

reaction losing about 9000 J of energy howmuch mass does it lose

9000 J = Δmc2 so Δm = 9000c2 = 9times1039times1016

= 10-13 kg (would we ever notice)

Solar Energy is Nuclear Using E= mc2

bull Thermonuclear fusion reactions in the sunrsquos centerndash Sun is 16 million degrees Celsius in its centerndash Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then heliumndash Reaction per atom 20 million times more energetic than chemical

reactions in general

4 protonsmass = 4029

4He nucleusmass = 40015

2 neutrinos photons (light)

27

E = mc2 in Sun

bull Helium nucleus is lighter than the four protonsbull Mass difference is 4029 - 40015 = 00276 amu

ndash 1 amu (atomic mass unit) is 16605times10-27 kgndash difference of 458times10-29 kgndash multiply by c2 to get 412times10-12 Jndash 1 mole (6022times1023 particles) of protons rarr 25times1012 Jndash typical chemical reactions are 100-200 kJmolendash nuclear fusion is ~20 million times more potent stuffndash Nuclear fusion is energy source of hydrogen bomb

Energy from Lightbull The tremendous energy from the sun is released as light So light

carries energybull Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiationbull Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequencybull Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellipbull All objects emit ldquolightrdquobull The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter moreradiation and color is ldquobluerrdquo

28

Emitted Radiationrsquos Color andIntensity depend on Temperature

Object

YouHeat LampCandle FlameBulb FilamentSunrsquos SurfaceNeutron StarMolecules in deep space

Temperature

~ 30 C~ 500 C~ 1700 C~ 2700 C~ 5500 C~ millions C

lt -272C

Color

Infrared (invisible)Dull redDim orangeYellowBrilliant whiteX-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted lightThe hotter it gets the more intense the radiation (more energy)

ldquoBlackbodyrdquo or Planck Spectrum

29

Same thing on logarithmic scale

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm(note 0degC = 273degK 300degK = 27degC = 81degF)

Okay but how much energybull The power given off of a surface in the form of light is

proportional to the fourth power of temperatureF = σT4 in Watts per square meter

ndash the constant σ is numerically 567times10-8 WordmK4m2

ndash easy to remember constant 5678ndash temperature must be in Kelvin

bull ordmK = ordmC + 273bull ordmC = (59)times(ordmF ndash32)

bull Example radiation from your body(567 times10-8) times(310)4 = 523 Watts per square meter(if naked in the cold of space donrsquot let this happen to you)

30

Radiant Energy continued

bull Example The sun is 5800ordmK on its surface soF = σT4 = (567times10-8)times(5800)4 = 64times107 Wm2

Summing over entire surface area of sun gives39times1026 W

bull Compare to total capacity of energy production onearth 33times1012 Wndash Single power plant typically 05ndash10 GW (109 W)

bull In earthly situations radiated power out partiallybalanced by radiated power in from other sourcesndash Not 523 Wm2 in 70ordmF room more like 100 Wm2

bull goes like σTh4 ndash σTc

4

Electrical Energybull Opposite charges attract so electrons are attracted to

protons This holds atoms togetherbull It takes energy to pull electrons off their atomsbull Electrons want to get back home to their protons They can

only travel through conductors like wires not throughinsulators like plastic paper or wood They will gothrough miles of wire to get home to their protons

bull This is how electricity works The electronrsquos energy canbe stolen as it goes home Can be used in many manyways

bull Note electricity is not a primary source of energy Energy(from burning coal nat gas from hydro wind nuke orsolar) is used to pull of electrons and that energy can bemoved through wires and got back at will

31

And those are the majorplayershellip

bull Wersquove now seen most of the major energyplayersndash work as force times distancendash kinetic energy (wind ocean currents)ndash gravitational potential energy (hydroelectric tidal)ndash chemical energy (fossil fuels batteries food biomass)ndash heat energy (power plants space heating)ndash mass-energy (nuclear sources sunrsquos energy)ndash radiant energy (solar energy)ndash electrical energy (energy of electrons separated from

their atoms)

Conservation and Exchange ofEnergy

Nothing Comes for Free

32

Energy is Conservedbull Conservation of Energy is different from Energy

Conservation the latter being about using energywisely

bull Conservation of Energy means energy is neithercreated nor destroyed The amount of energy inthe Universe is constant

bull Donrsquot we create energy at a power plantndash Oh that this were truemdashno we simply transform

energy at our power plantsbull Doesnrsquot the sun create energy

ndash Nopemdashit exchanges mass for energybull Donrsquot batteries give us new energy

ndash Nope just convert stored chemical energy to electricalenergy Someone had to put that energy in there

height referenceh

Energy Exchangebull Though the total energy of a system is constant

the form of the energy can changebull A simple example is that of a simple pendulum in

which a continual exchange goes on betweenkinetic and potential energy

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

33

Perpetual Motion

bull Why wonrsquot the pendulum swing foreverbull Itrsquos hard to design a system free of energy pathsbull The pendulum slows down by several mechanisms

ndash Friction at the contact point requires force to opposeforce acts through distance rarr work is done

ndash Air resistance must push through air with a force(through a distance) rarr work is done

ndash Gets some air swirling puts kinetic energy into air (notreally fair to separate these last two)

bull Perpetual motion means no loss of energyndash solar system orbits come very close

Some Energy Chains

bull A coffee mug with some gravitational potentialenergy is dropped

bull potential energy turns into kinetic energybull kinetic energy of the mug goes into

ndash ripping the mug apart (chemical breaking bonds)ndash sending the pieces flying (kinetic)ndash into soundndash into heating the floor and pieces through friction as the

pieces slide to a stopbull In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored inthe potential energy)

34

Gasoline Examplebull Put gas in your car containing 9 Calgbull Combust gas turning 9 Calg into kinetic energy of

explosionbull Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a wholebull That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water andsurrounding air) and friction of transmission system(heat) and noise of engine (heating the air) etc

bull Much of energy goes into stirring the air (ends up as heat)bull Apply the brakes and convert kinetic energy into heatbull It all ends up as waste heat ultimately

Bouncing Ballbull Superball has gravitational potential energybull Drop the ball and this becomes kinetic energybull Ball hits ground and compresses (force times

distance) storing energy in the springbull Ball releases this mechanically stored energy

and it goes back into kinetic form (bouncesup)

bull Inefficiencies in ldquospringrdquo end up heating theball and the floor and stirring the air a bit

bull In the end all is heat

35

Why donrsquot we get hotter andhotter

bull If all these processes end up as heat why arenrsquotwe continually getting hotter

bull If earth retained all its heat we would get hotterbull All of earthrsquos heat is radiated away

F = σT4

bull If we dump more power the temperature goes upthe radiated power increases dramaticallyndash comes to equilibrium power dumped = power radiatedndash stable against perturbation T tracks power budget

Rough numbers

bull How much power does the earth radiatebull F = σT4 for T = 288ordmK = 15ordmC is 390 Wm2

bull Summed over entire surface area (4πR2 where R= 6378000 meters) is 20times1017 W

bull Global production is 3times1012 Wbull Solar radiation incident on earth is 18times1017 W

ndash just solar luminosity of 39times1026 W divided bygeometrical fraction that points at earth

bull Amazing coincidence of numbers (or is ithellip)

36

No Energy for Free

bull No matter what you canrsquot create energy out ofnothing it has to come from somewhere

bull We can transform energy from one form toanother we can store energy we can utilizeenergy being conveyed from natural sources

bull The net energy of the entire Universe is constantbull The best we can do is scrape up some useful

crumbs

Examplesbull Unit conversion

ndash 100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Calndash 100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 Jndash 100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWhndash 10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWhndash How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86Calorieshour About what average person eats

ndash Gasoline is $3gal Electricity if $015kWh Which is moreexpensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh)= $008kWh for gasoline Gasoline is cheap in the USA

37

Examplesbull Power vs Energy (P=Etime E = P t t = EP)

ndash Car goes 60 miles in one hour and uses 3 gal of gas What wastotal power in Watts P=Et Power = (3 gal1 hour) = 3galhr(366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W[Alternative method 3 galhr (132000000 J1 gal) (1 hr3600sec) = 110000 Jsec = 110000 W

ndash 1000 W space heater is on for 3 hours How much does it cost ifelectricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr(1kW1000W) = 3kWh ($15kWh) = $45 [Alternative methodE = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000J (1 kWh3600000J) = 3 kWh Again 45 cents

ndash AAA Battery contains 33 Calories of chemical energy How longcan it run a 2 Watt light bulb time = EP time = 33 Calories2W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1hr3600 sec) = 19 hours

QuestionThe US uses about 7 Gbarrels of oil each year This couldbe converted into which of the following units

A Joules B Watts C QBtus D Dollars $ E Any of the above

38

QuestionIf one barrel of oil contains 1700 kWh of energy how manyWatts is 7 Gbarrelyear

A 1400 GW (Giga Watts)

B 14 GW

C 11900 W

D 119 MW

E 1 x 1011 W

QuestionIf the total yearly oil use in the US is about 1400 GW howmany 1000 MW nuclear reactors will need to be built toreplace all oil use with electricity

A Only one will be needed

B Around 14

C Around 140

D Around 1400

E Cant convert Watts to reactors power vs energy

39

More Power Examplesbull How much power does it take to lift 10 kg up 2 meters in 2

secondsmgh = (10 kg)times(10 ms2)times(2 m) = 200J

200 J in 2 seconds rarr 100 Wattsbull If you want to heat the 3 m cubic room by 10ordmC with a

1000 W space heater how long will it takeWe know from before that the room needs to have 360000 J addedto it so at 1000 W = 1000 Js this will take 360 seconds or sixminutes

But the walls need to be warmed up too so it will actually takelonger (and depends on quality of insulation etc)

A note on arithmetic of unitsbull You should carry units in your calculations and multiply and divide them

as if they were numbersbull Example the force of air drag is given bybull Fdrag = frac12cDrAv2

bull cD is a dimensionless drag coefficientbull r is the density of air 13 kgm3

bull A is the cross-sectional area of the body in m2

bull v is the velocity in msbull units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) =

kgmiddotmiddotmm22middotmiddotmm22

m3middotmiddotss22kgmiddotmiddotmm44

m3middotmiddotss22= = kgmiddotmiddotmsms22 = = NewtonsNewtons

17

QuestionKinetic energy is E = 12 m v2 Which has more energy

A 10 kg object going 100 ms

B 100 kg object going 10 ms

C 1 kg object going 1000 ms

D 1000 kg object going 1 ms

1 ms = 22 mph

Gravitational Potential Energybull It takes work to lift a mass against the pull (force) of

gravitybull The force of gravity is mg where m is the mass and g is

the gravitational accelerationF = mg (note similarity to F = ma)

ndash g = 98 ms2 on the surface of the earth or 32 fts2

bull Lifting a height h against the gravitational forcerequires an energy input (work) of

ΔE = W = F h = mghbull Rolling a boulder up a hill and perching it on the edge of a

cliff gives it gravitational potential energy that can be laterreleased when the roadrunner is down below

bull Water in river or hydroelectric plant is using potentialenergy that it got from being lifted up when Sun (solarenergy) evaporated the water

18

QuestionPotential energy is E = 10 m h (metric units) Which hasmore energy

A 1 ton of water at a height of 100 ft

B 100 tons of water at a height of 1 ft

C 200 lb (110 ton) of water at 1000 ft

D All of the above have same energy

1 ms = 22 mph

First Example of Energy Exchangebull When the boulder falls off the cliff it picks up

speed and therefore gains kinetic energybull Where does this energy come from

rArr from the gravitational potential energybull The higher the cliff the more kinetic energy the

boulder will have when it reaches the ground

mgh

becomes

frac12mv2

Energy is conserved sofrac12mv2 = mgh

Can even figure out v since v2 = 2gh

h

19

Examples of GravitationalPotential Energy

bull How much gravitational potential energy does a70 kg high-diver have on the 10 meter platform

mgh = (70 kg)times(10 ms2)times(10 m)= 7000 kgm2s2 = 7 kJ

7 kJ (1 Calorie4182kJ) = 16 CaloriesThis is amount of energy the diver used in climbing the

stairs (actually more than this since some energy waswasted) They got that energy from the food they ate

The Energy of Heatbull Hot things have more energy than their cold

counterpartsbull Heat is really just kinetic energy on microscopic

scales the vibration or otherwise fast motion ofindividual atomsmoleculesndash Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are randombull Heat is frequently quantified by calories (or Btu)

ndash One calorie (4184 J) raises one gram of H2O 1ordmCndash One Calorie (4184 J) raises one kilogram of H2O 1ordmCndash One Btu (1055 J) raises one pound of H2O 1ordmF

20

Energy of Heat continuedbull Food Calories are with the ldquobigrdquo C or kilocalories (kcal)bull Since water has a density of one gram per cubic centimeter 1

cal heats 1 cc of water 1ordmC and likewise 1 kcal (Calorie) heatsone liter of water 1ordmC In British Units 1 Btu heats 1 pound ofwater 1 degree Fahrenheitndash these are useful numbers to hang onto

bull Example to heat a 2-liter bottle of Coke from the 5ordmCrefrigerator temperature to 20ordmC room temperature requires 30Calories or 1225 kJ

bull Drink a pint (16 oz) of ice cold water (or coke) It weighs about1 pound To heat it to body temperature (986 degrees minus 32degrees or change of 666 degrees Takes about 67 BtuConvert to Calories 1 Calorie = 1kJ = 4 Btu so

67 Btu (1 Calorie 4 Btu) = 1675 Calories Since 16 oz ofcoke has 210 Calories and about 17 Calories are used justheating to your body temp you get less calories drinking it cold(or drinking quart of cold water ldquoburnsrdquo 17 Calories)

The Physics of Energy Formula List

P = ΔEΔtPower (rate of energy use)

F = σT4 (temperature to the fourthpower times a constant)

Radiative energy flux

E = mc2 (mass times speed oflight squared)

Mass energy

ΔE = cpmΔT (mass times changein temperature times heatcapacity)

Heat Energy

E = mgh (mass times height times10ms2)

(Grav) Potential Energy

KE = frac12mv2 (mass times velocitysquared)

Kinetic Energy

W = Fd (Force times distance)Work

Energy FormulaEnergy Form

21

Heat Capacitybull Different materials have different capacities to

hold heatndash Add the same energy to different materials and yoursquoll

get different temperature risesndash Quantified as heat capacityndash Water is exceptional with 4184 JkgordmCndash Most materials are about 1000 JkgordmC (including

wood air metals)bull Example to add 10ordmC to a room 3 meters on a side

(cubic) how much energy do we needair density is 13 kgm3 and we have 27 m3 so 35 kg ofair and we need 1000 J per kg per ordmC so we end upneeding 350000 J (= 836 Cal)

Important in designing solar heated houses Also reasonit is cooler near the coast than inland

Powerbull Power is simply energy exchanged

per unit time or how fast you getwork done (Watts = Joulessec)

bull One horsepower = 745 Wbull Perform 100 J of work in 1 s and

call it 100 Wbull Run upstairs raising your 70 kg

(700 N) mass 3 m (2100 J) in 3seconds rarr 700 W output

bull Shuttle puts out a few GW(gigawatts or 109 W) of power

bull A big electrical power plant putsout around a GW That is 1 BillionJoules per second House takes afew kW (kilowatt)

22

QuestionPower is Energy used per second P= energytime Whichhighest power

A Using 100 Calories in 10 minutes

B Using 1000 Calories in 100 minutes

C Using 10 Calories in 1 minute

D Using 1 Calorie in 6 seconds

E All of the above are the same power usage

1 Calorieminute = Watts

Wind Energy

bull Wind can be used as a source of energy (windmills sailingships etc)

bull Really just kinetic energybull Example wind passing through a square meter at 8 meters

per secondndash Each second we have 8 cubic metersndash Air has density of 13 kgm3 so (8 m3)times(13 kgm3) = 104 kg of

air each secondndash frac12mv2 = frac12times(104 kg)times(8 ms)2 = 333 Jndash 333 J every second rarr 333 Watts of available power per square

meter (but to get all of it yoursquod have to stop the wind)bull Stronger winds rarr more power (like v2)

23

Chemical Energy

bull Electrostatic energy (associated with chargedparticles like electrons) is stored in the chemicalbonds of substances

bull Rearranging these bonds can release energy (somereactions require energy to be put in)

bull Typical numbers are 100ndash200 kJ per molendash a mole is 6022times1023 moleculesparticlesndash typical molecules are tens of grams per molerarrworks

out to typical numbers like several thousand Joules pergram or a few Calories per gram (remember 1 Cal = 1kcal = 4187 J)

Chemical Energy Examples

bull Burning a wooden match releases about oneBtu or 1055 Joules (a match is about 03grams) so this is gt3000 Jg nearly 1 Calg

bull Burning coal releases about 20 kJ per gramof chemical energy or roughly 5 Calg

bull Burning gasoline yields about 39 kJ pergram or just over 9 Calg

bull Very few substances over about 11 Calg

24

Energy from Food

bull We get the energy to do the things we do out of food(stored solar energy in the form of chemical energy)

bull Energy sources recognized by our digestive systemsndash Carbohydrates 4 Calories per gramndash Proteins 4 Calories per gramndash Fats 9 Calories per gram (like gasoline) (9 is more than

4 so gain more weight eating same amount of fat thancarbs or protein)

ndash Roughly 3500 Caloriespound in your body fat Less inyour protein (muscle skin etc)

Our Human Energy Budget

bull A 2000 Calorie per daydiet means 2000times4184 J =8368000 J per day

bull 837 MJ in (24 hrday) times(60 minhr)times(60 secmin)= 86400 sec correspondsto 97 Watts of power

bull Even a couch-potato at1500 Calday burns 75 W

bull More active lifestylesrequire greater Caloricintake (more energy)

25

Nutrition Labelsbull Nutrition labels tell you about the

energy content of foodbull Note they use Calories with capitol Cbull Conversions Fat 9 Calg

Carbs 4 CalgProtein 4 Calg

bull This product has 72 Cal from fat 48Cal from carbohydrates and 32 Calfrom proteinndash sum is 152 Calories compare to label

bull 152 Cal = 636 kJ enough to climbabout 1000 meters (64 kg person)

bull 1kwh = 860 Cal or about 14 lb bodyfat

bull 1 gal of gas has 31000 Calories

Mass-energy

bull Einsteinrsquos famous relationE = mc2

relates mass to energybull In effect they are the same thing

ndash one can be transformed into the otherndash physicists speak generally of mass-energy

bull Seldom experienced in daily life directlyndash Happens at large scale in the center of the sun and in

nuclear bombs and reactorsndash Actually does happen at barely detectable level in all

energy transactions but the effect is tiny

26

E = mc2 Examples

bull The energy equivalent of one gram of material(any composition) is (0001 kg)times(30times108 ms)2

= 90times1013 J = 90000000000000 J = 90 TJndash Man thatrsquos bigndash Our global energy budget is equivalent to 1000 kgyr

(thatrsquos about 1 ton per year)bull If one gram of material undergoes a chemical

reaction losing about 9000 J of energy howmuch mass does it lose

9000 J = Δmc2 so Δm = 9000c2 = 9times1039times1016

= 10-13 kg (would we ever notice)

Solar Energy is Nuclear Using E= mc2

bull Thermonuclear fusion reactions in the sunrsquos centerndash Sun is 16 million degrees Celsius in its centerndash Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then heliumndash Reaction per atom 20 million times more energetic than chemical

reactions in general

4 protonsmass = 4029

4He nucleusmass = 40015

2 neutrinos photons (light)

27

E = mc2 in Sun

bull Helium nucleus is lighter than the four protonsbull Mass difference is 4029 - 40015 = 00276 amu

ndash 1 amu (atomic mass unit) is 16605times10-27 kgndash difference of 458times10-29 kgndash multiply by c2 to get 412times10-12 Jndash 1 mole (6022times1023 particles) of protons rarr 25times1012 Jndash typical chemical reactions are 100-200 kJmolendash nuclear fusion is ~20 million times more potent stuffndash Nuclear fusion is energy source of hydrogen bomb

Energy from Lightbull The tremendous energy from the sun is released as light So light

carries energybull Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiationbull Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequencybull Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellipbull All objects emit ldquolightrdquobull The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter moreradiation and color is ldquobluerrdquo

28

Emitted Radiationrsquos Color andIntensity depend on Temperature

Object

YouHeat LampCandle FlameBulb FilamentSunrsquos SurfaceNeutron StarMolecules in deep space

Temperature

~ 30 C~ 500 C~ 1700 C~ 2700 C~ 5500 C~ millions C

lt -272C

Color

Infrared (invisible)Dull redDim orangeYellowBrilliant whiteX-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted lightThe hotter it gets the more intense the radiation (more energy)

ldquoBlackbodyrdquo or Planck Spectrum

29

Same thing on logarithmic scale

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm(note 0degC = 273degK 300degK = 27degC = 81degF)

Okay but how much energybull The power given off of a surface in the form of light is

proportional to the fourth power of temperatureF = σT4 in Watts per square meter

ndash the constant σ is numerically 567times10-8 WordmK4m2

ndash easy to remember constant 5678ndash temperature must be in Kelvin

bull ordmK = ordmC + 273bull ordmC = (59)times(ordmF ndash32)

bull Example radiation from your body(567 times10-8) times(310)4 = 523 Watts per square meter(if naked in the cold of space donrsquot let this happen to you)

30

Radiant Energy continued

bull Example The sun is 5800ordmK on its surface soF = σT4 = (567times10-8)times(5800)4 = 64times107 Wm2

Summing over entire surface area of sun gives39times1026 W

bull Compare to total capacity of energy production onearth 33times1012 Wndash Single power plant typically 05ndash10 GW (109 W)

bull In earthly situations radiated power out partiallybalanced by radiated power in from other sourcesndash Not 523 Wm2 in 70ordmF room more like 100 Wm2

bull goes like σTh4 ndash σTc

4

Electrical Energybull Opposite charges attract so electrons are attracted to

protons This holds atoms togetherbull It takes energy to pull electrons off their atomsbull Electrons want to get back home to their protons They can

only travel through conductors like wires not throughinsulators like plastic paper or wood They will gothrough miles of wire to get home to their protons

bull This is how electricity works The electronrsquos energy canbe stolen as it goes home Can be used in many manyways

bull Note electricity is not a primary source of energy Energy(from burning coal nat gas from hydro wind nuke orsolar) is used to pull of electrons and that energy can bemoved through wires and got back at will

31

And those are the majorplayershellip

bull Wersquove now seen most of the major energyplayersndash work as force times distancendash kinetic energy (wind ocean currents)ndash gravitational potential energy (hydroelectric tidal)ndash chemical energy (fossil fuels batteries food biomass)ndash heat energy (power plants space heating)ndash mass-energy (nuclear sources sunrsquos energy)ndash radiant energy (solar energy)ndash electrical energy (energy of electrons separated from

their atoms)

Conservation and Exchange ofEnergy

Nothing Comes for Free

32

Energy is Conservedbull Conservation of Energy is different from Energy

Conservation the latter being about using energywisely

bull Conservation of Energy means energy is neithercreated nor destroyed The amount of energy inthe Universe is constant

bull Donrsquot we create energy at a power plantndash Oh that this were truemdashno we simply transform

energy at our power plantsbull Doesnrsquot the sun create energy

ndash Nopemdashit exchanges mass for energybull Donrsquot batteries give us new energy

ndash Nope just convert stored chemical energy to electricalenergy Someone had to put that energy in there

height referenceh

Energy Exchangebull Though the total energy of a system is constant

the form of the energy can changebull A simple example is that of a simple pendulum in

which a continual exchange goes on betweenkinetic and potential energy

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

33

Perpetual Motion

bull Why wonrsquot the pendulum swing foreverbull Itrsquos hard to design a system free of energy pathsbull The pendulum slows down by several mechanisms

ndash Friction at the contact point requires force to opposeforce acts through distance rarr work is done

ndash Air resistance must push through air with a force(through a distance) rarr work is done

ndash Gets some air swirling puts kinetic energy into air (notreally fair to separate these last two)

bull Perpetual motion means no loss of energyndash solar system orbits come very close

Some Energy Chains

bull A coffee mug with some gravitational potentialenergy is dropped

bull potential energy turns into kinetic energybull kinetic energy of the mug goes into

ndash ripping the mug apart (chemical breaking bonds)ndash sending the pieces flying (kinetic)ndash into soundndash into heating the floor and pieces through friction as the

pieces slide to a stopbull In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored inthe potential energy)

34

Gasoline Examplebull Put gas in your car containing 9 Calgbull Combust gas turning 9 Calg into kinetic energy of

explosionbull Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a wholebull That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water andsurrounding air) and friction of transmission system(heat) and noise of engine (heating the air) etc

bull Much of energy goes into stirring the air (ends up as heat)bull Apply the brakes and convert kinetic energy into heatbull It all ends up as waste heat ultimately

Bouncing Ballbull Superball has gravitational potential energybull Drop the ball and this becomes kinetic energybull Ball hits ground and compresses (force times

distance) storing energy in the springbull Ball releases this mechanically stored energy

and it goes back into kinetic form (bouncesup)

bull Inefficiencies in ldquospringrdquo end up heating theball and the floor and stirring the air a bit

bull In the end all is heat

35

Why donrsquot we get hotter andhotter

bull If all these processes end up as heat why arenrsquotwe continually getting hotter

bull If earth retained all its heat we would get hotterbull All of earthrsquos heat is radiated away

F = σT4

bull If we dump more power the temperature goes upthe radiated power increases dramaticallyndash comes to equilibrium power dumped = power radiatedndash stable against perturbation T tracks power budget

Rough numbers

bull How much power does the earth radiatebull F = σT4 for T = 288ordmK = 15ordmC is 390 Wm2

bull Summed over entire surface area (4πR2 where R= 6378000 meters) is 20times1017 W

bull Global production is 3times1012 Wbull Solar radiation incident on earth is 18times1017 W

ndash just solar luminosity of 39times1026 W divided bygeometrical fraction that points at earth

bull Amazing coincidence of numbers (or is ithellip)

36

No Energy for Free

bull No matter what you canrsquot create energy out ofnothing it has to come from somewhere

bull We can transform energy from one form toanother we can store energy we can utilizeenergy being conveyed from natural sources

bull The net energy of the entire Universe is constantbull The best we can do is scrape up some useful

crumbs

Examplesbull Unit conversion

ndash 100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Calndash 100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 Jndash 100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWhndash 10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWhndash How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86Calorieshour About what average person eats

ndash Gasoline is $3gal Electricity if $015kWh Which is moreexpensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh)= $008kWh for gasoline Gasoline is cheap in the USA

37

Examplesbull Power vs Energy (P=Etime E = P t t = EP)

ndash Car goes 60 miles in one hour and uses 3 gal of gas What wastotal power in Watts P=Et Power = (3 gal1 hour) = 3galhr(366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W[Alternative method 3 galhr (132000000 J1 gal) (1 hr3600sec) = 110000 Jsec = 110000 W

ndash 1000 W space heater is on for 3 hours How much does it cost ifelectricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr(1kW1000W) = 3kWh ($15kWh) = $45 [Alternative methodE = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000J (1 kWh3600000J) = 3 kWh Again 45 cents

ndash AAA Battery contains 33 Calories of chemical energy How longcan it run a 2 Watt light bulb time = EP time = 33 Calories2W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1hr3600 sec) = 19 hours

QuestionThe US uses about 7 Gbarrels of oil each year This couldbe converted into which of the following units

A Joules B Watts C QBtus D Dollars $ E Any of the above

38

QuestionIf one barrel of oil contains 1700 kWh of energy how manyWatts is 7 Gbarrelyear

A 1400 GW (Giga Watts)

B 14 GW

C 11900 W

D 119 MW

E 1 x 1011 W

QuestionIf the total yearly oil use in the US is about 1400 GW howmany 1000 MW nuclear reactors will need to be built toreplace all oil use with electricity

A Only one will be needed

B Around 14

C Around 140

D Around 1400

E Cant convert Watts to reactors power vs energy

39

More Power Examplesbull How much power does it take to lift 10 kg up 2 meters in 2

secondsmgh = (10 kg)times(10 ms2)times(2 m) = 200J

200 J in 2 seconds rarr 100 Wattsbull If you want to heat the 3 m cubic room by 10ordmC with a

1000 W space heater how long will it takeWe know from before that the room needs to have 360000 J addedto it so at 1000 W = 1000 Js this will take 360 seconds or sixminutes

But the walls need to be warmed up too so it will actually takelonger (and depends on quality of insulation etc)

A note on arithmetic of unitsbull You should carry units in your calculations and multiply and divide them

as if they were numbersbull Example the force of air drag is given bybull Fdrag = frac12cDrAv2

bull cD is a dimensionless drag coefficientbull r is the density of air 13 kgm3

bull A is the cross-sectional area of the body in m2

bull v is the velocity in msbull units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) =

kgmiddotmiddotmm22middotmiddotmm22

m3middotmiddotss22kgmiddotmiddotmm44

m3middotmiddotss22= = kgmiddotmiddotmsms22 = = NewtonsNewtons

18

QuestionPotential energy is E = 10 m h (metric units) Which hasmore energy

A 1 ton of water at a height of 100 ft

B 100 tons of water at a height of 1 ft

C 200 lb (110 ton) of water at 1000 ft

D All of the above have same energy

1 ms = 22 mph

First Example of Energy Exchangebull When the boulder falls off the cliff it picks up

speed and therefore gains kinetic energybull Where does this energy come from

rArr from the gravitational potential energybull The higher the cliff the more kinetic energy the

boulder will have when it reaches the ground

mgh

becomes

frac12mv2

Energy is conserved sofrac12mv2 = mgh

Can even figure out v since v2 = 2gh

h

19

Examples of GravitationalPotential Energy

bull How much gravitational potential energy does a70 kg high-diver have on the 10 meter platform

mgh = (70 kg)times(10 ms2)times(10 m)= 7000 kgm2s2 = 7 kJ

7 kJ (1 Calorie4182kJ) = 16 CaloriesThis is amount of energy the diver used in climbing the

stairs (actually more than this since some energy waswasted) They got that energy from the food they ate

The Energy of Heatbull Hot things have more energy than their cold

counterpartsbull Heat is really just kinetic energy on microscopic

scales the vibration or otherwise fast motion ofindividual atomsmoleculesndash Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are randombull Heat is frequently quantified by calories (or Btu)

ndash One calorie (4184 J) raises one gram of H2O 1ordmCndash One Calorie (4184 J) raises one kilogram of H2O 1ordmCndash One Btu (1055 J) raises one pound of H2O 1ordmF

20

Energy of Heat continuedbull Food Calories are with the ldquobigrdquo C or kilocalories (kcal)bull Since water has a density of one gram per cubic centimeter 1

cal heats 1 cc of water 1ordmC and likewise 1 kcal (Calorie) heatsone liter of water 1ordmC In British Units 1 Btu heats 1 pound ofwater 1 degree Fahrenheitndash these are useful numbers to hang onto

bull Example to heat a 2-liter bottle of Coke from the 5ordmCrefrigerator temperature to 20ordmC room temperature requires 30Calories or 1225 kJ

bull Drink a pint (16 oz) of ice cold water (or coke) It weighs about1 pound To heat it to body temperature (986 degrees minus 32degrees or change of 666 degrees Takes about 67 BtuConvert to Calories 1 Calorie = 1kJ = 4 Btu so

67 Btu (1 Calorie 4 Btu) = 1675 Calories Since 16 oz ofcoke has 210 Calories and about 17 Calories are used justheating to your body temp you get less calories drinking it cold(or drinking quart of cold water ldquoburnsrdquo 17 Calories)

The Physics of Energy Formula List

P = ΔEΔtPower (rate of energy use)

F = σT4 (temperature to the fourthpower times a constant)

Radiative energy flux

E = mc2 (mass times speed oflight squared)

Mass energy

ΔE = cpmΔT (mass times changein temperature times heatcapacity)

Heat Energy

E = mgh (mass times height times10ms2)

(Grav) Potential Energy

KE = frac12mv2 (mass times velocitysquared)

Kinetic Energy

W = Fd (Force times distance)Work

Energy FormulaEnergy Form

21

Heat Capacitybull Different materials have different capacities to

hold heatndash Add the same energy to different materials and yoursquoll

get different temperature risesndash Quantified as heat capacityndash Water is exceptional with 4184 JkgordmCndash Most materials are about 1000 JkgordmC (including

wood air metals)bull Example to add 10ordmC to a room 3 meters on a side

(cubic) how much energy do we needair density is 13 kgm3 and we have 27 m3 so 35 kg ofair and we need 1000 J per kg per ordmC so we end upneeding 350000 J (= 836 Cal)

Important in designing solar heated houses Also reasonit is cooler near the coast than inland

Powerbull Power is simply energy exchanged

per unit time or how fast you getwork done (Watts = Joulessec)

bull One horsepower = 745 Wbull Perform 100 J of work in 1 s and

call it 100 Wbull Run upstairs raising your 70 kg

(700 N) mass 3 m (2100 J) in 3seconds rarr 700 W output

bull Shuttle puts out a few GW(gigawatts or 109 W) of power

bull A big electrical power plant putsout around a GW That is 1 BillionJoules per second House takes afew kW (kilowatt)

22

QuestionPower is Energy used per second P= energytime Whichhighest power

A Using 100 Calories in 10 minutes

B Using 1000 Calories in 100 minutes

C Using 10 Calories in 1 minute

D Using 1 Calorie in 6 seconds

E All of the above are the same power usage

1 Calorieminute = Watts

Wind Energy

bull Wind can be used as a source of energy (windmills sailingships etc)

bull Really just kinetic energybull Example wind passing through a square meter at 8 meters

per secondndash Each second we have 8 cubic metersndash Air has density of 13 kgm3 so (8 m3)times(13 kgm3) = 104 kg of

air each secondndash frac12mv2 = frac12times(104 kg)times(8 ms)2 = 333 Jndash 333 J every second rarr 333 Watts of available power per square

meter (but to get all of it yoursquod have to stop the wind)bull Stronger winds rarr more power (like v2)

23

Chemical Energy

bull Electrostatic energy (associated with chargedparticles like electrons) is stored in the chemicalbonds of substances

bull Rearranging these bonds can release energy (somereactions require energy to be put in)

bull Typical numbers are 100ndash200 kJ per molendash a mole is 6022times1023 moleculesparticlesndash typical molecules are tens of grams per molerarrworks

out to typical numbers like several thousand Joules pergram or a few Calories per gram (remember 1 Cal = 1kcal = 4187 J)

Chemical Energy Examples

bull Burning a wooden match releases about oneBtu or 1055 Joules (a match is about 03grams) so this is gt3000 Jg nearly 1 Calg

bull Burning coal releases about 20 kJ per gramof chemical energy or roughly 5 Calg

bull Burning gasoline yields about 39 kJ pergram or just over 9 Calg

bull Very few substances over about 11 Calg

24

Energy from Food

bull We get the energy to do the things we do out of food(stored solar energy in the form of chemical energy)

bull Energy sources recognized by our digestive systemsndash Carbohydrates 4 Calories per gramndash Proteins 4 Calories per gramndash Fats 9 Calories per gram (like gasoline) (9 is more than

4 so gain more weight eating same amount of fat thancarbs or protein)

ndash Roughly 3500 Caloriespound in your body fat Less inyour protein (muscle skin etc)

Our Human Energy Budget

bull A 2000 Calorie per daydiet means 2000times4184 J =8368000 J per day

bull 837 MJ in (24 hrday) times(60 minhr)times(60 secmin)= 86400 sec correspondsto 97 Watts of power

bull Even a couch-potato at1500 Calday burns 75 W

bull More active lifestylesrequire greater Caloricintake (more energy)

25

Nutrition Labelsbull Nutrition labels tell you about the

energy content of foodbull Note they use Calories with capitol Cbull Conversions Fat 9 Calg

Carbs 4 CalgProtein 4 Calg

bull This product has 72 Cal from fat 48Cal from carbohydrates and 32 Calfrom proteinndash sum is 152 Calories compare to label

bull 152 Cal = 636 kJ enough to climbabout 1000 meters (64 kg person)

bull 1kwh = 860 Cal or about 14 lb bodyfat

bull 1 gal of gas has 31000 Calories

Mass-energy

bull Einsteinrsquos famous relationE = mc2

relates mass to energybull In effect they are the same thing

ndash one can be transformed into the otherndash physicists speak generally of mass-energy

bull Seldom experienced in daily life directlyndash Happens at large scale in the center of the sun and in

nuclear bombs and reactorsndash Actually does happen at barely detectable level in all

energy transactions but the effect is tiny

26

E = mc2 Examples

bull The energy equivalent of one gram of material(any composition) is (0001 kg)times(30times108 ms)2

= 90times1013 J = 90000000000000 J = 90 TJndash Man thatrsquos bigndash Our global energy budget is equivalent to 1000 kgyr

(thatrsquos about 1 ton per year)bull If one gram of material undergoes a chemical

reaction losing about 9000 J of energy howmuch mass does it lose

9000 J = Δmc2 so Δm = 9000c2 = 9times1039times1016

= 10-13 kg (would we ever notice)

Solar Energy is Nuclear Using E= mc2

bull Thermonuclear fusion reactions in the sunrsquos centerndash Sun is 16 million degrees Celsius in its centerndash Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then heliumndash Reaction per atom 20 million times more energetic than chemical

reactions in general

4 protonsmass = 4029

4He nucleusmass = 40015

2 neutrinos photons (light)

27

E = mc2 in Sun

bull Helium nucleus is lighter than the four protonsbull Mass difference is 4029 - 40015 = 00276 amu

ndash 1 amu (atomic mass unit) is 16605times10-27 kgndash difference of 458times10-29 kgndash multiply by c2 to get 412times10-12 Jndash 1 mole (6022times1023 particles) of protons rarr 25times1012 Jndash typical chemical reactions are 100-200 kJmolendash nuclear fusion is ~20 million times more potent stuffndash Nuclear fusion is energy source of hydrogen bomb

Energy from Lightbull The tremendous energy from the sun is released as light So light

carries energybull Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiationbull Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequencybull Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellipbull All objects emit ldquolightrdquobull The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter moreradiation and color is ldquobluerrdquo

28

Emitted Radiationrsquos Color andIntensity depend on Temperature

Object

YouHeat LampCandle FlameBulb FilamentSunrsquos SurfaceNeutron StarMolecules in deep space

Temperature

~ 30 C~ 500 C~ 1700 C~ 2700 C~ 5500 C~ millions C

lt -272C

Color

Infrared (invisible)Dull redDim orangeYellowBrilliant whiteX-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted lightThe hotter it gets the more intense the radiation (more energy)

ldquoBlackbodyrdquo or Planck Spectrum

29

Same thing on logarithmic scale

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm(note 0degC = 273degK 300degK = 27degC = 81degF)

Okay but how much energybull The power given off of a surface in the form of light is

proportional to the fourth power of temperatureF = σT4 in Watts per square meter

ndash the constant σ is numerically 567times10-8 WordmK4m2

ndash easy to remember constant 5678ndash temperature must be in Kelvin

bull ordmK = ordmC + 273bull ordmC = (59)times(ordmF ndash32)

bull Example radiation from your body(567 times10-8) times(310)4 = 523 Watts per square meter(if naked in the cold of space donrsquot let this happen to you)

30

Radiant Energy continued

bull Example The sun is 5800ordmK on its surface soF = σT4 = (567times10-8)times(5800)4 = 64times107 Wm2

Summing over entire surface area of sun gives39times1026 W

bull Compare to total capacity of energy production onearth 33times1012 Wndash Single power plant typically 05ndash10 GW (109 W)

bull In earthly situations radiated power out partiallybalanced by radiated power in from other sourcesndash Not 523 Wm2 in 70ordmF room more like 100 Wm2

bull goes like σTh4 ndash σTc

4

Electrical Energybull Opposite charges attract so electrons are attracted to

protons This holds atoms togetherbull It takes energy to pull electrons off their atomsbull Electrons want to get back home to their protons They can

only travel through conductors like wires not throughinsulators like plastic paper or wood They will gothrough miles of wire to get home to their protons

bull This is how electricity works The electronrsquos energy canbe stolen as it goes home Can be used in many manyways

bull Note electricity is not a primary source of energy Energy(from burning coal nat gas from hydro wind nuke orsolar) is used to pull of electrons and that energy can bemoved through wires and got back at will

31

And those are the majorplayershellip

bull Wersquove now seen most of the major energyplayersndash work as force times distancendash kinetic energy (wind ocean currents)ndash gravitational potential energy (hydroelectric tidal)ndash chemical energy (fossil fuels batteries food biomass)ndash heat energy (power plants space heating)ndash mass-energy (nuclear sources sunrsquos energy)ndash radiant energy (solar energy)ndash electrical energy (energy of electrons separated from

their atoms)

Conservation and Exchange ofEnergy

Nothing Comes for Free

32

Energy is Conservedbull Conservation of Energy is different from Energy

Conservation the latter being about using energywisely

bull Conservation of Energy means energy is neithercreated nor destroyed The amount of energy inthe Universe is constant

bull Donrsquot we create energy at a power plantndash Oh that this were truemdashno we simply transform

energy at our power plantsbull Doesnrsquot the sun create energy

ndash Nopemdashit exchanges mass for energybull Donrsquot batteries give us new energy

ndash Nope just convert stored chemical energy to electricalenergy Someone had to put that energy in there

height referenceh

Energy Exchangebull Though the total energy of a system is constant

the form of the energy can changebull A simple example is that of a simple pendulum in

which a continual exchange goes on betweenkinetic and potential energy

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

33

Perpetual Motion

bull Why wonrsquot the pendulum swing foreverbull Itrsquos hard to design a system free of energy pathsbull The pendulum slows down by several mechanisms

ndash Friction at the contact point requires force to opposeforce acts through distance rarr work is done

ndash Air resistance must push through air with a force(through a distance) rarr work is done

ndash Gets some air swirling puts kinetic energy into air (notreally fair to separate these last two)

bull Perpetual motion means no loss of energyndash solar system orbits come very close

Some Energy Chains

bull A coffee mug with some gravitational potentialenergy is dropped

bull potential energy turns into kinetic energybull kinetic energy of the mug goes into

ndash ripping the mug apart (chemical breaking bonds)ndash sending the pieces flying (kinetic)ndash into soundndash into heating the floor and pieces through friction as the

pieces slide to a stopbull In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored inthe potential energy)

34

Gasoline Examplebull Put gas in your car containing 9 Calgbull Combust gas turning 9 Calg into kinetic energy of

explosionbull Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a wholebull That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water andsurrounding air) and friction of transmission system(heat) and noise of engine (heating the air) etc

bull Much of energy goes into stirring the air (ends up as heat)bull Apply the brakes and convert kinetic energy into heatbull It all ends up as waste heat ultimately

Bouncing Ballbull Superball has gravitational potential energybull Drop the ball and this becomes kinetic energybull Ball hits ground and compresses (force times

distance) storing energy in the springbull Ball releases this mechanically stored energy

and it goes back into kinetic form (bouncesup)

bull Inefficiencies in ldquospringrdquo end up heating theball and the floor and stirring the air a bit

bull In the end all is heat

35

Why donrsquot we get hotter andhotter

bull If all these processes end up as heat why arenrsquotwe continually getting hotter

bull If earth retained all its heat we would get hotterbull All of earthrsquos heat is radiated away

F = σT4

bull If we dump more power the temperature goes upthe radiated power increases dramaticallyndash comes to equilibrium power dumped = power radiatedndash stable against perturbation T tracks power budget

Rough numbers

bull How much power does the earth radiatebull F = σT4 for T = 288ordmK = 15ordmC is 390 Wm2

bull Summed over entire surface area (4πR2 where R= 6378000 meters) is 20times1017 W

bull Global production is 3times1012 Wbull Solar radiation incident on earth is 18times1017 W

ndash just solar luminosity of 39times1026 W divided bygeometrical fraction that points at earth

bull Amazing coincidence of numbers (or is ithellip)

36

No Energy for Free

bull No matter what you canrsquot create energy out ofnothing it has to come from somewhere

bull We can transform energy from one form toanother we can store energy we can utilizeenergy being conveyed from natural sources

bull The net energy of the entire Universe is constantbull The best we can do is scrape up some useful

crumbs

Examplesbull Unit conversion

ndash 100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Calndash 100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 Jndash 100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWhndash 10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWhndash How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86Calorieshour About what average person eats

ndash Gasoline is $3gal Electricity if $015kWh Which is moreexpensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh)= $008kWh for gasoline Gasoline is cheap in the USA

37

Examplesbull Power vs Energy (P=Etime E = P t t = EP)

ndash Car goes 60 miles in one hour and uses 3 gal of gas What wastotal power in Watts P=Et Power = (3 gal1 hour) = 3galhr(366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W[Alternative method 3 galhr (132000000 J1 gal) (1 hr3600sec) = 110000 Jsec = 110000 W

ndash 1000 W space heater is on for 3 hours How much does it cost ifelectricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr(1kW1000W) = 3kWh ($15kWh) = $45 [Alternative methodE = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000J (1 kWh3600000J) = 3 kWh Again 45 cents

ndash AAA Battery contains 33 Calories of chemical energy How longcan it run a 2 Watt light bulb time = EP time = 33 Calories2W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1hr3600 sec) = 19 hours

QuestionThe US uses about 7 Gbarrels of oil each year This couldbe converted into which of the following units

A Joules B Watts C QBtus D Dollars $ E Any of the above

38

QuestionIf one barrel of oil contains 1700 kWh of energy how manyWatts is 7 Gbarrelyear

A 1400 GW (Giga Watts)

B 14 GW

C 11900 W

D 119 MW

E 1 x 1011 W

QuestionIf the total yearly oil use in the US is about 1400 GW howmany 1000 MW nuclear reactors will need to be built toreplace all oil use with electricity

A Only one will be needed

B Around 14

C Around 140

D Around 1400

E Cant convert Watts to reactors power vs energy

39

More Power Examplesbull How much power does it take to lift 10 kg up 2 meters in 2

secondsmgh = (10 kg)times(10 ms2)times(2 m) = 200J

200 J in 2 seconds rarr 100 Wattsbull If you want to heat the 3 m cubic room by 10ordmC with a

1000 W space heater how long will it takeWe know from before that the room needs to have 360000 J addedto it so at 1000 W = 1000 Js this will take 360 seconds or sixminutes

But the walls need to be warmed up too so it will actually takelonger (and depends on quality of insulation etc)

A note on arithmetic of unitsbull You should carry units in your calculations and multiply and divide them

as if they were numbersbull Example the force of air drag is given bybull Fdrag = frac12cDrAv2

bull cD is a dimensionless drag coefficientbull r is the density of air 13 kgm3

bull A is the cross-sectional area of the body in m2

bull v is the velocity in msbull units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) =

kgmiddotmiddotmm22middotmiddotmm22

m3middotmiddotss22kgmiddotmiddotmm44

m3middotmiddotss22= = kgmiddotmiddotmsms22 = = NewtonsNewtons

19

Examples of GravitationalPotential Energy

bull How much gravitational potential energy does a70 kg high-diver have on the 10 meter platform

mgh = (70 kg)times(10 ms2)times(10 m)= 7000 kgm2s2 = 7 kJ

7 kJ (1 Calorie4182kJ) = 16 CaloriesThis is amount of energy the diver used in climbing the

stairs (actually more than this since some energy waswasted) They got that energy from the food they ate

The Energy of Heatbull Hot things have more energy than their cold

counterpartsbull Heat is really just kinetic energy on microscopic

scales the vibration or otherwise fast motion ofindividual atomsmoleculesndash Even though itrsquos kinetic energy itrsquos hard to derive the

same useful work out of it because the motions are randombull Heat is frequently quantified by calories (or Btu)

ndash One calorie (4184 J) raises one gram of H2O 1ordmCndash One Calorie (4184 J) raises one kilogram of H2O 1ordmCndash One Btu (1055 J) raises one pound of H2O 1ordmF

20

Energy of Heat continuedbull Food Calories are with the ldquobigrdquo C or kilocalories (kcal)bull Since water has a density of one gram per cubic centimeter 1

cal heats 1 cc of water 1ordmC and likewise 1 kcal (Calorie) heatsone liter of water 1ordmC In British Units 1 Btu heats 1 pound ofwater 1 degree Fahrenheitndash these are useful numbers to hang onto

bull Example to heat a 2-liter bottle of Coke from the 5ordmCrefrigerator temperature to 20ordmC room temperature requires 30Calories or 1225 kJ

bull Drink a pint (16 oz) of ice cold water (or coke) It weighs about1 pound To heat it to body temperature (986 degrees minus 32degrees or change of 666 degrees Takes about 67 BtuConvert to Calories 1 Calorie = 1kJ = 4 Btu so

67 Btu (1 Calorie 4 Btu) = 1675 Calories Since 16 oz ofcoke has 210 Calories and about 17 Calories are used justheating to your body temp you get less calories drinking it cold(or drinking quart of cold water ldquoburnsrdquo 17 Calories)

The Physics of Energy Formula List

P = ΔEΔtPower (rate of energy use)

F = σT4 (temperature to the fourthpower times a constant)

Radiative energy flux

E = mc2 (mass times speed oflight squared)

Mass energy

ΔE = cpmΔT (mass times changein temperature times heatcapacity)

Heat Energy

E = mgh (mass times height times10ms2)

(Grav) Potential Energy

KE = frac12mv2 (mass times velocitysquared)

Kinetic Energy

W = Fd (Force times distance)Work

Energy FormulaEnergy Form

21

Heat Capacitybull Different materials have different capacities to

hold heatndash Add the same energy to different materials and yoursquoll

get different temperature risesndash Quantified as heat capacityndash Water is exceptional with 4184 JkgordmCndash Most materials are about 1000 JkgordmC (including

wood air metals)bull Example to add 10ordmC to a room 3 meters on a side

(cubic) how much energy do we needair density is 13 kgm3 and we have 27 m3 so 35 kg ofair and we need 1000 J per kg per ordmC so we end upneeding 350000 J (= 836 Cal)

Important in designing solar heated houses Also reasonit is cooler near the coast than inland

Powerbull Power is simply energy exchanged

per unit time or how fast you getwork done (Watts = Joulessec)

bull One horsepower = 745 Wbull Perform 100 J of work in 1 s and

call it 100 Wbull Run upstairs raising your 70 kg

(700 N) mass 3 m (2100 J) in 3seconds rarr 700 W output

bull Shuttle puts out a few GW(gigawatts or 109 W) of power

bull A big electrical power plant putsout around a GW That is 1 BillionJoules per second House takes afew kW (kilowatt)

22

QuestionPower is Energy used per second P= energytime Whichhighest power

A Using 100 Calories in 10 minutes

B Using 1000 Calories in 100 minutes

C Using 10 Calories in 1 minute

D Using 1 Calorie in 6 seconds

E All of the above are the same power usage

1 Calorieminute = Watts

Wind Energy

bull Wind can be used as a source of energy (windmills sailingships etc)

bull Really just kinetic energybull Example wind passing through a square meter at 8 meters

per secondndash Each second we have 8 cubic metersndash Air has density of 13 kgm3 so (8 m3)times(13 kgm3) = 104 kg of

air each secondndash frac12mv2 = frac12times(104 kg)times(8 ms)2 = 333 Jndash 333 J every second rarr 333 Watts of available power per square

meter (but to get all of it yoursquod have to stop the wind)bull Stronger winds rarr more power (like v2)

23

Chemical Energy

bull Electrostatic energy (associated with chargedparticles like electrons) is stored in the chemicalbonds of substances

bull Rearranging these bonds can release energy (somereactions require energy to be put in)

bull Typical numbers are 100ndash200 kJ per molendash a mole is 6022times1023 moleculesparticlesndash typical molecules are tens of grams per molerarrworks

out to typical numbers like several thousand Joules pergram or a few Calories per gram (remember 1 Cal = 1kcal = 4187 J)

Chemical Energy Examples

bull Burning a wooden match releases about oneBtu or 1055 Joules (a match is about 03grams) so this is gt3000 Jg nearly 1 Calg

bull Burning coal releases about 20 kJ per gramof chemical energy or roughly 5 Calg

bull Burning gasoline yields about 39 kJ pergram or just over 9 Calg

bull Very few substances over about 11 Calg

24

Energy from Food

bull We get the energy to do the things we do out of food(stored solar energy in the form of chemical energy)

bull Energy sources recognized by our digestive systemsndash Carbohydrates 4 Calories per gramndash Proteins 4 Calories per gramndash Fats 9 Calories per gram (like gasoline) (9 is more than

4 so gain more weight eating same amount of fat thancarbs or protein)

ndash Roughly 3500 Caloriespound in your body fat Less inyour protein (muscle skin etc)

Our Human Energy Budget

bull A 2000 Calorie per daydiet means 2000times4184 J =8368000 J per day

bull 837 MJ in (24 hrday) times(60 minhr)times(60 secmin)= 86400 sec correspondsto 97 Watts of power

bull Even a couch-potato at1500 Calday burns 75 W

bull More active lifestylesrequire greater Caloricintake (more energy)

25

Nutrition Labelsbull Nutrition labels tell you about the

energy content of foodbull Note they use Calories with capitol Cbull Conversions Fat 9 Calg

Carbs 4 CalgProtein 4 Calg

bull This product has 72 Cal from fat 48Cal from carbohydrates and 32 Calfrom proteinndash sum is 152 Calories compare to label

bull 152 Cal = 636 kJ enough to climbabout 1000 meters (64 kg person)

bull 1kwh = 860 Cal or about 14 lb bodyfat

bull 1 gal of gas has 31000 Calories

Mass-energy

bull Einsteinrsquos famous relationE = mc2

relates mass to energybull In effect they are the same thing

ndash one can be transformed into the otherndash physicists speak generally of mass-energy

bull Seldom experienced in daily life directlyndash Happens at large scale in the center of the sun and in

nuclear bombs and reactorsndash Actually does happen at barely detectable level in all

energy transactions but the effect is tiny

26

E = mc2 Examples

bull The energy equivalent of one gram of material(any composition) is (0001 kg)times(30times108 ms)2

= 90times1013 J = 90000000000000 J = 90 TJndash Man thatrsquos bigndash Our global energy budget is equivalent to 1000 kgyr

(thatrsquos about 1 ton per year)bull If one gram of material undergoes a chemical

reaction losing about 9000 J of energy howmuch mass does it lose

9000 J = Δmc2 so Δm = 9000c2 = 9times1039times1016

= 10-13 kg (would we ever notice)

Solar Energy is Nuclear Using E= mc2

bull Thermonuclear fusion reactions in the sunrsquos centerndash Sun is 16 million degrees Celsius in its centerndash Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then heliumndash Reaction per atom 20 million times more energetic than chemical

reactions in general

4 protonsmass = 4029

4He nucleusmass = 40015

2 neutrinos photons (light)

27

E = mc2 in Sun

bull Helium nucleus is lighter than the four protonsbull Mass difference is 4029 - 40015 = 00276 amu

ndash 1 amu (atomic mass unit) is 16605times10-27 kgndash difference of 458times10-29 kgndash multiply by c2 to get 412times10-12 Jndash 1 mole (6022times1023 particles) of protons rarr 25times1012 Jndash typical chemical reactions are 100-200 kJmolendash nuclear fusion is ~20 million times more potent stuffndash Nuclear fusion is energy source of hydrogen bomb

Energy from Lightbull The tremendous energy from the sun is released as light So light

carries energybull Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiationbull Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequencybull Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellipbull All objects emit ldquolightrdquobull The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter moreradiation and color is ldquobluerrdquo

28

Emitted Radiationrsquos Color andIntensity depend on Temperature

Object

YouHeat LampCandle FlameBulb FilamentSunrsquos SurfaceNeutron StarMolecules in deep space

Temperature

~ 30 C~ 500 C~ 1700 C~ 2700 C~ 5500 C~ millions C

lt -272C

Color

Infrared (invisible)Dull redDim orangeYellowBrilliant whiteX-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted lightThe hotter it gets the more intense the radiation (more energy)

ldquoBlackbodyrdquo or Planck Spectrum

29

Same thing on logarithmic scale

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm(note 0degC = 273degK 300degK = 27degC = 81degF)

Okay but how much energybull The power given off of a surface in the form of light is

proportional to the fourth power of temperatureF = σT4 in Watts per square meter

ndash the constant σ is numerically 567times10-8 WordmK4m2

ndash easy to remember constant 5678ndash temperature must be in Kelvin

bull ordmK = ordmC + 273bull ordmC = (59)times(ordmF ndash32)

bull Example radiation from your body(567 times10-8) times(310)4 = 523 Watts per square meter(if naked in the cold of space donrsquot let this happen to you)

30

Radiant Energy continued

bull Example The sun is 5800ordmK on its surface soF = σT4 = (567times10-8)times(5800)4 = 64times107 Wm2

Summing over entire surface area of sun gives39times1026 W

bull Compare to total capacity of energy production onearth 33times1012 Wndash Single power plant typically 05ndash10 GW (109 W)

bull In earthly situations radiated power out partiallybalanced by radiated power in from other sourcesndash Not 523 Wm2 in 70ordmF room more like 100 Wm2

bull goes like σTh4 ndash σTc

4

Electrical Energybull Opposite charges attract so electrons are attracted to

protons This holds atoms togetherbull It takes energy to pull electrons off their atomsbull Electrons want to get back home to their protons They can

only travel through conductors like wires not throughinsulators like plastic paper or wood They will gothrough miles of wire to get home to their protons

bull This is how electricity works The electronrsquos energy canbe stolen as it goes home Can be used in many manyways

bull Note electricity is not a primary source of energy Energy(from burning coal nat gas from hydro wind nuke orsolar) is used to pull of electrons and that energy can bemoved through wires and got back at will

31

And those are the majorplayershellip

bull Wersquove now seen most of the major energyplayersndash work as force times distancendash kinetic energy (wind ocean currents)ndash gravitational potential energy (hydroelectric tidal)ndash chemical energy (fossil fuels batteries food biomass)ndash heat energy (power plants space heating)ndash mass-energy (nuclear sources sunrsquos energy)ndash radiant energy (solar energy)ndash electrical energy (energy of electrons separated from

their atoms)

Conservation and Exchange ofEnergy

Nothing Comes for Free

32

Energy is Conservedbull Conservation of Energy is different from Energy

Conservation the latter being about using energywisely

bull Conservation of Energy means energy is neithercreated nor destroyed The amount of energy inthe Universe is constant

bull Donrsquot we create energy at a power plantndash Oh that this were truemdashno we simply transform

energy at our power plantsbull Doesnrsquot the sun create energy

ndash Nopemdashit exchanges mass for energybull Donrsquot batteries give us new energy

ndash Nope just convert stored chemical energy to electricalenergy Someone had to put that energy in there

height referenceh

Energy Exchangebull Though the total energy of a system is constant

the form of the energy can changebull A simple example is that of a simple pendulum in

which a continual exchange goes on betweenkinetic and potential energy

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

33

Perpetual Motion

bull Why wonrsquot the pendulum swing foreverbull Itrsquos hard to design a system free of energy pathsbull The pendulum slows down by several mechanisms

ndash Friction at the contact point requires force to opposeforce acts through distance rarr work is done

ndash Air resistance must push through air with a force(through a distance) rarr work is done

ndash Gets some air swirling puts kinetic energy into air (notreally fair to separate these last two)

bull Perpetual motion means no loss of energyndash solar system orbits come very close

Some Energy Chains

bull A coffee mug with some gravitational potentialenergy is dropped

bull potential energy turns into kinetic energybull kinetic energy of the mug goes into

ndash ripping the mug apart (chemical breaking bonds)ndash sending the pieces flying (kinetic)ndash into soundndash into heating the floor and pieces through friction as the

pieces slide to a stopbull In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored inthe potential energy)

34

Gasoline Examplebull Put gas in your car containing 9 Calgbull Combust gas turning 9 Calg into kinetic energy of

explosionbull Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a wholebull That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water andsurrounding air) and friction of transmission system(heat) and noise of engine (heating the air) etc

bull Much of energy goes into stirring the air (ends up as heat)bull Apply the brakes and convert kinetic energy into heatbull It all ends up as waste heat ultimately

Bouncing Ballbull Superball has gravitational potential energybull Drop the ball and this becomes kinetic energybull Ball hits ground and compresses (force times

distance) storing energy in the springbull Ball releases this mechanically stored energy

and it goes back into kinetic form (bouncesup)

bull Inefficiencies in ldquospringrdquo end up heating theball and the floor and stirring the air a bit

bull In the end all is heat

35

Why donrsquot we get hotter andhotter

bull If all these processes end up as heat why arenrsquotwe continually getting hotter

bull If earth retained all its heat we would get hotterbull All of earthrsquos heat is radiated away

F = σT4

bull If we dump more power the temperature goes upthe radiated power increases dramaticallyndash comes to equilibrium power dumped = power radiatedndash stable against perturbation T tracks power budget

Rough numbers

bull How much power does the earth radiatebull F = σT4 for T = 288ordmK = 15ordmC is 390 Wm2

bull Summed over entire surface area (4πR2 where R= 6378000 meters) is 20times1017 W

bull Global production is 3times1012 Wbull Solar radiation incident on earth is 18times1017 W

ndash just solar luminosity of 39times1026 W divided bygeometrical fraction that points at earth

bull Amazing coincidence of numbers (or is ithellip)

36

No Energy for Free

bull No matter what you canrsquot create energy out ofnothing it has to come from somewhere

bull We can transform energy from one form toanother we can store energy we can utilizeenergy being conveyed from natural sources

bull The net energy of the entire Universe is constantbull The best we can do is scrape up some useful

crumbs

Examplesbull Unit conversion

ndash 100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Calndash 100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 Jndash 100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWhndash 10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWhndash How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86Calorieshour About what average person eats

ndash Gasoline is $3gal Electricity if $015kWh Which is moreexpensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh)= $008kWh for gasoline Gasoline is cheap in the USA

37

Examplesbull Power vs Energy (P=Etime E = P t t = EP)

ndash Car goes 60 miles in one hour and uses 3 gal of gas What wastotal power in Watts P=Et Power = (3 gal1 hour) = 3galhr(366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W[Alternative method 3 galhr (132000000 J1 gal) (1 hr3600sec) = 110000 Jsec = 110000 W

ndash 1000 W space heater is on for 3 hours How much does it cost ifelectricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr(1kW1000W) = 3kWh ($15kWh) = $45 [Alternative methodE = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000J (1 kWh3600000J) = 3 kWh Again 45 cents

ndash AAA Battery contains 33 Calories of chemical energy How longcan it run a 2 Watt light bulb time = EP time = 33 Calories2W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1hr3600 sec) = 19 hours

QuestionThe US uses about 7 Gbarrels of oil each year This couldbe converted into which of the following units

A Joules B Watts C QBtus D Dollars $ E Any of the above

38

QuestionIf one barrel of oil contains 1700 kWh of energy how manyWatts is 7 Gbarrelyear

A 1400 GW (Giga Watts)

B 14 GW

C 11900 W

D 119 MW

E 1 x 1011 W

QuestionIf the total yearly oil use in the US is about 1400 GW howmany 1000 MW nuclear reactors will need to be built toreplace all oil use with electricity

A Only one will be needed

B Around 14

C Around 140

D Around 1400

E Cant convert Watts to reactors power vs energy

39

More Power Examplesbull How much power does it take to lift 10 kg up 2 meters in 2

secondsmgh = (10 kg)times(10 ms2)times(2 m) = 200J

200 J in 2 seconds rarr 100 Wattsbull If you want to heat the 3 m cubic room by 10ordmC with a

1000 W space heater how long will it takeWe know from before that the room needs to have 360000 J addedto it so at 1000 W = 1000 Js this will take 360 seconds or sixminutes

But the walls need to be warmed up too so it will actually takelonger (and depends on quality of insulation etc)

A note on arithmetic of unitsbull You should carry units in your calculations and multiply and divide them

as if they were numbersbull Example the force of air drag is given bybull Fdrag = frac12cDrAv2

bull cD is a dimensionless drag coefficientbull r is the density of air 13 kgm3

bull A is the cross-sectional area of the body in m2

bull v is the velocity in msbull units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) =

kgmiddotmiddotmm22middotmiddotmm22

m3middotmiddotss22kgmiddotmiddotmm44

m3middotmiddotss22= = kgmiddotmiddotmsms22 = = NewtonsNewtons

20

Energy of Heat continuedbull Food Calories are with the ldquobigrdquo C or kilocalories (kcal)bull Since water has a density of one gram per cubic centimeter 1

cal heats 1 cc of water 1ordmC and likewise 1 kcal (Calorie) heatsone liter of water 1ordmC In British Units 1 Btu heats 1 pound ofwater 1 degree Fahrenheitndash these are useful numbers to hang onto

bull Example to heat a 2-liter bottle of Coke from the 5ordmCrefrigerator temperature to 20ordmC room temperature requires 30Calories or 1225 kJ

bull Drink a pint (16 oz) of ice cold water (or coke) It weighs about1 pound To heat it to body temperature (986 degrees minus 32degrees or change of 666 degrees Takes about 67 BtuConvert to Calories 1 Calorie = 1kJ = 4 Btu so

67 Btu (1 Calorie 4 Btu) = 1675 Calories Since 16 oz ofcoke has 210 Calories and about 17 Calories are used justheating to your body temp you get less calories drinking it cold(or drinking quart of cold water ldquoburnsrdquo 17 Calories)

The Physics of Energy Formula List

P = ΔEΔtPower (rate of energy use)

F = σT4 (temperature to the fourthpower times a constant)

Radiative energy flux

E = mc2 (mass times speed oflight squared)

Mass energy

ΔE = cpmΔT (mass times changein temperature times heatcapacity)

Heat Energy

E = mgh (mass times height times10ms2)

(Grav) Potential Energy

KE = frac12mv2 (mass times velocitysquared)

Kinetic Energy

W = Fd (Force times distance)Work

Energy FormulaEnergy Form

21

Heat Capacitybull Different materials have different capacities to

hold heatndash Add the same energy to different materials and yoursquoll

get different temperature risesndash Quantified as heat capacityndash Water is exceptional with 4184 JkgordmCndash Most materials are about 1000 JkgordmC (including

wood air metals)bull Example to add 10ordmC to a room 3 meters on a side

(cubic) how much energy do we needair density is 13 kgm3 and we have 27 m3 so 35 kg ofair and we need 1000 J per kg per ordmC so we end upneeding 350000 J (= 836 Cal)

Important in designing solar heated houses Also reasonit is cooler near the coast than inland

Powerbull Power is simply energy exchanged

per unit time or how fast you getwork done (Watts = Joulessec)

bull One horsepower = 745 Wbull Perform 100 J of work in 1 s and

call it 100 Wbull Run upstairs raising your 70 kg

(700 N) mass 3 m (2100 J) in 3seconds rarr 700 W output

bull Shuttle puts out a few GW(gigawatts or 109 W) of power

bull A big electrical power plant putsout around a GW That is 1 BillionJoules per second House takes afew kW (kilowatt)

22

QuestionPower is Energy used per second P= energytime Whichhighest power

A Using 100 Calories in 10 minutes

B Using 1000 Calories in 100 minutes

C Using 10 Calories in 1 minute

D Using 1 Calorie in 6 seconds

E All of the above are the same power usage

1 Calorieminute = Watts

Wind Energy

bull Wind can be used as a source of energy (windmills sailingships etc)

bull Really just kinetic energybull Example wind passing through a square meter at 8 meters

per secondndash Each second we have 8 cubic metersndash Air has density of 13 kgm3 so (8 m3)times(13 kgm3) = 104 kg of

air each secondndash frac12mv2 = frac12times(104 kg)times(8 ms)2 = 333 Jndash 333 J every second rarr 333 Watts of available power per square

meter (but to get all of it yoursquod have to stop the wind)bull Stronger winds rarr more power (like v2)

23

Chemical Energy

bull Electrostatic energy (associated with chargedparticles like electrons) is stored in the chemicalbonds of substances

bull Rearranging these bonds can release energy (somereactions require energy to be put in)

bull Typical numbers are 100ndash200 kJ per molendash a mole is 6022times1023 moleculesparticlesndash typical molecules are tens of grams per molerarrworks

out to typical numbers like several thousand Joules pergram or a few Calories per gram (remember 1 Cal = 1kcal = 4187 J)

Chemical Energy Examples

bull Burning a wooden match releases about oneBtu or 1055 Joules (a match is about 03grams) so this is gt3000 Jg nearly 1 Calg

bull Burning coal releases about 20 kJ per gramof chemical energy or roughly 5 Calg

bull Burning gasoline yields about 39 kJ pergram or just over 9 Calg

bull Very few substances over about 11 Calg

24

Energy from Food

bull We get the energy to do the things we do out of food(stored solar energy in the form of chemical energy)

bull Energy sources recognized by our digestive systemsndash Carbohydrates 4 Calories per gramndash Proteins 4 Calories per gramndash Fats 9 Calories per gram (like gasoline) (9 is more than

4 so gain more weight eating same amount of fat thancarbs or protein)

ndash Roughly 3500 Caloriespound in your body fat Less inyour protein (muscle skin etc)

Our Human Energy Budget

bull A 2000 Calorie per daydiet means 2000times4184 J =8368000 J per day

bull 837 MJ in (24 hrday) times(60 minhr)times(60 secmin)= 86400 sec correspondsto 97 Watts of power

bull Even a couch-potato at1500 Calday burns 75 W

bull More active lifestylesrequire greater Caloricintake (more energy)

25

Nutrition Labelsbull Nutrition labels tell you about the

energy content of foodbull Note they use Calories with capitol Cbull Conversions Fat 9 Calg

Carbs 4 CalgProtein 4 Calg

bull This product has 72 Cal from fat 48Cal from carbohydrates and 32 Calfrom proteinndash sum is 152 Calories compare to label

bull 152 Cal = 636 kJ enough to climbabout 1000 meters (64 kg person)

bull 1kwh = 860 Cal or about 14 lb bodyfat

bull 1 gal of gas has 31000 Calories

Mass-energy

bull Einsteinrsquos famous relationE = mc2

relates mass to energybull In effect they are the same thing

ndash one can be transformed into the otherndash physicists speak generally of mass-energy

bull Seldom experienced in daily life directlyndash Happens at large scale in the center of the sun and in

nuclear bombs and reactorsndash Actually does happen at barely detectable level in all

energy transactions but the effect is tiny

26

E = mc2 Examples

bull The energy equivalent of one gram of material(any composition) is (0001 kg)times(30times108 ms)2

= 90times1013 J = 90000000000000 J = 90 TJndash Man thatrsquos bigndash Our global energy budget is equivalent to 1000 kgyr

(thatrsquos about 1 ton per year)bull If one gram of material undergoes a chemical

reaction losing about 9000 J of energy howmuch mass does it lose

9000 J = Δmc2 so Δm = 9000c2 = 9times1039times1016

= 10-13 kg (would we ever notice)

Solar Energy is Nuclear Using E= mc2

bull Thermonuclear fusion reactions in the sunrsquos centerndash Sun is 16 million degrees Celsius in its centerndash Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then heliumndash Reaction per atom 20 million times more energetic than chemical

reactions in general

4 protonsmass = 4029

4He nucleusmass = 40015

2 neutrinos photons (light)

27

E = mc2 in Sun

bull Helium nucleus is lighter than the four protonsbull Mass difference is 4029 - 40015 = 00276 amu

ndash 1 amu (atomic mass unit) is 16605times10-27 kgndash difference of 458times10-29 kgndash multiply by c2 to get 412times10-12 Jndash 1 mole (6022times1023 particles) of protons rarr 25times1012 Jndash typical chemical reactions are 100-200 kJmolendash nuclear fusion is ~20 million times more potent stuffndash Nuclear fusion is energy source of hydrogen bomb

Energy from Lightbull The tremendous energy from the sun is released as light So light

carries energybull Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiationbull Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequencybull Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellipbull All objects emit ldquolightrdquobull The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter moreradiation and color is ldquobluerrdquo

28

Emitted Radiationrsquos Color andIntensity depend on Temperature

Object

YouHeat LampCandle FlameBulb FilamentSunrsquos SurfaceNeutron StarMolecules in deep space

Temperature

~ 30 C~ 500 C~ 1700 C~ 2700 C~ 5500 C~ millions C

lt -272C

Color

Infrared (invisible)Dull redDim orangeYellowBrilliant whiteX-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted lightThe hotter it gets the more intense the radiation (more energy)

ldquoBlackbodyrdquo or Planck Spectrum

29

Same thing on logarithmic scale

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm(note 0degC = 273degK 300degK = 27degC = 81degF)

Okay but how much energybull The power given off of a surface in the form of light is

proportional to the fourth power of temperatureF = σT4 in Watts per square meter

ndash the constant σ is numerically 567times10-8 WordmK4m2

ndash easy to remember constant 5678ndash temperature must be in Kelvin

bull ordmK = ordmC + 273bull ordmC = (59)times(ordmF ndash32)

bull Example radiation from your body(567 times10-8) times(310)4 = 523 Watts per square meter(if naked in the cold of space donrsquot let this happen to you)

30

Radiant Energy continued

bull Example The sun is 5800ordmK on its surface soF = σT4 = (567times10-8)times(5800)4 = 64times107 Wm2

Summing over entire surface area of sun gives39times1026 W

bull Compare to total capacity of energy production onearth 33times1012 Wndash Single power plant typically 05ndash10 GW (109 W)

bull In earthly situations radiated power out partiallybalanced by radiated power in from other sourcesndash Not 523 Wm2 in 70ordmF room more like 100 Wm2

bull goes like σTh4 ndash σTc

4

Electrical Energybull Opposite charges attract so electrons are attracted to

protons This holds atoms togetherbull It takes energy to pull electrons off their atomsbull Electrons want to get back home to their protons They can

only travel through conductors like wires not throughinsulators like plastic paper or wood They will gothrough miles of wire to get home to their protons

bull This is how electricity works The electronrsquos energy canbe stolen as it goes home Can be used in many manyways

bull Note electricity is not a primary source of energy Energy(from burning coal nat gas from hydro wind nuke orsolar) is used to pull of electrons and that energy can bemoved through wires and got back at will

31

And those are the majorplayershellip

bull Wersquove now seen most of the major energyplayersndash work as force times distancendash kinetic energy (wind ocean currents)ndash gravitational potential energy (hydroelectric tidal)ndash chemical energy (fossil fuels batteries food biomass)ndash heat energy (power plants space heating)ndash mass-energy (nuclear sources sunrsquos energy)ndash radiant energy (solar energy)ndash electrical energy (energy of electrons separated from

their atoms)

Conservation and Exchange ofEnergy

Nothing Comes for Free

32

Energy is Conservedbull Conservation of Energy is different from Energy

Conservation the latter being about using energywisely

bull Conservation of Energy means energy is neithercreated nor destroyed The amount of energy inthe Universe is constant

bull Donrsquot we create energy at a power plantndash Oh that this were truemdashno we simply transform

energy at our power plantsbull Doesnrsquot the sun create energy

ndash Nopemdashit exchanges mass for energybull Donrsquot batteries give us new energy

ndash Nope just convert stored chemical energy to electricalenergy Someone had to put that energy in there

height referenceh

Energy Exchangebull Though the total energy of a system is constant

the form of the energy can changebull A simple example is that of a simple pendulum in

which a continual exchange goes on betweenkinetic and potential energy

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

33

Perpetual Motion

bull Why wonrsquot the pendulum swing foreverbull Itrsquos hard to design a system free of energy pathsbull The pendulum slows down by several mechanisms

ndash Friction at the contact point requires force to opposeforce acts through distance rarr work is done

ndash Air resistance must push through air with a force(through a distance) rarr work is done

ndash Gets some air swirling puts kinetic energy into air (notreally fair to separate these last two)

bull Perpetual motion means no loss of energyndash solar system orbits come very close

Some Energy Chains

bull A coffee mug with some gravitational potentialenergy is dropped

bull potential energy turns into kinetic energybull kinetic energy of the mug goes into

ndash ripping the mug apart (chemical breaking bonds)ndash sending the pieces flying (kinetic)ndash into soundndash into heating the floor and pieces through friction as the

pieces slide to a stopbull In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored inthe potential energy)

34

Gasoline Examplebull Put gas in your car containing 9 Calgbull Combust gas turning 9 Calg into kinetic energy of

explosionbull Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a wholebull That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water andsurrounding air) and friction of transmission system(heat) and noise of engine (heating the air) etc

bull Much of energy goes into stirring the air (ends up as heat)bull Apply the brakes and convert kinetic energy into heatbull It all ends up as waste heat ultimately

Bouncing Ballbull Superball has gravitational potential energybull Drop the ball and this becomes kinetic energybull Ball hits ground and compresses (force times

distance) storing energy in the springbull Ball releases this mechanically stored energy

and it goes back into kinetic form (bouncesup)

bull Inefficiencies in ldquospringrdquo end up heating theball and the floor and stirring the air a bit

bull In the end all is heat

35

Why donrsquot we get hotter andhotter

bull If all these processes end up as heat why arenrsquotwe continually getting hotter

bull If earth retained all its heat we would get hotterbull All of earthrsquos heat is radiated away

F = σT4

bull If we dump more power the temperature goes upthe radiated power increases dramaticallyndash comes to equilibrium power dumped = power radiatedndash stable against perturbation T tracks power budget

Rough numbers

bull How much power does the earth radiatebull F = σT4 for T = 288ordmK = 15ordmC is 390 Wm2

bull Summed over entire surface area (4πR2 where R= 6378000 meters) is 20times1017 W

bull Global production is 3times1012 Wbull Solar radiation incident on earth is 18times1017 W

ndash just solar luminosity of 39times1026 W divided bygeometrical fraction that points at earth

bull Amazing coincidence of numbers (or is ithellip)

36

No Energy for Free

bull No matter what you canrsquot create energy out ofnothing it has to come from somewhere

bull We can transform energy from one form toanother we can store energy we can utilizeenergy being conveyed from natural sources

bull The net energy of the entire Universe is constantbull The best we can do is scrape up some useful

crumbs

Examplesbull Unit conversion

ndash 100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Calndash 100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 Jndash 100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWhndash 10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWhndash How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86Calorieshour About what average person eats

ndash Gasoline is $3gal Electricity if $015kWh Which is moreexpensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh)= $008kWh for gasoline Gasoline is cheap in the USA

37

Examplesbull Power vs Energy (P=Etime E = P t t = EP)

ndash Car goes 60 miles in one hour and uses 3 gal of gas What wastotal power in Watts P=Et Power = (3 gal1 hour) = 3galhr(366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W[Alternative method 3 galhr (132000000 J1 gal) (1 hr3600sec) = 110000 Jsec = 110000 W

ndash 1000 W space heater is on for 3 hours How much does it cost ifelectricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr(1kW1000W) = 3kWh ($15kWh) = $45 [Alternative methodE = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000J (1 kWh3600000J) = 3 kWh Again 45 cents

ndash AAA Battery contains 33 Calories of chemical energy How longcan it run a 2 Watt light bulb time = EP time = 33 Calories2W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1hr3600 sec) = 19 hours

QuestionThe US uses about 7 Gbarrels of oil each year This couldbe converted into which of the following units

A Joules B Watts C QBtus D Dollars $ E Any of the above

38

QuestionIf one barrel of oil contains 1700 kWh of energy how manyWatts is 7 Gbarrelyear

A 1400 GW (Giga Watts)

B 14 GW

C 11900 W

D 119 MW

E 1 x 1011 W

QuestionIf the total yearly oil use in the US is about 1400 GW howmany 1000 MW nuclear reactors will need to be built toreplace all oil use with electricity

A Only one will be needed

B Around 14

C Around 140

D Around 1400

E Cant convert Watts to reactors power vs energy

39

More Power Examplesbull How much power does it take to lift 10 kg up 2 meters in 2

secondsmgh = (10 kg)times(10 ms2)times(2 m) = 200J

200 J in 2 seconds rarr 100 Wattsbull If you want to heat the 3 m cubic room by 10ordmC with a

1000 W space heater how long will it takeWe know from before that the room needs to have 360000 J addedto it so at 1000 W = 1000 Js this will take 360 seconds or sixminutes

But the walls need to be warmed up too so it will actually takelonger (and depends on quality of insulation etc)

A note on arithmetic of unitsbull You should carry units in your calculations and multiply and divide them

as if they were numbersbull Example the force of air drag is given bybull Fdrag = frac12cDrAv2

bull cD is a dimensionless drag coefficientbull r is the density of air 13 kgm3

bull A is the cross-sectional area of the body in m2

bull v is the velocity in msbull units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) =

kgmiddotmiddotmm22middotmiddotmm22

m3middotmiddotss22kgmiddotmiddotmm44

m3middotmiddotss22= = kgmiddotmiddotmsms22 = = NewtonsNewtons

21

Heat Capacitybull Different materials have different capacities to

hold heatndash Add the same energy to different materials and yoursquoll

get different temperature risesndash Quantified as heat capacityndash Water is exceptional with 4184 JkgordmCndash Most materials are about 1000 JkgordmC (including

wood air metals)bull Example to add 10ordmC to a room 3 meters on a side

(cubic) how much energy do we needair density is 13 kgm3 and we have 27 m3 so 35 kg ofair and we need 1000 J per kg per ordmC so we end upneeding 350000 J (= 836 Cal)

Important in designing solar heated houses Also reasonit is cooler near the coast than inland

Powerbull Power is simply energy exchanged

per unit time or how fast you getwork done (Watts = Joulessec)

bull One horsepower = 745 Wbull Perform 100 J of work in 1 s and

call it 100 Wbull Run upstairs raising your 70 kg

(700 N) mass 3 m (2100 J) in 3seconds rarr 700 W output

bull Shuttle puts out a few GW(gigawatts or 109 W) of power

bull A big electrical power plant putsout around a GW That is 1 BillionJoules per second House takes afew kW (kilowatt)

22

QuestionPower is Energy used per second P= energytime Whichhighest power

A Using 100 Calories in 10 minutes

B Using 1000 Calories in 100 minutes

C Using 10 Calories in 1 minute

D Using 1 Calorie in 6 seconds

E All of the above are the same power usage

1 Calorieminute = Watts

Wind Energy

bull Wind can be used as a source of energy (windmills sailingships etc)

bull Really just kinetic energybull Example wind passing through a square meter at 8 meters

per secondndash Each second we have 8 cubic metersndash Air has density of 13 kgm3 so (8 m3)times(13 kgm3) = 104 kg of

air each secondndash frac12mv2 = frac12times(104 kg)times(8 ms)2 = 333 Jndash 333 J every second rarr 333 Watts of available power per square

meter (but to get all of it yoursquod have to stop the wind)bull Stronger winds rarr more power (like v2)

23

Chemical Energy

bull Electrostatic energy (associated with chargedparticles like electrons) is stored in the chemicalbonds of substances

bull Rearranging these bonds can release energy (somereactions require energy to be put in)

bull Typical numbers are 100ndash200 kJ per molendash a mole is 6022times1023 moleculesparticlesndash typical molecules are tens of grams per molerarrworks

out to typical numbers like several thousand Joules pergram or a few Calories per gram (remember 1 Cal = 1kcal = 4187 J)

Chemical Energy Examples

bull Burning a wooden match releases about oneBtu or 1055 Joules (a match is about 03grams) so this is gt3000 Jg nearly 1 Calg

bull Burning coal releases about 20 kJ per gramof chemical energy or roughly 5 Calg

bull Burning gasoline yields about 39 kJ pergram or just over 9 Calg

bull Very few substances over about 11 Calg

24

Energy from Food

bull We get the energy to do the things we do out of food(stored solar energy in the form of chemical energy)

bull Energy sources recognized by our digestive systemsndash Carbohydrates 4 Calories per gramndash Proteins 4 Calories per gramndash Fats 9 Calories per gram (like gasoline) (9 is more than

4 so gain more weight eating same amount of fat thancarbs or protein)

ndash Roughly 3500 Caloriespound in your body fat Less inyour protein (muscle skin etc)

Our Human Energy Budget

bull A 2000 Calorie per daydiet means 2000times4184 J =8368000 J per day

bull 837 MJ in (24 hrday) times(60 minhr)times(60 secmin)= 86400 sec correspondsto 97 Watts of power

bull Even a couch-potato at1500 Calday burns 75 W

bull More active lifestylesrequire greater Caloricintake (more energy)

25

Nutrition Labelsbull Nutrition labels tell you about the

energy content of foodbull Note they use Calories with capitol Cbull Conversions Fat 9 Calg

Carbs 4 CalgProtein 4 Calg

bull This product has 72 Cal from fat 48Cal from carbohydrates and 32 Calfrom proteinndash sum is 152 Calories compare to label

bull 152 Cal = 636 kJ enough to climbabout 1000 meters (64 kg person)

bull 1kwh = 860 Cal or about 14 lb bodyfat

bull 1 gal of gas has 31000 Calories

Mass-energy

bull Einsteinrsquos famous relationE = mc2

relates mass to energybull In effect they are the same thing

ndash one can be transformed into the otherndash physicists speak generally of mass-energy

bull Seldom experienced in daily life directlyndash Happens at large scale in the center of the sun and in

nuclear bombs and reactorsndash Actually does happen at barely detectable level in all

energy transactions but the effect is tiny

26

E = mc2 Examples

bull The energy equivalent of one gram of material(any composition) is (0001 kg)times(30times108 ms)2

= 90times1013 J = 90000000000000 J = 90 TJndash Man thatrsquos bigndash Our global energy budget is equivalent to 1000 kgyr

(thatrsquos about 1 ton per year)bull If one gram of material undergoes a chemical

reaction losing about 9000 J of energy howmuch mass does it lose

9000 J = Δmc2 so Δm = 9000c2 = 9times1039times1016

= 10-13 kg (would we ever notice)

Solar Energy is Nuclear Using E= mc2

bull Thermonuclear fusion reactions in the sunrsquos centerndash Sun is 16 million degrees Celsius in its centerndash Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then heliumndash Reaction per atom 20 million times more energetic than chemical

reactions in general

4 protonsmass = 4029

4He nucleusmass = 40015

2 neutrinos photons (light)

27

E = mc2 in Sun

bull Helium nucleus is lighter than the four protonsbull Mass difference is 4029 - 40015 = 00276 amu

ndash 1 amu (atomic mass unit) is 16605times10-27 kgndash difference of 458times10-29 kgndash multiply by c2 to get 412times10-12 Jndash 1 mole (6022times1023 particles) of protons rarr 25times1012 Jndash typical chemical reactions are 100-200 kJmolendash nuclear fusion is ~20 million times more potent stuffndash Nuclear fusion is energy source of hydrogen bomb

Energy from Lightbull The tremendous energy from the sun is released as light So light

carries energybull Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiationbull Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequencybull Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellipbull All objects emit ldquolightrdquobull The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter moreradiation and color is ldquobluerrdquo

28

Emitted Radiationrsquos Color andIntensity depend on Temperature

Object

YouHeat LampCandle FlameBulb FilamentSunrsquos SurfaceNeutron StarMolecules in deep space

Temperature

~ 30 C~ 500 C~ 1700 C~ 2700 C~ 5500 C~ millions C

lt -272C

Color

Infrared (invisible)Dull redDim orangeYellowBrilliant whiteX-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted lightThe hotter it gets the more intense the radiation (more energy)

ldquoBlackbodyrdquo or Planck Spectrum

29

Same thing on logarithmic scale

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm(note 0degC = 273degK 300degK = 27degC = 81degF)

Okay but how much energybull The power given off of a surface in the form of light is

proportional to the fourth power of temperatureF = σT4 in Watts per square meter

ndash the constant σ is numerically 567times10-8 WordmK4m2

ndash easy to remember constant 5678ndash temperature must be in Kelvin

bull ordmK = ordmC + 273bull ordmC = (59)times(ordmF ndash32)

bull Example radiation from your body(567 times10-8) times(310)4 = 523 Watts per square meter(if naked in the cold of space donrsquot let this happen to you)

30

Radiant Energy continued

bull Example The sun is 5800ordmK on its surface soF = σT4 = (567times10-8)times(5800)4 = 64times107 Wm2

Summing over entire surface area of sun gives39times1026 W

bull Compare to total capacity of energy production onearth 33times1012 Wndash Single power plant typically 05ndash10 GW (109 W)

bull In earthly situations radiated power out partiallybalanced by radiated power in from other sourcesndash Not 523 Wm2 in 70ordmF room more like 100 Wm2

bull goes like σTh4 ndash σTc

4

Electrical Energybull Opposite charges attract so electrons are attracted to

protons This holds atoms togetherbull It takes energy to pull electrons off their atomsbull Electrons want to get back home to their protons They can

only travel through conductors like wires not throughinsulators like plastic paper or wood They will gothrough miles of wire to get home to their protons

bull This is how electricity works The electronrsquos energy canbe stolen as it goes home Can be used in many manyways

bull Note electricity is not a primary source of energy Energy(from burning coal nat gas from hydro wind nuke orsolar) is used to pull of electrons and that energy can bemoved through wires and got back at will

31

And those are the majorplayershellip

bull Wersquove now seen most of the major energyplayersndash work as force times distancendash kinetic energy (wind ocean currents)ndash gravitational potential energy (hydroelectric tidal)ndash chemical energy (fossil fuels batteries food biomass)ndash heat energy (power plants space heating)ndash mass-energy (nuclear sources sunrsquos energy)ndash radiant energy (solar energy)ndash electrical energy (energy of electrons separated from

their atoms)

Conservation and Exchange ofEnergy

Nothing Comes for Free

32

Energy is Conservedbull Conservation of Energy is different from Energy

Conservation the latter being about using energywisely

bull Conservation of Energy means energy is neithercreated nor destroyed The amount of energy inthe Universe is constant

bull Donrsquot we create energy at a power plantndash Oh that this were truemdashno we simply transform

energy at our power plantsbull Doesnrsquot the sun create energy

ndash Nopemdashit exchanges mass for energybull Donrsquot batteries give us new energy

ndash Nope just convert stored chemical energy to electricalenergy Someone had to put that energy in there

height referenceh

Energy Exchangebull Though the total energy of a system is constant

the form of the energy can changebull A simple example is that of a simple pendulum in

which a continual exchange goes on betweenkinetic and potential energy

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

33

Perpetual Motion

bull Why wonrsquot the pendulum swing foreverbull Itrsquos hard to design a system free of energy pathsbull The pendulum slows down by several mechanisms

ndash Friction at the contact point requires force to opposeforce acts through distance rarr work is done

ndash Air resistance must push through air with a force(through a distance) rarr work is done

ndash Gets some air swirling puts kinetic energy into air (notreally fair to separate these last two)

bull Perpetual motion means no loss of energyndash solar system orbits come very close

Some Energy Chains

bull A coffee mug with some gravitational potentialenergy is dropped

bull potential energy turns into kinetic energybull kinetic energy of the mug goes into

ndash ripping the mug apart (chemical breaking bonds)ndash sending the pieces flying (kinetic)ndash into soundndash into heating the floor and pieces through friction as the

pieces slide to a stopbull In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored inthe potential energy)

34

Gasoline Examplebull Put gas in your car containing 9 Calgbull Combust gas turning 9 Calg into kinetic energy of

explosionbull Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a wholebull That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water andsurrounding air) and friction of transmission system(heat) and noise of engine (heating the air) etc

bull Much of energy goes into stirring the air (ends up as heat)bull Apply the brakes and convert kinetic energy into heatbull It all ends up as waste heat ultimately

Bouncing Ballbull Superball has gravitational potential energybull Drop the ball and this becomes kinetic energybull Ball hits ground and compresses (force times

distance) storing energy in the springbull Ball releases this mechanically stored energy

and it goes back into kinetic form (bouncesup)

bull Inefficiencies in ldquospringrdquo end up heating theball and the floor and stirring the air a bit

bull In the end all is heat

35

Why donrsquot we get hotter andhotter

bull If all these processes end up as heat why arenrsquotwe continually getting hotter

bull If earth retained all its heat we would get hotterbull All of earthrsquos heat is radiated away

F = σT4

bull If we dump more power the temperature goes upthe radiated power increases dramaticallyndash comes to equilibrium power dumped = power radiatedndash stable against perturbation T tracks power budget

Rough numbers

bull How much power does the earth radiatebull F = σT4 for T = 288ordmK = 15ordmC is 390 Wm2

bull Summed over entire surface area (4πR2 where R= 6378000 meters) is 20times1017 W

bull Global production is 3times1012 Wbull Solar radiation incident on earth is 18times1017 W

ndash just solar luminosity of 39times1026 W divided bygeometrical fraction that points at earth

bull Amazing coincidence of numbers (or is ithellip)

36

No Energy for Free

bull No matter what you canrsquot create energy out ofnothing it has to come from somewhere

bull We can transform energy from one form toanother we can store energy we can utilizeenergy being conveyed from natural sources

bull The net energy of the entire Universe is constantbull The best we can do is scrape up some useful

crumbs

Examplesbull Unit conversion

ndash 100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Calndash 100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 Jndash 100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWhndash 10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWhndash How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86Calorieshour About what average person eats

ndash Gasoline is $3gal Electricity if $015kWh Which is moreexpensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh)= $008kWh for gasoline Gasoline is cheap in the USA

37

Examplesbull Power vs Energy (P=Etime E = P t t = EP)

ndash Car goes 60 miles in one hour and uses 3 gal of gas What wastotal power in Watts P=Et Power = (3 gal1 hour) = 3galhr(366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W[Alternative method 3 galhr (132000000 J1 gal) (1 hr3600sec) = 110000 Jsec = 110000 W

ndash 1000 W space heater is on for 3 hours How much does it cost ifelectricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr(1kW1000W) = 3kWh ($15kWh) = $45 [Alternative methodE = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000J (1 kWh3600000J) = 3 kWh Again 45 cents

ndash AAA Battery contains 33 Calories of chemical energy How longcan it run a 2 Watt light bulb time = EP time = 33 Calories2W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1hr3600 sec) = 19 hours

QuestionThe US uses about 7 Gbarrels of oil each year This couldbe converted into which of the following units

A Joules B Watts C QBtus D Dollars $ E Any of the above

38

QuestionIf one barrel of oil contains 1700 kWh of energy how manyWatts is 7 Gbarrelyear

A 1400 GW (Giga Watts)

B 14 GW

C 11900 W

D 119 MW

E 1 x 1011 W

QuestionIf the total yearly oil use in the US is about 1400 GW howmany 1000 MW nuclear reactors will need to be built toreplace all oil use with electricity

A Only one will be needed

B Around 14

C Around 140

D Around 1400

E Cant convert Watts to reactors power vs energy

39

More Power Examplesbull How much power does it take to lift 10 kg up 2 meters in 2

secondsmgh = (10 kg)times(10 ms2)times(2 m) = 200J

200 J in 2 seconds rarr 100 Wattsbull If you want to heat the 3 m cubic room by 10ordmC with a

1000 W space heater how long will it takeWe know from before that the room needs to have 360000 J addedto it so at 1000 W = 1000 Js this will take 360 seconds or sixminutes

But the walls need to be warmed up too so it will actually takelonger (and depends on quality of insulation etc)

A note on arithmetic of unitsbull You should carry units in your calculations and multiply and divide them

as if they were numbersbull Example the force of air drag is given bybull Fdrag = frac12cDrAv2

bull cD is a dimensionless drag coefficientbull r is the density of air 13 kgm3

bull A is the cross-sectional area of the body in m2

bull v is the velocity in msbull units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) =

kgmiddotmiddotmm22middotmiddotmm22

m3middotmiddotss22kgmiddotmiddotmm44

m3middotmiddotss22= = kgmiddotmiddotmsms22 = = NewtonsNewtons

22

QuestionPower is Energy used per second P= energytime Whichhighest power

A Using 100 Calories in 10 minutes

B Using 1000 Calories in 100 minutes

C Using 10 Calories in 1 minute

D Using 1 Calorie in 6 seconds

E All of the above are the same power usage

1 Calorieminute = Watts

Wind Energy

bull Wind can be used as a source of energy (windmills sailingships etc)

bull Really just kinetic energybull Example wind passing through a square meter at 8 meters

per secondndash Each second we have 8 cubic metersndash Air has density of 13 kgm3 so (8 m3)times(13 kgm3) = 104 kg of

air each secondndash frac12mv2 = frac12times(104 kg)times(8 ms)2 = 333 Jndash 333 J every second rarr 333 Watts of available power per square

meter (but to get all of it yoursquod have to stop the wind)bull Stronger winds rarr more power (like v2)

23

Chemical Energy

bull Electrostatic energy (associated with chargedparticles like electrons) is stored in the chemicalbonds of substances

bull Rearranging these bonds can release energy (somereactions require energy to be put in)

bull Typical numbers are 100ndash200 kJ per molendash a mole is 6022times1023 moleculesparticlesndash typical molecules are tens of grams per molerarrworks

out to typical numbers like several thousand Joules pergram or a few Calories per gram (remember 1 Cal = 1kcal = 4187 J)

Chemical Energy Examples

bull Burning a wooden match releases about oneBtu or 1055 Joules (a match is about 03grams) so this is gt3000 Jg nearly 1 Calg

bull Burning coal releases about 20 kJ per gramof chemical energy or roughly 5 Calg

bull Burning gasoline yields about 39 kJ pergram or just over 9 Calg

bull Very few substances over about 11 Calg

24

Energy from Food

bull We get the energy to do the things we do out of food(stored solar energy in the form of chemical energy)

bull Energy sources recognized by our digestive systemsndash Carbohydrates 4 Calories per gramndash Proteins 4 Calories per gramndash Fats 9 Calories per gram (like gasoline) (9 is more than

4 so gain more weight eating same amount of fat thancarbs or protein)

ndash Roughly 3500 Caloriespound in your body fat Less inyour protein (muscle skin etc)

Our Human Energy Budget

bull A 2000 Calorie per daydiet means 2000times4184 J =8368000 J per day

bull 837 MJ in (24 hrday) times(60 minhr)times(60 secmin)= 86400 sec correspondsto 97 Watts of power

bull Even a couch-potato at1500 Calday burns 75 W

bull More active lifestylesrequire greater Caloricintake (more energy)

25

Nutrition Labelsbull Nutrition labels tell you about the

energy content of foodbull Note they use Calories with capitol Cbull Conversions Fat 9 Calg

Carbs 4 CalgProtein 4 Calg

bull This product has 72 Cal from fat 48Cal from carbohydrates and 32 Calfrom proteinndash sum is 152 Calories compare to label

bull 152 Cal = 636 kJ enough to climbabout 1000 meters (64 kg person)

bull 1kwh = 860 Cal or about 14 lb bodyfat

bull 1 gal of gas has 31000 Calories

Mass-energy

bull Einsteinrsquos famous relationE = mc2

relates mass to energybull In effect they are the same thing

ndash one can be transformed into the otherndash physicists speak generally of mass-energy

bull Seldom experienced in daily life directlyndash Happens at large scale in the center of the sun and in

nuclear bombs and reactorsndash Actually does happen at barely detectable level in all

energy transactions but the effect is tiny

26

E = mc2 Examples

bull The energy equivalent of one gram of material(any composition) is (0001 kg)times(30times108 ms)2

= 90times1013 J = 90000000000000 J = 90 TJndash Man thatrsquos bigndash Our global energy budget is equivalent to 1000 kgyr

(thatrsquos about 1 ton per year)bull If one gram of material undergoes a chemical

reaction losing about 9000 J of energy howmuch mass does it lose

9000 J = Δmc2 so Δm = 9000c2 = 9times1039times1016

= 10-13 kg (would we ever notice)

Solar Energy is Nuclear Using E= mc2

bull Thermonuclear fusion reactions in the sunrsquos centerndash Sun is 16 million degrees Celsius in its centerndash Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then heliumndash Reaction per atom 20 million times more energetic than chemical

reactions in general

4 protonsmass = 4029

4He nucleusmass = 40015

2 neutrinos photons (light)

27

E = mc2 in Sun

bull Helium nucleus is lighter than the four protonsbull Mass difference is 4029 - 40015 = 00276 amu

ndash 1 amu (atomic mass unit) is 16605times10-27 kgndash difference of 458times10-29 kgndash multiply by c2 to get 412times10-12 Jndash 1 mole (6022times1023 particles) of protons rarr 25times1012 Jndash typical chemical reactions are 100-200 kJmolendash nuclear fusion is ~20 million times more potent stuffndash Nuclear fusion is energy source of hydrogen bomb

Energy from Lightbull The tremendous energy from the sun is released as light So light

carries energybull Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiationbull Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequencybull Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellipbull All objects emit ldquolightrdquobull The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter moreradiation and color is ldquobluerrdquo

28

Emitted Radiationrsquos Color andIntensity depend on Temperature

Object

YouHeat LampCandle FlameBulb FilamentSunrsquos SurfaceNeutron StarMolecules in deep space

Temperature

~ 30 C~ 500 C~ 1700 C~ 2700 C~ 5500 C~ millions C

lt -272C

Color

Infrared (invisible)Dull redDim orangeYellowBrilliant whiteX-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted lightThe hotter it gets the more intense the radiation (more energy)

ldquoBlackbodyrdquo or Planck Spectrum

29

Same thing on logarithmic scale

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm(note 0degC = 273degK 300degK = 27degC = 81degF)

Okay but how much energybull The power given off of a surface in the form of light is

proportional to the fourth power of temperatureF = σT4 in Watts per square meter

ndash the constant σ is numerically 567times10-8 WordmK4m2

ndash easy to remember constant 5678ndash temperature must be in Kelvin

bull ordmK = ordmC + 273bull ordmC = (59)times(ordmF ndash32)

bull Example radiation from your body(567 times10-8) times(310)4 = 523 Watts per square meter(if naked in the cold of space donrsquot let this happen to you)

30

Radiant Energy continued

bull Example The sun is 5800ordmK on its surface soF = σT4 = (567times10-8)times(5800)4 = 64times107 Wm2

Summing over entire surface area of sun gives39times1026 W

bull Compare to total capacity of energy production onearth 33times1012 Wndash Single power plant typically 05ndash10 GW (109 W)

bull In earthly situations radiated power out partiallybalanced by radiated power in from other sourcesndash Not 523 Wm2 in 70ordmF room more like 100 Wm2

bull goes like σTh4 ndash σTc

4

Electrical Energybull Opposite charges attract so electrons are attracted to

protons This holds atoms togetherbull It takes energy to pull electrons off their atomsbull Electrons want to get back home to their protons They can

only travel through conductors like wires not throughinsulators like plastic paper or wood They will gothrough miles of wire to get home to their protons

bull This is how electricity works The electronrsquos energy canbe stolen as it goes home Can be used in many manyways

bull Note electricity is not a primary source of energy Energy(from burning coal nat gas from hydro wind nuke orsolar) is used to pull of electrons and that energy can bemoved through wires and got back at will

31

And those are the majorplayershellip

bull Wersquove now seen most of the major energyplayersndash work as force times distancendash kinetic energy (wind ocean currents)ndash gravitational potential energy (hydroelectric tidal)ndash chemical energy (fossil fuels batteries food biomass)ndash heat energy (power plants space heating)ndash mass-energy (nuclear sources sunrsquos energy)ndash radiant energy (solar energy)ndash electrical energy (energy of electrons separated from

their atoms)

Conservation and Exchange ofEnergy

Nothing Comes for Free

32

Energy is Conservedbull Conservation of Energy is different from Energy

Conservation the latter being about using energywisely

bull Conservation of Energy means energy is neithercreated nor destroyed The amount of energy inthe Universe is constant

bull Donrsquot we create energy at a power plantndash Oh that this were truemdashno we simply transform

energy at our power plantsbull Doesnrsquot the sun create energy

ndash Nopemdashit exchanges mass for energybull Donrsquot batteries give us new energy

ndash Nope just convert stored chemical energy to electricalenergy Someone had to put that energy in there

height referenceh

Energy Exchangebull Though the total energy of a system is constant

the form of the energy can changebull A simple example is that of a simple pendulum in

which a continual exchange goes on betweenkinetic and potential energy

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

33

Perpetual Motion

bull Why wonrsquot the pendulum swing foreverbull Itrsquos hard to design a system free of energy pathsbull The pendulum slows down by several mechanisms

ndash Friction at the contact point requires force to opposeforce acts through distance rarr work is done

ndash Air resistance must push through air with a force(through a distance) rarr work is done

ndash Gets some air swirling puts kinetic energy into air (notreally fair to separate these last two)

bull Perpetual motion means no loss of energyndash solar system orbits come very close

Some Energy Chains

bull A coffee mug with some gravitational potentialenergy is dropped

bull potential energy turns into kinetic energybull kinetic energy of the mug goes into

ndash ripping the mug apart (chemical breaking bonds)ndash sending the pieces flying (kinetic)ndash into soundndash into heating the floor and pieces through friction as the

pieces slide to a stopbull In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored inthe potential energy)

34

Gasoline Examplebull Put gas in your car containing 9 Calgbull Combust gas turning 9 Calg into kinetic energy of

explosionbull Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a wholebull That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water andsurrounding air) and friction of transmission system(heat) and noise of engine (heating the air) etc

bull Much of energy goes into stirring the air (ends up as heat)bull Apply the brakes and convert kinetic energy into heatbull It all ends up as waste heat ultimately

Bouncing Ballbull Superball has gravitational potential energybull Drop the ball and this becomes kinetic energybull Ball hits ground and compresses (force times

distance) storing energy in the springbull Ball releases this mechanically stored energy

and it goes back into kinetic form (bouncesup)

bull Inefficiencies in ldquospringrdquo end up heating theball and the floor and stirring the air a bit

bull In the end all is heat

35

Why donrsquot we get hotter andhotter

bull If all these processes end up as heat why arenrsquotwe continually getting hotter

bull If earth retained all its heat we would get hotterbull All of earthrsquos heat is radiated away

F = σT4

bull If we dump more power the temperature goes upthe radiated power increases dramaticallyndash comes to equilibrium power dumped = power radiatedndash stable against perturbation T tracks power budget

Rough numbers

bull How much power does the earth radiatebull F = σT4 for T = 288ordmK = 15ordmC is 390 Wm2

bull Summed over entire surface area (4πR2 where R= 6378000 meters) is 20times1017 W

bull Global production is 3times1012 Wbull Solar radiation incident on earth is 18times1017 W

ndash just solar luminosity of 39times1026 W divided bygeometrical fraction that points at earth

bull Amazing coincidence of numbers (or is ithellip)

36

No Energy for Free

bull No matter what you canrsquot create energy out ofnothing it has to come from somewhere

bull We can transform energy from one form toanother we can store energy we can utilizeenergy being conveyed from natural sources

bull The net energy of the entire Universe is constantbull The best we can do is scrape up some useful

crumbs

Examplesbull Unit conversion

ndash 100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Calndash 100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 Jndash 100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWhndash 10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWhndash How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86Calorieshour About what average person eats

ndash Gasoline is $3gal Electricity if $015kWh Which is moreexpensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh)= $008kWh for gasoline Gasoline is cheap in the USA

37

Examplesbull Power vs Energy (P=Etime E = P t t = EP)

ndash Car goes 60 miles in one hour and uses 3 gal of gas What wastotal power in Watts P=Et Power = (3 gal1 hour) = 3galhr(366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W[Alternative method 3 galhr (132000000 J1 gal) (1 hr3600sec) = 110000 Jsec = 110000 W

ndash 1000 W space heater is on for 3 hours How much does it cost ifelectricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr(1kW1000W) = 3kWh ($15kWh) = $45 [Alternative methodE = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000J (1 kWh3600000J) = 3 kWh Again 45 cents

ndash AAA Battery contains 33 Calories of chemical energy How longcan it run a 2 Watt light bulb time = EP time = 33 Calories2W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1hr3600 sec) = 19 hours

QuestionThe US uses about 7 Gbarrels of oil each year This couldbe converted into which of the following units

A Joules B Watts C QBtus D Dollars $ E Any of the above

38

QuestionIf one barrel of oil contains 1700 kWh of energy how manyWatts is 7 Gbarrelyear

A 1400 GW (Giga Watts)

B 14 GW

C 11900 W

D 119 MW

E 1 x 1011 W

QuestionIf the total yearly oil use in the US is about 1400 GW howmany 1000 MW nuclear reactors will need to be built toreplace all oil use with electricity

A Only one will be needed

B Around 14

C Around 140

D Around 1400

E Cant convert Watts to reactors power vs energy

39

More Power Examplesbull How much power does it take to lift 10 kg up 2 meters in 2

secondsmgh = (10 kg)times(10 ms2)times(2 m) = 200J

200 J in 2 seconds rarr 100 Wattsbull If you want to heat the 3 m cubic room by 10ordmC with a

1000 W space heater how long will it takeWe know from before that the room needs to have 360000 J addedto it so at 1000 W = 1000 Js this will take 360 seconds or sixminutes

But the walls need to be warmed up too so it will actually takelonger (and depends on quality of insulation etc)

A note on arithmetic of unitsbull You should carry units in your calculations and multiply and divide them

as if they were numbersbull Example the force of air drag is given bybull Fdrag = frac12cDrAv2

bull cD is a dimensionless drag coefficientbull r is the density of air 13 kgm3

bull A is the cross-sectional area of the body in m2

bull v is the velocity in msbull units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) =

kgmiddotmiddotmm22middotmiddotmm22

m3middotmiddotss22kgmiddotmiddotmm44

m3middotmiddotss22= = kgmiddotmiddotmsms22 = = NewtonsNewtons

23

Chemical Energy

bull Electrostatic energy (associated with chargedparticles like electrons) is stored in the chemicalbonds of substances

bull Rearranging these bonds can release energy (somereactions require energy to be put in)

bull Typical numbers are 100ndash200 kJ per molendash a mole is 6022times1023 moleculesparticlesndash typical molecules are tens of grams per molerarrworks

out to typical numbers like several thousand Joules pergram or a few Calories per gram (remember 1 Cal = 1kcal = 4187 J)

Chemical Energy Examples

bull Burning a wooden match releases about oneBtu or 1055 Joules (a match is about 03grams) so this is gt3000 Jg nearly 1 Calg

bull Burning coal releases about 20 kJ per gramof chemical energy or roughly 5 Calg

bull Burning gasoline yields about 39 kJ pergram or just over 9 Calg

bull Very few substances over about 11 Calg

24

Energy from Food

bull We get the energy to do the things we do out of food(stored solar energy in the form of chemical energy)

bull Energy sources recognized by our digestive systemsndash Carbohydrates 4 Calories per gramndash Proteins 4 Calories per gramndash Fats 9 Calories per gram (like gasoline) (9 is more than

4 so gain more weight eating same amount of fat thancarbs or protein)

ndash Roughly 3500 Caloriespound in your body fat Less inyour protein (muscle skin etc)

Our Human Energy Budget

bull A 2000 Calorie per daydiet means 2000times4184 J =8368000 J per day

bull 837 MJ in (24 hrday) times(60 minhr)times(60 secmin)= 86400 sec correspondsto 97 Watts of power

bull Even a couch-potato at1500 Calday burns 75 W

bull More active lifestylesrequire greater Caloricintake (more energy)

25

Nutrition Labelsbull Nutrition labels tell you about the

energy content of foodbull Note they use Calories with capitol Cbull Conversions Fat 9 Calg

Carbs 4 CalgProtein 4 Calg

bull This product has 72 Cal from fat 48Cal from carbohydrates and 32 Calfrom proteinndash sum is 152 Calories compare to label

bull 152 Cal = 636 kJ enough to climbabout 1000 meters (64 kg person)

bull 1kwh = 860 Cal or about 14 lb bodyfat

bull 1 gal of gas has 31000 Calories

Mass-energy

bull Einsteinrsquos famous relationE = mc2

relates mass to energybull In effect they are the same thing

ndash one can be transformed into the otherndash physicists speak generally of mass-energy

bull Seldom experienced in daily life directlyndash Happens at large scale in the center of the sun and in

nuclear bombs and reactorsndash Actually does happen at barely detectable level in all

energy transactions but the effect is tiny

26

E = mc2 Examples

bull The energy equivalent of one gram of material(any composition) is (0001 kg)times(30times108 ms)2

= 90times1013 J = 90000000000000 J = 90 TJndash Man thatrsquos bigndash Our global energy budget is equivalent to 1000 kgyr

(thatrsquos about 1 ton per year)bull If one gram of material undergoes a chemical

reaction losing about 9000 J of energy howmuch mass does it lose

9000 J = Δmc2 so Δm = 9000c2 = 9times1039times1016

= 10-13 kg (would we ever notice)

Solar Energy is Nuclear Using E= mc2

bull Thermonuclear fusion reactions in the sunrsquos centerndash Sun is 16 million degrees Celsius in its centerndash Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then heliumndash Reaction per atom 20 million times more energetic than chemical

reactions in general

4 protonsmass = 4029

4He nucleusmass = 40015

2 neutrinos photons (light)

27

E = mc2 in Sun

bull Helium nucleus is lighter than the four protonsbull Mass difference is 4029 - 40015 = 00276 amu

ndash 1 amu (atomic mass unit) is 16605times10-27 kgndash difference of 458times10-29 kgndash multiply by c2 to get 412times10-12 Jndash 1 mole (6022times1023 particles) of protons rarr 25times1012 Jndash typical chemical reactions are 100-200 kJmolendash nuclear fusion is ~20 million times more potent stuffndash Nuclear fusion is energy source of hydrogen bomb

Energy from Lightbull The tremendous energy from the sun is released as light So light

carries energybull Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiationbull Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequencybull Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellipbull All objects emit ldquolightrdquobull The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter moreradiation and color is ldquobluerrdquo

28

Emitted Radiationrsquos Color andIntensity depend on Temperature

Object

YouHeat LampCandle FlameBulb FilamentSunrsquos SurfaceNeutron StarMolecules in deep space

Temperature

~ 30 C~ 500 C~ 1700 C~ 2700 C~ 5500 C~ millions C

lt -272C

Color

Infrared (invisible)Dull redDim orangeYellowBrilliant whiteX-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted lightThe hotter it gets the more intense the radiation (more energy)

ldquoBlackbodyrdquo or Planck Spectrum

29

Same thing on logarithmic scale

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm(note 0degC = 273degK 300degK = 27degC = 81degF)

Okay but how much energybull The power given off of a surface in the form of light is

proportional to the fourth power of temperatureF = σT4 in Watts per square meter

ndash the constant σ is numerically 567times10-8 WordmK4m2

ndash easy to remember constant 5678ndash temperature must be in Kelvin

bull ordmK = ordmC + 273bull ordmC = (59)times(ordmF ndash32)

bull Example radiation from your body(567 times10-8) times(310)4 = 523 Watts per square meter(if naked in the cold of space donrsquot let this happen to you)

30

Radiant Energy continued

bull Example The sun is 5800ordmK on its surface soF = σT4 = (567times10-8)times(5800)4 = 64times107 Wm2

Summing over entire surface area of sun gives39times1026 W

bull Compare to total capacity of energy production onearth 33times1012 Wndash Single power plant typically 05ndash10 GW (109 W)

bull In earthly situations radiated power out partiallybalanced by radiated power in from other sourcesndash Not 523 Wm2 in 70ordmF room more like 100 Wm2

bull goes like σTh4 ndash σTc

4

Electrical Energybull Opposite charges attract so electrons are attracted to

protons This holds atoms togetherbull It takes energy to pull electrons off their atomsbull Electrons want to get back home to their protons They can

only travel through conductors like wires not throughinsulators like plastic paper or wood They will gothrough miles of wire to get home to their protons

bull This is how electricity works The electronrsquos energy canbe stolen as it goes home Can be used in many manyways

bull Note electricity is not a primary source of energy Energy(from burning coal nat gas from hydro wind nuke orsolar) is used to pull of electrons and that energy can bemoved through wires and got back at will

31

And those are the majorplayershellip

bull Wersquove now seen most of the major energyplayersndash work as force times distancendash kinetic energy (wind ocean currents)ndash gravitational potential energy (hydroelectric tidal)ndash chemical energy (fossil fuels batteries food biomass)ndash heat energy (power plants space heating)ndash mass-energy (nuclear sources sunrsquos energy)ndash radiant energy (solar energy)ndash electrical energy (energy of electrons separated from

their atoms)

Conservation and Exchange ofEnergy

Nothing Comes for Free

32

Energy is Conservedbull Conservation of Energy is different from Energy

Conservation the latter being about using energywisely

bull Conservation of Energy means energy is neithercreated nor destroyed The amount of energy inthe Universe is constant

bull Donrsquot we create energy at a power plantndash Oh that this were truemdashno we simply transform

energy at our power plantsbull Doesnrsquot the sun create energy

ndash Nopemdashit exchanges mass for energybull Donrsquot batteries give us new energy

ndash Nope just convert stored chemical energy to electricalenergy Someone had to put that energy in there

height referenceh

Energy Exchangebull Though the total energy of a system is constant

the form of the energy can changebull A simple example is that of a simple pendulum in

which a continual exchange goes on betweenkinetic and potential energy

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

33

Perpetual Motion

bull Why wonrsquot the pendulum swing foreverbull Itrsquos hard to design a system free of energy pathsbull The pendulum slows down by several mechanisms

ndash Friction at the contact point requires force to opposeforce acts through distance rarr work is done

ndash Air resistance must push through air with a force(through a distance) rarr work is done

ndash Gets some air swirling puts kinetic energy into air (notreally fair to separate these last two)

bull Perpetual motion means no loss of energyndash solar system orbits come very close

Some Energy Chains

bull A coffee mug with some gravitational potentialenergy is dropped

bull potential energy turns into kinetic energybull kinetic energy of the mug goes into

ndash ripping the mug apart (chemical breaking bonds)ndash sending the pieces flying (kinetic)ndash into soundndash into heating the floor and pieces through friction as the

pieces slide to a stopbull In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored inthe potential energy)

34

Gasoline Examplebull Put gas in your car containing 9 Calgbull Combust gas turning 9 Calg into kinetic energy of

explosionbull Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a wholebull That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water andsurrounding air) and friction of transmission system(heat) and noise of engine (heating the air) etc

bull Much of energy goes into stirring the air (ends up as heat)bull Apply the brakes and convert kinetic energy into heatbull It all ends up as waste heat ultimately

Bouncing Ballbull Superball has gravitational potential energybull Drop the ball and this becomes kinetic energybull Ball hits ground and compresses (force times

distance) storing energy in the springbull Ball releases this mechanically stored energy

and it goes back into kinetic form (bouncesup)

bull Inefficiencies in ldquospringrdquo end up heating theball and the floor and stirring the air a bit

bull In the end all is heat

35

Why donrsquot we get hotter andhotter

bull If all these processes end up as heat why arenrsquotwe continually getting hotter

bull If earth retained all its heat we would get hotterbull All of earthrsquos heat is radiated away

F = σT4

bull If we dump more power the temperature goes upthe radiated power increases dramaticallyndash comes to equilibrium power dumped = power radiatedndash stable against perturbation T tracks power budget

Rough numbers

bull How much power does the earth radiatebull F = σT4 for T = 288ordmK = 15ordmC is 390 Wm2

bull Summed over entire surface area (4πR2 where R= 6378000 meters) is 20times1017 W

bull Global production is 3times1012 Wbull Solar radiation incident on earth is 18times1017 W

ndash just solar luminosity of 39times1026 W divided bygeometrical fraction that points at earth

bull Amazing coincidence of numbers (or is ithellip)

36

No Energy for Free

bull No matter what you canrsquot create energy out ofnothing it has to come from somewhere

bull We can transform energy from one form toanother we can store energy we can utilizeenergy being conveyed from natural sources

bull The net energy of the entire Universe is constantbull The best we can do is scrape up some useful

crumbs

Examplesbull Unit conversion

ndash 100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Calndash 100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 Jndash 100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWhndash 10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWhndash How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86Calorieshour About what average person eats

ndash Gasoline is $3gal Electricity if $015kWh Which is moreexpensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh)= $008kWh for gasoline Gasoline is cheap in the USA

37

Examplesbull Power vs Energy (P=Etime E = P t t = EP)

ndash Car goes 60 miles in one hour and uses 3 gal of gas What wastotal power in Watts P=Et Power = (3 gal1 hour) = 3galhr(366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W[Alternative method 3 galhr (132000000 J1 gal) (1 hr3600sec) = 110000 Jsec = 110000 W

ndash 1000 W space heater is on for 3 hours How much does it cost ifelectricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr(1kW1000W) = 3kWh ($15kWh) = $45 [Alternative methodE = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000J (1 kWh3600000J) = 3 kWh Again 45 cents

ndash AAA Battery contains 33 Calories of chemical energy How longcan it run a 2 Watt light bulb time = EP time = 33 Calories2W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1hr3600 sec) = 19 hours

QuestionThe US uses about 7 Gbarrels of oil each year This couldbe converted into which of the following units

A Joules B Watts C QBtus D Dollars $ E Any of the above

38

QuestionIf one barrel of oil contains 1700 kWh of energy how manyWatts is 7 Gbarrelyear

A 1400 GW (Giga Watts)

B 14 GW

C 11900 W

D 119 MW

E 1 x 1011 W

QuestionIf the total yearly oil use in the US is about 1400 GW howmany 1000 MW nuclear reactors will need to be built toreplace all oil use with electricity

A Only one will be needed

B Around 14

C Around 140

D Around 1400

E Cant convert Watts to reactors power vs energy

39

More Power Examplesbull How much power does it take to lift 10 kg up 2 meters in 2

secondsmgh = (10 kg)times(10 ms2)times(2 m) = 200J

200 J in 2 seconds rarr 100 Wattsbull If you want to heat the 3 m cubic room by 10ordmC with a

1000 W space heater how long will it takeWe know from before that the room needs to have 360000 J addedto it so at 1000 W = 1000 Js this will take 360 seconds or sixminutes

But the walls need to be warmed up too so it will actually takelonger (and depends on quality of insulation etc)

A note on arithmetic of unitsbull You should carry units in your calculations and multiply and divide them

as if they were numbersbull Example the force of air drag is given bybull Fdrag = frac12cDrAv2

bull cD is a dimensionless drag coefficientbull r is the density of air 13 kgm3

bull A is the cross-sectional area of the body in m2

bull v is the velocity in msbull units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) =

kgmiddotmiddotmm22middotmiddotmm22

m3middotmiddotss22kgmiddotmiddotmm44

m3middotmiddotss22= = kgmiddotmiddotmsms22 = = NewtonsNewtons

24

Energy from Food

bull We get the energy to do the things we do out of food(stored solar energy in the form of chemical energy)

bull Energy sources recognized by our digestive systemsndash Carbohydrates 4 Calories per gramndash Proteins 4 Calories per gramndash Fats 9 Calories per gram (like gasoline) (9 is more than

4 so gain more weight eating same amount of fat thancarbs or protein)

ndash Roughly 3500 Caloriespound in your body fat Less inyour protein (muscle skin etc)

Our Human Energy Budget

bull A 2000 Calorie per daydiet means 2000times4184 J =8368000 J per day

bull 837 MJ in (24 hrday) times(60 minhr)times(60 secmin)= 86400 sec correspondsto 97 Watts of power

bull Even a couch-potato at1500 Calday burns 75 W

bull More active lifestylesrequire greater Caloricintake (more energy)

25

Nutrition Labelsbull Nutrition labels tell you about the

energy content of foodbull Note they use Calories with capitol Cbull Conversions Fat 9 Calg

Carbs 4 CalgProtein 4 Calg

bull This product has 72 Cal from fat 48Cal from carbohydrates and 32 Calfrom proteinndash sum is 152 Calories compare to label

bull 152 Cal = 636 kJ enough to climbabout 1000 meters (64 kg person)

bull 1kwh = 860 Cal or about 14 lb bodyfat

bull 1 gal of gas has 31000 Calories

Mass-energy

bull Einsteinrsquos famous relationE = mc2

relates mass to energybull In effect they are the same thing

ndash one can be transformed into the otherndash physicists speak generally of mass-energy

bull Seldom experienced in daily life directlyndash Happens at large scale in the center of the sun and in

nuclear bombs and reactorsndash Actually does happen at barely detectable level in all

energy transactions but the effect is tiny

26

E = mc2 Examples

bull The energy equivalent of one gram of material(any composition) is (0001 kg)times(30times108 ms)2

= 90times1013 J = 90000000000000 J = 90 TJndash Man thatrsquos bigndash Our global energy budget is equivalent to 1000 kgyr

(thatrsquos about 1 ton per year)bull If one gram of material undergoes a chemical

reaction losing about 9000 J of energy howmuch mass does it lose

9000 J = Δmc2 so Δm = 9000c2 = 9times1039times1016

= 10-13 kg (would we ever notice)

Solar Energy is Nuclear Using E= mc2

bull Thermonuclear fusion reactions in the sunrsquos centerndash Sun is 16 million degrees Celsius in its centerndash Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then heliumndash Reaction per atom 20 million times more energetic than chemical

reactions in general

4 protonsmass = 4029

4He nucleusmass = 40015

2 neutrinos photons (light)

27

E = mc2 in Sun

bull Helium nucleus is lighter than the four protonsbull Mass difference is 4029 - 40015 = 00276 amu

ndash 1 amu (atomic mass unit) is 16605times10-27 kgndash difference of 458times10-29 kgndash multiply by c2 to get 412times10-12 Jndash 1 mole (6022times1023 particles) of protons rarr 25times1012 Jndash typical chemical reactions are 100-200 kJmolendash nuclear fusion is ~20 million times more potent stuffndash Nuclear fusion is energy source of hydrogen bomb

Energy from Lightbull The tremendous energy from the sun is released as light So light

carries energybull Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiationbull Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequencybull Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellipbull All objects emit ldquolightrdquobull The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter moreradiation and color is ldquobluerrdquo

28

Emitted Radiationrsquos Color andIntensity depend on Temperature

Object

YouHeat LampCandle FlameBulb FilamentSunrsquos SurfaceNeutron StarMolecules in deep space

Temperature

~ 30 C~ 500 C~ 1700 C~ 2700 C~ 5500 C~ millions C

lt -272C

Color

Infrared (invisible)Dull redDim orangeYellowBrilliant whiteX-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted lightThe hotter it gets the more intense the radiation (more energy)

ldquoBlackbodyrdquo or Planck Spectrum

29

Same thing on logarithmic scale

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm(note 0degC = 273degK 300degK = 27degC = 81degF)

Okay but how much energybull The power given off of a surface in the form of light is

proportional to the fourth power of temperatureF = σT4 in Watts per square meter

ndash the constant σ is numerically 567times10-8 WordmK4m2

ndash easy to remember constant 5678ndash temperature must be in Kelvin

bull ordmK = ordmC + 273bull ordmC = (59)times(ordmF ndash32)

bull Example radiation from your body(567 times10-8) times(310)4 = 523 Watts per square meter(if naked in the cold of space donrsquot let this happen to you)

30

Radiant Energy continued

bull Example The sun is 5800ordmK on its surface soF = σT4 = (567times10-8)times(5800)4 = 64times107 Wm2

Summing over entire surface area of sun gives39times1026 W

bull Compare to total capacity of energy production onearth 33times1012 Wndash Single power plant typically 05ndash10 GW (109 W)

bull In earthly situations radiated power out partiallybalanced by radiated power in from other sourcesndash Not 523 Wm2 in 70ordmF room more like 100 Wm2

bull goes like σTh4 ndash σTc

4

Electrical Energybull Opposite charges attract so electrons are attracted to

protons This holds atoms togetherbull It takes energy to pull electrons off their atomsbull Electrons want to get back home to their protons They can

only travel through conductors like wires not throughinsulators like plastic paper or wood They will gothrough miles of wire to get home to their protons

bull This is how electricity works The electronrsquos energy canbe stolen as it goes home Can be used in many manyways

bull Note electricity is not a primary source of energy Energy(from burning coal nat gas from hydro wind nuke orsolar) is used to pull of electrons and that energy can bemoved through wires and got back at will

31

And those are the majorplayershellip

bull Wersquove now seen most of the major energyplayersndash work as force times distancendash kinetic energy (wind ocean currents)ndash gravitational potential energy (hydroelectric tidal)ndash chemical energy (fossil fuels batteries food biomass)ndash heat energy (power plants space heating)ndash mass-energy (nuclear sources sunrsquos energy)ndash radiant energy (solar energy)ndash electrical energy (energy of electrons separated from

their atoms)

Conservation and Exchange ofEnergy

Nothing Comes for Free

32

Energy is Conservedbull Conservation of Energy is different from Energy

Conservation the latter being about using energywisely

bull Conservation of Energy means energy is neithercreated nor destroyed The amount of energy inthe Universe is constant

bull Donrsquot we create energy at a power plantndash Oh that this were truemdashno we simply transform

energy at our power plantsbull Doesnrsquot the sun create energy

ndash Nopemdashit exchanges mass for energybull Donrsquot batteries give us new energy

ndash Nope just convert stored chemical energy to electricalenergy Someone had to put that energy in there

height referenceh

Energy Exchangebull Though the total energy of a system is constant

the form of the energy can changebull A simple example is that of a simple pendulum in

which a continual exchange goes on betweenkinetic and potential energy

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

33

Perpetual Motion

bull Why wonrsquot the pendulum swing foreverbull Itrsquos hard to design a system free of energy pathsbull The pendulum slows down by several mechanisms

ndash Friction at the contact point requires force to opposeforce acts through distance rarr work is done

ndash Air resistance must push through air with a force(through a distance) rarr work is done

ndash Gets some air swirling puts kinetic energy into air (notreally fair to separate these last two)

bull Perpetual motion means no loss of energyndash solar system orbits come very close

Some Energy Chains

bull A coffee mug with some gravitational potentialenergy is dropped

bull potential energy turns into kinetic energybull kinetic energy of the mug goes into

ndash ripping the mug apart (chemical breaking bonds)ndash sending the pieces flying (kinetic)ndash into soundndash into heating the floor and pieces through friction as the

pieces slide to a stopbull In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored inthe potential energy)

34

Gasoline Examplebull Put gas in your car containing 9 Calgbull Combust gas turning 9 Calg into kinetic energy of

explosionbull Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a wholebull That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water andsurrounding air) and friction of transmission system(heat) and noise of engine (heating the air) etc

bull Much of energy goes into stirring the air (ends up as heat)bull Apply the brakes and convert kinetic energy into heatbull It all ends up as waste heat ultimately

Bouncing Ballbull Superball has gravitational potential energybull Drop the ball and this becomes kinetic energybull Ball hits ground and compresses (force times

distance) storing energy in the springbull Ball releases this mechanically stored energy

and it goes back into kinetic form (bouncesup)

bull Inefficiencies in ldquospringrdquo end up heating theball and the floor and stirring the air a bit

bull In the end all is heat

35

Why donrsquot we get hotter andhotter

bull If all these processes end up as heat why arenrsquotwe continually getting hotter

bull If earth retained all its heat we would get hotterbull All of earthrsquos heat is radiated away

F = σT4

bull If we dump more power the temperature goes upthe radiated power increases dramaticallyndash comes to equilibrium power dumped = power radiatedndash stable against perturbation T tracks power budget

Rough numbers

bull How much power does the earth radiatebull F = σT4 for T = 288ordmK = 15ordmC is 390 Wm2

bull Summed over entire surface area (4πR2 where R= 6378000 meters) is 20times1017 W

bull Global production is 3times1012 Wbull Solar radiation incident on earth is 18times1017 W

ndash just solar luminosity of 39times1026 W divided bygeometrical fraction that points at earth

bull Amazing coincidence of numbers (or is ithellip)

36

No Energy for Free

bull No matter what you canrsquot create energy out ofnothing it has to come from somewhere

bull We can transform energy from one form toanother we can store energy we can utilizeenergy being conveyed from natural sources

bull The net energy of the entire Universe is constantbull The best we can do is scrape up some useful

crumbs

Examplesbull Unit conversion

ndash 100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Calndash 100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 Jndash 100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWhndash 10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWhndash How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86Calorieshour About what average person eats

ndash Gasoline is $3gal Electricity if $015kWh Which is moreexpensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh)= $008kWh for gasoline Gasoline is cheap in the USA

37

Examplesbull Power vs Energy (P=Etime E = P t t = EP)

ndash Car goes 60 miles in one hour and uses 3 gal of gas What wastotal power in Watts P=Et Power = (3 gal1 hour) = 3galhr(366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W[Alternative method 3 galhr (132000000 J1 gal) (1 hr3600sec) = 110000 Jsec = 110000 W

ndash 1000 W space heater is on for 3 hours How much does it cost ifelectricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr(1kW1000W) = 3kWh ($15kWh) = $45 [Alternative methodE = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000J (1 kWh3600000J) = 3 kWh Again 45 cents

ndash AAA Battery contains 33 Calories of chemical energy How longcan it run a 2 Watt light bulb time = EP time = 33 Calories2W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1hr3600 sec) = 19 hours

QuestionThe US uses about 7 Gbarrels of oil each year This couldbe converted into which of the following units

A Joules B Watts C QBtus D Dollars $ E Any of the above

38

QuestionIf one barrel of oil contains 1700 kWh of energy how manyWatts is 7 Gbarrelyear

A 1400 GW (Giga Watts)

B 14 GW

C 11900 W

D 119 MW

E 1 x 1011 W

QuestionIf the total yearly oil use in the US is about 1400 GW howmany 1000 MW nuclear reactors will need to be built toreplace all oil use with electricity

A Only one will be needed

B Around 14

C Around 140

D Around 1400

E Cant convert Watts to reactors power vs energy

39

More Power Examplesbull How much power does it take to lift 10 kg up 2 meters in 2

secondsmgh = (10 kg)times(10 ms2)times(2 m) = 200J

200 J in 2 seconds rarr 100 Wattsbull If you want to heat the 3 m cubic room by 10ordmC with a

1000 W space heater how long will it takeWe know from before that the room needs to have 360000 J addedto it so at 1000 W = 1000 Js this will take 360 seconds or sixminutes

But the walls need to be warmed up too so it will actually takelonger (and depends on quality of insulation etc)

A note on arithmetic of unitsbull You should carry units in your calculations and multiply and divide them

as if they were numbersbull Example the force of air drag is given bybull Fdrag = frac12cDrAv2

bull cD is a dimensionless drag coefficientbull r is the density of air 13 kgm3

bull A is the cross-sectional area of the body in m2

bull v is the velocity in msbull units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) =

kgmiddotmiddotmm22middotmiddotmm22

m3middotmiddotss22kgmiddotmiddotmm44

m3middotmiddotss22= = kgmiddotmiddotmsms22 = = NewtonsNewtons

25

Nutrition Labelsbull Nutrition labels tell you about the

energy content of foodbull Note they use Calories with capitol Cbull Conversions Fat 9 Calg

Carbs 4 CalgProtein 4 Calg

bull This product has 72 Cal from fat 48Cal from carbohydrates and 32 Calfrom proteinndash sum is 152 Calories compare to label

bull 152 Cal = 636 kJ enough to climbabout 1000 meters (64 kg person)

bull 1kwh = 860 Cal or about 14 lb bodyfat

bull 1 gal of gas has 31000 Calories

Mass-energy

bull Einsteinrsquos famous relationE = mc2

relates mass to energybull In effect they are the same thing

ndash one can be transformed into the otherndash physicists speak generally of mass-energy

bull Seldom experienced in daily life directlyndash Happens at large scale in the center of the sun and in

nuclear bombs and reactorsndash Actually does happen at barely detectable level in all

energy transactions but the effect is tiny

26

E = mc2 Examples

bull The energy equivalent of one gram of material(any composition) is (0001 kg)times(30times108 ms)2

= 90times1013 J = 90000000000000 J = 90 TJndash Man thatrsquos bigndash Our global energy budget is equivalent to 1000 kgyr

(thatrsquos about 1 ton per year)bull If one gram of material undergoes a chemical

reaction losing about 9000 J of energy howmuch mass does it lose

9000 J = Δmc2 so Δm = 9000c2 = 9times1039times1016

= 10-13 kg (would we ever notice)

Solar Energy is Nuclear Using E= mc2

bull Thermonuclear fusion reactions in the sunrsquos centerndash Sun is 16 million degrees Celsius in its centerndash Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then heliumndash Reaction per atom 20 million times more energetic than chemical

reactions in general

4 protonsmass = 4029

4He nucleusmass = 40015

2 neutrinos photons (light)

27

E = mc2 in Sun

bull Helium nucleus is lighter than the four protonsbull Mass difference is 4029 - 40015 = 00276 amu

ndash 1 amu (atomic mass unit) is 16605times10-27 kgndash difference of 458times10-29 kgndash multiply by c2 to get 412times10-12 Jndash 1 mole (6022times1023 particles) of protons rarr 25times1012 Jndash typical chemical reactions are 100-200 kJmolendash nuclear fusion is ~20 million times more potent stuffndash Nuclear fusion is energy source of hydrogen bomb

Energy from Lightbull The tremendous energy from the sun is released as light So light

carries energybull Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiationbull Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequencybull Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellipbull All objects emit ldquolightrdquobull The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter moreradiation and color is ldquobluerrdquo

28

Emitted Radiationrsquos Color andIntensity depend on Temperature

Object

YouHeat LampCandle FlameBulb FilamentSunrsquos SurfaceNeutron StarMolecules in deep space

Temperature

~ 30 C~ 500 C~ 1700 C~ 2700 C~ 5500 C~ millions C

lt -272C

Color

Infrared (invisible)Dull redDim orangeYellowBrilliant whiteX-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted lightThe hotter it gets the more intense the radiation (more energy)

ldquoBlackbodyrdquo or Planck Spectrum

29

Same thing on logarithmic scale

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm(note 0degC = 273degK 300degK = 27degC = 81degF)

Okay but how much energybull The power given off of a surface in the form of light is

proportional to the fourth power of temperatureF = σT4 in Watts per square meter

ndash the constant σ is numerically 567times10-8 WordmK4m2

ndash easy to remember constant 5678ndash temperature must be in Kelvin

bull ordmK = ordmC + 273bull ordmC = (59)times(ordmF ndash32)

bull Example radiation from your body(567 times10-8) times(310)4 = 523 Watts per square meter(if naked in the cold of space donrsquot let this happen to you)

30

Radiant Energy continued

bull Example The sun is 5800ordmK on its surface soF = σT4 = (567times10-8)times(5800)4 = 64times107 Wm2

Summing over entire surface area of sun gives39times1026 W

bull Compare to total capacity of energy production onearth 33times1012 Wndash Single power plant typically 05ndash10 GW (109 W)

bull In earthly situations radiated power out partiallybalanced by radiated power in from other sourcesndash Not 523 Wm2 in 70ordmF room more like 100 Wm2

bull goes like σTh4 ndash σTc

4

Electrical Energybull Opposite charges attract so electrons are attracted to

protons This holds atoms togetherbull It takes energy to pull electrons off their atomsbull Electrons want to get back home to their protons They can

only travel through conductors like wires not throughinsulators like plastic paper or wood They will gothrough miles of wire to get home to their protons

bull This is how electricity works The electronrsquos energy canbe stolen as it goes home Can be used in many manyways

bull Note electricity is not a primary source of energy Energy(from burning coal nat gas from hydro wind nuke orsolar) is used to pull of electrons and that energy can bemoved through wires and got back at will

31

And those are the majorplayershellip

bull Wersquove now seen most of the major energyplayersndash work as force times distancendash kinetic energy (wind ocean currents)ndash gravitational potential energy (hydroelectric tidal)ndash chemical energy (fossil fuels batteries food biomass)ndash heat energy (power plants space heating)ndash mass-energy (nuclear sources sunrsquos energy)ndash radiant energy (solar energy)ndash electrical energy (energy of electrons separated from

their atoms)

Conservation and Exchange ofEnergy

Nothing Comes for Free

32

Energy is Conservedbull Conservation of Energy is different from Energy

Conservation the latter being about using energywisely

bull Conservation of Energy means energy is neithercreated nor destroyed The amount of energy inthe Universe is constant

bull Donrsquot we create energy at a power plantndash Oh that this were truemdashno we simply transform

energy at our power plantsbull Doesnrsquot the sun create energy

ndash Nopemdashit exchanges mass for energybull Donrsquot batteries give us new energy

ndash Nope just convert stored chemical energy to electricalenergy Someone had to put that energy in there

height referenceh

Energy Exchangebull Though the total energy of a system is constant

the form of the energy can changebull A simple example is that of a simple pendulum in

which a continual exchange goes on betweenkinetic and potential energy

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

33

Perpetual Motion

bull Why wonrsquot the pendulum swing foreverbull Itrsquos hard to design a system free of energy pathsbull The pendulum slows down by several mechanisms

ndash Friction at the contact point requires force to opposeforce acts through distance rarr work is done

ndash Air resistance must push through air with a force(through a distance) rarr work is done

ndash Gets some air swirling puts kinetic energy into air (notreally fair to separate these last two)

bull Perpetual motion means no loss of energyndash solar system orbits come very close

Some Energy Chains

bull A coffee mug with some gravitational potentialenergy is dropped

bull potential energy turns into kinetic energybull kinetic energy of the mug goes into

ndash ripping the mug apart (chemical breaking bonds)ndash sending the pieces flying (kinetic)ndash into soundndash into heating the floor and pieces through friction as the

pieces slide to a stopbull In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored inthe potential energy)

34

Gasoline Examplebull Put gas in your car containing 9 Calgbull Combust gas turning 9 Calg into kinetic energy of

explosionbull Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a wholebull That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water andsurrounding air) and friction of transmission system(heat) and noise of engine (heating the air) etc

bull Much of energy goes into stirring the air (ends up as heat)bull Apply the brakes and convert kinetic energy into heatbull It all ends up as waste heat ultimately

Bouncing Ballbull Superball has gravitational potential energybull Drop the ball and this becomes kinetic energybull Ball hits ground and compresses (force times

distance) storing energy in the springbull Ball releases this mechanically stored energy

and it goes back into kinetic form (bouncesup)

bull Inefficiencies in ldquospringrdquo end up heating theball and the floor and stirring the air a bit

bull In the end all is heat

35

Why donrsquot we get hotter andhotter

bull If all these processes end up as heat why arenrsquotwe continually getting hotter

bull If earth retained all its heat we would get hotterbull All of earthrsquos heat is radiated away

F = σT4

bull If we dump more power the temperature goes upthe radiated power increases dramaticallyndash comes to equilibrium power dumped = power radiatedndash stable against perturbation T tracks power budget

Rough numbers

bull How much power does the earth radiatebull F = σT4 for T = 288ordmK = 15ordmC is 390 Wm2

bull Summed over entire surface area (4πR2 where R= 6378000 meters) is 20times1017 W

bull Global production is 3times1012 Wbull Solar radiation incident on earth is 18times1017 W

ndash just solar luminosity of 39times1026 W divided bygeometrical fraction that points at earth

bull Amazing coincidence of numbers (or is ithellip)

36

No Energy for Free

bull No matter what you canrsquot create energy out ofnothing it has to come from somewhere

bull We can transform energy from one form toanother we can store energy we can utilizeenergy being conveyed from natural sources

bull The net energy of the entire Universe is constantbull The best we can do is scrape up some useful

crumbs

Examplesbull Unit conversion

ndash 100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Calndash 100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 Jndash 100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWhndash 10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWhndash How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86Calorieshour About what average person eats

ndash Gasoline is $3gal Electricity if $015kWh Which is moreexpensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh)= $008kWh for gasoline Gasoline is cheap in the USA

37

Examplesbull Power vs Energy (P=Etime E = P t t = EP)

ndash Car goes 60 miles in one hour and uses 3 gal of gas What wastotal power in Watts P=Et Power = (3 gal1 hour) = 3galhr(366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W[Alternative method 3 galhr (132000000 J1 gal) (1 hr3600sec) = 110000 Jsec = 110000 W

ndash 1000 W space heater is on for 3 hours How much does it cost ifelectricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr(1kW1000W) = 3kWh ($15kWh) = $45 [Alternative methodE = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000J (1 kWh3600000J) = 3 kWh Again 45 cents

ndash AAA Battery contains 33 Calories of chemical energy How longcan it run a 2 Watt light bulb time = EP time = 33 Calories2W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1hr3600 sec) = 19 hours

QuestionThe US uses about 7 Gbarrels of oil each year This couldbe converted into which of the following units

A Joules B Watts C QBtus D Dollars $ E Any of the above

38

QuestionIf one barrel of oil contains 1700 kWh of energy how manyWatts is 7 Gbarrelyear

A 1400 GW (Giga Watts)

B 14 GW

C 11900 W

D 119 MW

E 1 x 1011 W

QuestionIf the total yearly oil use in the US is about 1400 GW howmany 1000 MW nuclear reactors will need to be built toreplace all oil use with electricity

A Only one will be needed

B Around 14

C Around 140

D Around 1400

E Cant convert Watts to reactors power vs energy

39

More Power Examplesbull How much power does it take to lift 10 kg up 2 meters in 2

secondsmgh = (10 kg)times(10 ms2)times(2 m) = 200J

200 J in 2 seconds rarr 100 Wattsbull If you want to heat the 3 m cubic room by 10ordmC with a

1000 W space heater how long will it takeWe know from before that the room needs to have 360000 J addedto it so at 1000 W = 1000 Js this will take 360 seconds or sixminutes

But the walls need to be warmed up too so it will actually takelonger (and depends on quality of insulation etc)

A note on arithmetic of unitsbull You should carry units in your calculations and multiply and divide them

as if they were numbersbull Example the force of air drag is given bybull Fdrag = frac12cDrAv2

bull cD is a dimensionless drag coefficientbull r is the density of air 13 kgm3

bull A is the cross-sectional area of the body in m2

bull v is the velocity in msbull units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) =

kgmiddotmiddotmm22middotmiddotmm22

m3middotmiddotss22kgmiddotmiddotmm44

m3middotmiddotss22= = kgmiddotmiddotmsms22 = = NewtonsNewtons

26

E = mc2 Examples

bull The energy equivalent of one gram of material(any composition) is (0001 kg)times(30times108 ms)2

= 90times1013 J = 90000000000000 J = 90 TJndash Man thatrsquos bigndash Our global energy budget is equivalent to 1000 kgyr

(thatrsquos about 1 ton per year)bull If one gram of material undergoes a chemical

reaction losing about 9000 J of energy howmuch mass does it lose

9000 J = Δmc2 so Δm = 9000c2 = 9times1039times1016

= 10-13 kg (would we ever notice)

Solar Energy is Nuclear Using E= mc2

bull Thermonuclear fusion reactions in the sunrsquos centerndash Sun is 16 million degrees Celsius in its centerndash Enough energy to ram protons together (despite mutual repulsion)

and make deuterium then heliumndash Reaction per atom 20 million times more energetic than chemical

reactions in general

4 protonsmass = 4029

4He nucleusmass = 40015

2 neutrinos photons (light)

27

E = mc2 in Sun

bull Helium nucleus is lighter than the four protonsbull Mass difference is 4029 - 40015 = 00276 amu

ndash 1 amu (atomic mass unit) is 16605times10-27 kgndash difference of 458times10-29 kgndash multiply by c2 to get 412times10-12 Jndash 1 mole (6022times1023 particles) of protons rarr 25times1012 Jndash typical chemical reactions are 100-200 kJmolendash nuclear fusion is ~20 million times more potent stuffndash Nuclear fusion is energy source of hydrogen bomb

Energy from Lightbull The tremendous energy from the sun is released as light So light

carries energybull Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiationbull Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequencybull Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellipbull All objects emit ldquolightrdquobull The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter moreradiation and color is ldquobluerrdquo

28

Emitted Radiationrsquos Color andIntensity depend on Temperature

Object

YouHeat LampCandle FlameBulb FilamentSunrsquos SurfaceNeutron StarMolecules in deep space

Temperature

~ 30 C~ 500 C~ 1700 C~ 2700 C~ 5500 C~ millions C

lt -272C

Color

Infrared (invisible)Dull redDim orangeYellowBrilliant whiteX-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted lightThe hotter it gets the more intense the radiation (more energy)

ldquoBlackbodyrdquo or Planck Spectrum

29

Same thing on logarithmic scale

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm(note 0degC = 273degK 300degK = 27degC = 81degF)

Okay but how much energybull The power given off of a surface in the form of light is

proportional to the fourth power of temperatureF = σT4 in Watts per square meter

ndash the constant σ is numerically 567times10-8 WordmK4m2

ndash easy to remember constant 5678ndash temperature must be in Kelvin

bull ordmK = ordmC + 273bull ordmC = (59)times(ordmF ndash32)

bull Example radiation from your body(567 times10-8) times(310)4 = 523 Watts per square meter(if naked in the cold of space donrsquot let this happen to you)

30

Radiant Energy continued

bull Example The sun is 5800ordmK on its surface soF = σT4 = (567times10-8)times(5800)4 = 64times107 Wm2

Summing over entire surface area of sun gives39times1026 W

bull Compare to total capacity of energy production onearth 33times1012 Wndash Single power plant typically 05ndash10 GW (109 W)

bull In earthly situations radiated power out partiallybalanced by radiated power in from other sourcesndash Not 523 Wm2 in 70ordmF room more like 100 Wm2

bull goes like σTh4 ndash σTc

4

Electrical Energybull Opposite charges attract so electrons are attracted to

protons This holds atoms togetherbull It takes energy to pull electrons off their atomsbull Electrons want to get back home to their protons They can

only travel through conductors like wires not throughinsulators like plastic paper or wood They will gothrough miles of wire to get home to their protons

bull This is how electricity works The electronrsquos energy canbe stolen as it goes home Can be used in many manyways

bull Note electricity is not a primary source of energy Energy(from burning coal nat gas from hydro wind nuke orsolar) is used to pull of electrons and that energy can bemoved through wires and got back at will

31

And those are the majorplayershellip

bull Wersquove now seen most of the major energyplayersndash work as force times distancendash kinetic energy (wind ocean currents)ndash gravitational potential energy (hydroelectric tidal)ndash chemical energy (fossil fuels batteries food biomass)ndash heat energy (power plants space heating)ndash mass-energy (nuclear sources sunrsquos energy)ndash radiant energy (solar energy)ndash electrical energy (energy of electrons separated from

their atoms)

Conservation and Exchange ofEnergy

Nothing Comes for Free

32

Energy is Conservedbull Conservation of Energy is different from Energy

Conservation the latter being about using energywisely

bull Conservation of Energy means energy is neithercreated nor destroyed The amount of energy inthe Universe is constant

bull Donrsquot we create energy at a power plantndash Oh that this were truemdashno we simply transform

energy at our power plantsbull Doesnrsquot the sun create energy

ndash Nopemdashit exchanges mass for energybull Donrsquot batteries give us new energy

ndash Nope just convert stored chemical energy to electricalenergy Someone had to put that energy in there

height referenceh

Energy Exchangebull Though the total energy of a system is constant

the form of the energy can changebull A simple example is that of a simple pendulum in

which a continual exchange goes on betweenkinetic and potential energy

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

33

Perpetual Motion

bull Why wonrsquot the pendulum swing foreverbull Itrsquos hard to design a system free of energy pathsbull The pendulum slows down by several mechanisms

ndash Friction at the contact point requires force to opposeforce acts through distance rarr work is done

ndash Air resistance must push through air with a force(through a distance) rarr work is done

ndash Gets some air swirling puts kinetic energy into air (notreally fair to separate these last two)

bull Perpetual motion means no loss of energyndash solar system orbits come very close

Some Energy Chains

bull A coffee mug with some gravitational potentialenergy is dropped

bull potential energy turns into kinetic energybull kinetic energy of the mug goes into

ndash ripping the mug apart (chemical breaking bonds)ndash sending the pieces flying (kinetic)ndash into soundndash into heating the floor and pieces through friction as the

pieces slide to a stopbull In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored inthe potential energy)

34

Gasoline Examplebull Put gas in your car containing 9 Calgbull Combust gas turning 9 Calg into kinetic energy of

explosionbull Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a wholebull That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water andsurrounding air) and friction of transmission system(heat) and noise of engine (heating the air) etc

bull Much of energy goes into stirring the air (ends up as heat)bull Apply the brakes and convert kinetic energy into heatbull It all ends up as waste heat ultimately

Bouncing Ballbull Superball has gravitational potential energybull Drop the ball and this becomes kinetic energybull Ball hits ground and compresses (force times

distance) storing energy in the springbull Ball releases this mechanically stored energy

and it goes back into kinetic form (bouncesup)

bull Inefficiencies in ldquospringrdquo end up heating theball and the floor and stirring the air a bit

bull In the end all is heat

35

Why donrsquot we get hotter andhotter

bull If all these processes end up as heat why arenrsquotwe continually getting hotter

bull If earth retained all its heat we would get hotterbull All of earthrsquos heat is radiated away

F = σT4

bull If we dump more power the temperature goes upthe radiated power increases dramaticallyndash comes to equilibrium power dumped = power radiatedndash stable against perturbation T tracks power budget

Rough numbers

bull How much power does the earth radiatebull F = σT4 for T = 288ordmK = 15ordmC is 390 Wm2

bull Summed over entire surface area (4πR2 where R= 6378000 meters) is 20times1017 W

bull Global production is 3times1012 Wbull Solar radiation incident on earth is 18times1017 W

ndash just solar luminosity of 39times1026 W divided bygeometrical fraction that points at earth

bull Amazing coincidence of numbers (or is ithellip)

36

No Energy for Free

bull No matter what you canrsquot create energy out ofnothing it has to come from somewhere

bull We can transform energy from one form toanother we can store energy we can utilizeenergy being conveyed from natural sources

bull The net energy of the entire Universe is constantbull The best we can do is scrape up some useful

crumbs

Examplesbull Unit conversion

ndash 100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Calndash 100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 Jndash 100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWhndash 10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWhndash How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86Calorieshour About what average person eats

ndash Gasoline is $3gal Electricity if $015kWh Which is moreexpensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh)= $008kWh for gasoline Gasoline is cheap in the USA

37

Examplesbull Power vs Energy (P=Etime E = P t t = EP)

ndash Car goes 60 miles in one hour and uses 3 gal of gas What wastotal power in Watts P=Et Power = (3 gal1 hour) = 3galhr(366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W[Alternative method 3 galhr (132000000 J1 gal) (1 hr3600sec) = 110000 Jsec = 110000 W

ndash 1000 W space heater is on for 3 hours How much does it cost ifelectricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr(1kW1000W) = 3kWh ($15kWh) = $45 [Alternative methodE = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000J (1 kWh3600000J) = 3 kWh Again 45 cents

ndash AAA Battery contains 33 Calories of chemical energy How longcan it run a 2 Watt light bulb time = EP time = 33 Calories2W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1hr3600 sec) = 19 hours

QuestionThe US uses about 7 Gbarrels of oil each year This couldbe converted into which of the following units

A Joules B Watts C QBtus D Dollars $ E Any of the above

38

QuestionIf one barrel of oil contains 1700 kWh of energy how manyWatts is 7 Gbarrelyear

A 1400 GW (Giga Watts)

B 14 GW

C 11900 W

D 119 MW

E 1 x 1011 W

QuestionIf the total yearly oil use in the US is about 1400 GW howmany 1000 MW nuclear reactors will need to be built toreplace all oil use with electricity

A Only one will be needed

B Around 14

C Around 140

D Around 1400

E Cant convert Watts to reactors power vs energy

39

More Power Examplesbull How much power does it take to lift 10 kg up 2 meters in 2

secondsmgh = (10 kg)times(10 ms2)times(2 m) = 200J

200 J in 2 seconds rarr 100 Wattsbull If you want to heat the 3 m cubic room by 10ordmC with a

1000 W space heater how long will it takeWe know from before that the room needs to have 360000 J addedto it so at 1000 W = 1000 Js this will take 360 seconds or sixminutes

But the walls need to be warmed up too so it will actually takelonger (and depends on quality of insulation etc)

A note on arithmetic of unitsbull You should carry units in your calculations and multiply and divide them

as if they were numbersbull Example the force of air drag is given bybull Fdrag = frac12cDrAv2

bull cD is a dimensionless drag coefficientbull r is the density of air 13 kgm3

bull A is the cross-sectional area of the body in m2

bull v is the velocity in msbull units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) =

kgmiddotmiddotmm22middotmiddotmm22

m3middotmiddotss22kgmiddotmiddotmm44

m3middotmiddotss22= = kgmiddotmiddotmsms22 = = NewtonsNewtons

27

E = mc2 in Sun

bull Helium nucleus is lighter than the four protonsbull Mass difference is 4029 - 40015 = 00276 amu

ndash 1 amu (atomic mass unit) is 16605times10-27 kgndash difference of 458times10-29 kgndash multiply by c2 to get 412times10-12 Jndash 1 mole (6022times1023 particles) of protons rarr 25times1012 Jndash typical chemical reactions are 100-200 kJmolendash nuclear fusion is ~20 million times more potent stuffndash Nuclear fusion is energy source of hydrogen bomb

Energy from Lightbull The tremendous energy from the sun is released as light So light

carries energybull Light is one form of electromagnetic radiation radio microwave

infrared visible light ultra-violet X-ray gamma ray radiationbull Wiggling electrons create EM radiation the faster the wiggling the

more energy and the higher the frequencybull Best way to get actual amount of energy in light is using

ldquoblackbodyrdquo radiation or thermal radiationhellipbull All objects emit ldquolightrdquobull The color and intensity of the emitted radiation

depend on the objectrsquos temperature hotter moreradiation and color is ldquobluerrdquo

28

Emitted Radiationrsquos Color andIntensity depend on Temperature

Object

YouHeat LampCandle FlameBulb FilamentSunrsquos SurfaceNeutron StarMolecules in deep space

Temperature

~ 30 C~ 500 C~ 1700 C~ 2700 C~ 5500 C~ millions C

lt -272C

Color

Infrared (invisible)Dull redDim orangeYellowBrilliant whiteX-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted lightThe hotter it gets the more intense the radiation (more energy)

ldquoBlackbodyrdquo or Planck Spectrum

29

Same thing on logarithmic scale

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm(note 0degC = 273degK 300degK = 27degC = 81degF)

Okay but how much energybull The power given off of a surface in the form of light is

proportional to the fourth power of temperatureF = σT4 in Watts per square meter

ndash the constant σ is numerically 567times10-8 WordmK4m2

ndash easy to remember constant 5678ndash temperature must be in Kelvin

bull ordmK = ordmC + 273bull ordmC = (59)times(ordmF ndash32)

bull Example radiation from your body(567 times10-8) times(310)4 = 523 Watts per square meter(if naked in the cold of space donrsquot let this happen to you)

30

Radiant Energy continued

bull Example The sun is 5800ordmK on its surface soF = σT4 = (567times10-8)times(5800)4 = 64times107 Wm2

Summing over entire surface area of sun gives39times1026 W

bull Compare to total capacity of energy production onearth 33times1012 Wndash Single power plant typically 05ndash10 GW (109 W)

bull In earthly situations radiated power out partiallybalanced by radiated power in from other sourcesndash Not 523 Wm2 in 70ordmF room more like 100 Wm2

bull goes like σTh4 ndash σTc

4

Electrical Energybull Opposite charges attract so electrons are attracted to

protons This holds atoms togetherbull It takes energy to pull electrons off their atomsbull Electrons want to get back home to their protons They can

only travel through conductors like wires not throughinsulators like plastic paper or wood They will gothrough miles of wire to get home to their protons

bull This is how electricity works The electronrsquos energy canbe stolen as it goes home Can be used in many manyways

bull Note electricity is not a primary source of energy Energy(from burning coal nat gas from hydro wind nuke orsolar) is used to pull of electrons and that energy can bemoved through wires and got back at will

31

And those are the majorplayershellip

bull Wersquove now seen most of the major energyplayersndash work as force times distancendash kinetic energy (wind ocean currents)ndash gravitational potential energy (hydroelectric tidal)ndash chemical energy (fossil fuels batteries food biomass)ndash heat energy (power plants space heating)ndash mass-energy (nuclear sources sunrsquos energy)ndash radiant energy (solar energy)ndash electrical energy (energy of electrons separated from

their atoms)

Conservation and Exchange ofEnergy

Nothing Comes for Free

32

Energy is Conservedbull Conservation of Energy is different from Energy

Conservation the latter being about using energywisely

bull Conservation of Energy means energy is neithercreated nor destroyed The amount of energy inthe Universe is constant

bull Donrsquot we create energy at a power plantndash Oh that this were truemdashno we simply transform

energy at our power plantsbull Doesnrsquot the sun create energy

ndash Nopemdashit exchanges mass for energybull Donrsquot batteries give us new energy

ndash Nope just convert stored chemical energy to electricalenergy Someone had to put that energy in there

height referenceh

Energy Exchangebull Though the total energy of a system is constant

the form of the energy can changebull A simple example is that of a simple pendulum in

which a continual exchange goes on betweenkinetic and potential energy

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

33

Perpetual Motion

bull Why wonrsquot the pendulum swing foreverbull Itrsquos hard to design a system free of energy pathsbull The pendulum slows down by several mechanisms

ndash Friction at the contact point requires force to opposeforce acts through distance rarr work is done

ndash Air resistance must push through air with a force(through a distance) rarr work is done

ndash Gets some air swirling puts kinetic energy into air (notreally fair to separate these last two)

bull Perpetual motion means no loss of energyndash solar system orbits come very close

Some Energy Chains

bull A coffee mug with some gravitational potentialenergy is dropped

bull potential energy turns into kinetic energybull kinetic energy of the mug goes into

ndash ripping the mug apart (chemical breaking bonds)ndash sending the pieces flying (kinetic)ndash into soundndash into heating the floor and pieces through friction as the

pieces slide to a stopbull In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored inthe potential energy)

34

Gasoline Examplebull Put gas in your car containing 9 Calgbull Combust gas turning 9 Calg into kinetic energy of

explosionbull Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a wholebull That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water andsurrounding air) and friction of transmission system(heat) and noise of engine (heating the air) etc

bull Much of energy goes into stirring the air (ends up as heat)bull Apply the brakes and convert kinetic energy into heatbull It all ends up as waste heat ultimately

Bouncing Ballbull Superball has gravitational potential energybull Drop the ball and this becomes kinetic energybull Ball hits ground and compresses (force times

distance) storing energy in the springbull Ball releases this mechanically stored energy

and it goes back into kinetic form (bouncesup)

bull Inefficiencies in ldquospringrdquo end up heating theball and the floor and stirring the air a bit

bull In the end all is heat

35

Why donrsquot we get hotter andhotter

bull If all these processes end up as heat why arenrsquotwe continually getting hotter

bull If earth retained all its heat we would get hotterbull All of earthrsquos heat is radiated away

F = σT4

bull If we dump more power the temperature goes upthe radiated power increases dramaticallyndash comes to equilibrium power dumped = power radiatedndash stable against perturbation T tracks power budget

Rough numbers

bull How much power does the earth radiatebull F = σT4 for T = 288ordmK = 15ordmC is 390 Wm2

bull Summed over entire surface area (4πR2 where R= 6378000 meters) is 20times1017 W

bull Global production is 3times1012 Wbull Solar radiation incident on earth is 18times1017 W

ndash just solar luminosity of 39times1026 W divided bygeometrical fraction that points at earth

bull Amazing coincidence of numbers (or is ithellip)

36

No Energy for Free

bull No matter what you canrsquot create energy out ofnothing it has to come from somewhere

bull We can transform energy from one form toanother we can store energy we can utilizeenergy being conveyed from natural sources

bull The net energy of the entire Universe is constantbull The best we can do is scrape up some useful

crumbs

Examplesbull Unit conversion

ndash 100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Calndash 100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 Jndash 100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWhndash 10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWhndash How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86Calorieshour About what average person eats

ndash Gasoline is $3gal Electricity if $015kWh Which is moreexpensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh)= $008kWh for gasoline Gasoline is cheap in the USA

37

Examplesbull Power vs Energy (P=Etime E = P t t = EP)

ndash Car goes 60 miles in one hour and uses 3 gal of gas What wastotal power in Watts P=Et Power = (3 gal1 hour) = 3galhr(366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W[Alternative method 3 galhr (132000000 J1 gal) (1 hr3600sec) = 110000 Jsec = 110000 W

ndash 1000 W space heater is on for 3 hours How much does it cost ifelectricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr(1kW1000W) = 3kWh ($15kWh) = $45 [Alternative methodE = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000J (1 kWh3600000J) = 3 kWh Again 45 cents

ndash AAA Battery contains 33 Calories of chemical energy How longcan it run a 2 Watt light bulb time = EP time = 33 Calories2W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1hr3600 sec) = 19 hours

QuestionThe US uses about 7 Gbarrels of oil each year This couldbe converted into which of the following units

A Joules B Watts C QBtus D Dollars $ E Any of the above

38

QuestionIf one barrel of oil contains 1700 kWh of energy how manyWatts is 7 Gbarrelyear

A 1400 GW (Giga Watts)

B 14 GW

C 11900 W

D 119 MW

E 1 x 1011 W

QuestionIf the total yearly oil use in the US is about 1400 GW howmany 1000 MW nuclear reactors will need to be built toreplace all oil use with electricity

A Only one will be needed

B Around 14

C Around 140

D Around 1400

E Cant convert Watts to reactors power vs energy

39

More Power Examplesbull How much power does it take to lift 10 kg up 2 meters in 2

secondsmgh = (10 kg)times(10 ms2)times(2 m) = 200J

200 J in 2 seconds rarr 100 Wattsbull If you want to heat the 3 m cubic room by 10ordmC with a

1000 W space heater how long will it takeWe know from before that the room needs to have 360000 J addedto it so at 1000 W = 1000 Js this will take 360 seconds or sixminutes

But the walls need to be warmed up too so it will actually takelonger (and depends on quality of insulation etc)

A note on arithmetic of unitsbull You should carry units in your calculations and multiply and divide them

as if they were numbersbull Example the force of air drag is given bybull Fdrag = frac12cDrAv2

bull cD is a dimensionless drag coefficientbull r is the density of air 13 kgm3

bull A is the cross-sectional area of the body in m2

bull v is the velocity in msbull units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) =

kgmiddotmiddotmm22middotmiddotmm22

m3middotmiddotss22kgmiddotmiddotmm44

m3middotmiddotss22= = kgmiddotmiddotmsms22 = = NewtonsNewtons

28

Emitted Radiationrsquos Color andIntensity depend on Temperature

Object

YouHeat LampCandle FlameBulb FilamentSunrsquos SurfaceNeutron StarMolecules in deep space

Temperature

~ 30 C~ 500 C~ 1700 C~ 2700 C~ 5500 C~ millions C

lt -272C

Color

Infrared (invisible)Dull redDim orangeYellowBrilliant whiteX-rays

Microwave or radio

The hotter it gets the ldquobluerrdquo the emitted lightThe hotter it gets the more intense the radiation (more energy)

ldquoBlackbodyrdquo or Planck Spectrum

29

Same thing on logarithmic scale

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm(note 0degC = 273degK 300degK = 27degC = 81degF)

Okay but how much energybull The power given off of a surface in the form of light is

proportional to the fourth power of temperatureF = σT4 in Watts per square meter

ndash the constant σ is numerically 567times10-8 WordmK4m2

ndash easy to remember constant 5678ndash temperature must be in Kelvin

bull ordmK = ordmC + 273bull ordmC = (59)times(ordmF ndash32)

bull Example radiation from your body(567 times10-8) times(310)4 = 523 Watts per square meter(if naked in the cold of space donrsquot let this happen to you)

30

Radiant Energy continued

bull Example The sun is 5800ordmK on its surface soF = σT4 = (567times10-8)times(5800)4 = 64times107 Wm2

Summing over entire surface area of sun gives39times1026 W

bull Compare to total capacity of energy production onearth 33times1012 Wndash Single power plant typically 05ndash10 GW (109 W)

bull In earthly situations radiated power out partiallybalanced by radiated power in from other sourcesndash Not 523 Wm2 in 70ordmF room more like 100 Wm2

bull goes like σTh4 ndash σTc

4

Electrical Energybull Opposite charges attract so electrons are attracted to

protons This holds atoms togetherbull It takes energy to pull electrons off their atomsbull Electrons want to get back home to their protons They can

only travel through conductors like wires not throughinsulators like plastic paper or wood They will gothrough miles of wire to get home to their protons

bull This is how electricity works The electronrsquos energy canbe stolen as it goes home Can be used in many manyways

bull Note electricity is not a primary source of energy Energy(from burning coal nat gas from hydro wind nuke orsolar) is used to pull of electrons and that energy can bemoved through wires and got back at will

31

And those are the majorplayershellip

bull Wersquove now seen most of the major energyplayersndash work as force times distancendash kinetic energy (wind ocean currents)ndash gravitational potential energy (hydroelectric tidal)ndash chemical energy (fossil fuels batteries food biomass)ndash heat energy (power plants space heating)ndash mass-energy (nuclear sources sunrsquos energy)ndash radiant energy (solar energy)ndash electrical energy (energy of electrons separated from

their atoms)

Conservation and Exchange ofEnergy

Nothing Comes for Free

32

Energy is Conservedbull Conservation of Energy is different from Energy

Conservation the latter being about using energywisely

bull Conservation of Energy means energy is neithercreated nor destroyed The amount of energy inthe Universe is constant

bull Donrsquot we create energy at a power plantndash Oh that this were truemdashno we simply transform

energy at our power plantsbull Doesnrsquot the sun create energy

ndash Nopemdashit exchanges mass for energybull Donrsquot batteries give us new energy

ndash Nope just convert stored chemical energy to electricalenergy Someone had to put that energy in there

height referenceh

Energy Exchangebull Though the total energy of a system is constant

the form of the energy can changebull A simple example is that of a simple pendulum in

which a continual exchange goes on betweenkinetic and potential energy

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

33

Perpetual Motion

bull Why wonrsquot the pendulum swing foreverbull Itrsquos hard to design a system free of energy pathsbull The pendulum slows down by several mechanisms

ndash Friction at the contact point requires force to opposeforce acts through distance rarr work is done

ndash Air resistance must push through air with a force(through a distance) rarr work is done

ndash Gets some air swirling puts kinetic energy into air (notreally fair to separate these last two)

bull Perpetual motion means no loss of energyndash solar system orbits come very close

Some Energy Chains

bull A coffee mug with some gravitational potentialenergy is dropped

bull potential energy turns into kinetic energybull kinetic energy of the mug goes into

ndash ripping the mug apart (chemical breaking bonds)ndash sending the pieces flying (kinetic)ndash into soundndash into heating the floor and pieces through friction as the

pieces slide to a stopbull In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored inthe potential energy)

34

Gasoline Examplebull Put gas in your car containing 9 Calgbull Combust gas turning 9 Calg into kinetic energy of

explosionbull Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a wholebull That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water andsurrounding air) and friction of transmission system(heat) and noise of engine (heating the air) etc

bull Much of energy goes into stirring the air (ends up as heat)bull Apply the brakes and convert kinetic energy into heatbull It all ends up as waste heat ultimately

Bouncing Ballbull Superball has gravitational potential energybull Drop the ball and this becomes kinetic energybull Ball hits ground and compresses (force times

distance) storing energy in the springbull Ball releases this mechanically stored energy

and it goes back into kinetic form (bouncesup)

bull Inefficiencies in ldquospringrdquo end up heating theball and the floor and stirring the air a bit

bull In the end all is heat

35

Why donrsquot we get hotter andhotter

bull If all these processes end up as heat why arenrsquotwe continually getting hotter

bull If earth retained all its heat we would get hotterbull All of earthrsquos heat is radiated away

F = σT4

bull If we dump more power the temperature goes upthe radiated power increases dramaticallyndash comes to equilibrium power dumped = power radiatedndash stable against perturbation T tracks power budget

Rough numbers

bull How much power does the earth radiatebull F = σT4 for T = 288ordmK = 15ordmC is 390 Wm2

bull Summed over entire surface area (4πR2 where R= 6378000 meters) is 20times1017 W

bull Global production is 3times1012 Wbull Solar radiation incident on earth is 18times1017 W

ndash just solar luminosity of 39times1026 W divided bygeometrical fraction that points at earth

bull Amazing coincidence of numbers (or is ithellip)

36

No Energy for Free

bull No matter what you canrsquot create energy out ofnothing it has to come from somewhere

bull We can transform energy from one form toanother we can store energy we can utilizeenergy being conveyed from natural sources

bull The net energy of the entire Universe is constantbull The best we can do is scrape up some useful

crumbs

Examplesbull Unit conversion

ndash 100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Calndash 100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 Jndash 100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWhndash 10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWhndash How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86Calorieshour About what average person eats

ndash Gasoline is $3gal Electricity if $015kWh Which is moreexpensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh)= $008kWh for gasoline Gasoline is cheap in the USA

37

Examplesbull Power vs Energy (P=Etime E = P t t = EP)

ndash Car goes 60 miles in one hour and uses 3 gal of gas What wastotal power in Watts P=Et Power = (3 gal1 hour) = 3galhr(366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W[Alternative method 3 galhr (132000000 J1 gal) (1 hr3600sec) = 110000 Jsec = 110000 W

ndash 1000 W space heater is on for 3 hours How much does it cost ifelectricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr(1kW1000W) = 3kWh ($15kWh) = $45 [Alternative methodE = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000J (1 kWh3600000J) = 3 kWh Again 45 cents

ndash AAA Battery contains 33 Calories of chemical energy How longcan it run a 2 Watt light bulb time = EP time = 33 Calories2W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1hr3600 sec) = 19 hours

QuestionThe US uses about 7 Gbarrels of oil each year This couldbe converted into which of the following units

A Joules B Watts C QBtus D Dollars $ E Any of the above

38

QuestionIf one barrel of oil contains 1700 kWh of energy how manyWatts is 7 Gbarrelyear

A 1400 GW (Giga Watts)

B 14 GW

C 11900 W

D 119 MW

E 1 x 1011 W

QuestionIf the total yearly oil use in the US is about 1400 GW howmany 1000 MW nuclear reactors will need to be built toreplace all oil use with electricity

A Only one will be needed

B Around 14

C Around 140

D Around 1400

E Cant convert Watts to reactors power vs energy

39

More Power Examplesbull How much power does it take to lift 10 kg up 2 meters in 2

secondsmgh = (10 kg)times(10 ms2)times(2 m) = 200J

200 J in 2 seconds rarr 100 Wattsbull If you want to heat the 3 m cubic room by 10ordmC with a

1000 W space heater how long will it takeWe know from before that the room needs to have 360000 J addedto it so at 1000 W = 1000 Js this will take 360 seconds or sixminutes

But the walls need to be warmed up too so it will actually takelonger (and depends on quality of insulation etc)

A note on arithmetic of unitsbull You should carry units in your calculations and multiply and divide them

as if they were numbersbull Example the force of air drag is given bybull Fdrag = frac12cDrAv2

bull cD is a dimensionless drag coefficientbull r is the density of air 13 kgm3

bull A is the cross-sectional area of the body in m2

bull v is the velocity in msbull units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) =

kgmiddotmiddotmm22middotmiddotmm22

m3middotmiddotss22kgmiddotmiddotmm44

m3middotmiddotss22= = kgmiddotmiddotmsms22 = = NewtonsNewtons

29

Same thing on logarithmic scale

Sun peaks in visible band (05 microns) light bulbs at 1 microm we at 10 microm(note 0degC = 273degK 300degK = 27degC = 81degF)

Okay but how much energybull The power given off of a surface in the form of light is

proportional to the fourth power of temperatureF = σT4 in Watts per square meter

ndash the constant σ is numerically 567times10-8 WordmK4m2

ndash easy to remember constant 5678ndash temperature must be in Kelvin

bull ordmK = ordmC + 273bull ordmC = (59)times(ordmF ndash32)

bull Example radiation from your body(567 times10-8) times(310)4 = 523 Watts per square meter(if naked in the cold of space donrsquot let this happen to you)

30

Radiant Energy continued

bull Example The sun is 5800ordmK on its surface soF = σT4 = (567times10-8)times(5800)4 = 64times107 Wm2

Summing over entire surface area of sun gives39times1026 W

bull Compare to total capacity of energy production onearth 33times1012 Wndash Single power plant typically 05ndash10 GW (109 W)

bull In earthly situations radiated power out partiallybalanced by radiated power in from other sourcesndash Not 523 Wm2 in 70ordmF room more like 100 Wm2

bull goes like σTh4 ndash σTc

4

Electrical Energybull Opposite charges attract so electrons are attracted to

protons This holds atoms togetherbull It takes energy to pull electrons off their atomsbull Electrons want to get back home to their protons They can

only travel through conductors like wires not throughinsulators like plastic paper or wood They will gothrough miles of wire to get home to their protons

bull This is how electricity works The electronrsquos energy canbe stolen as it goes home Can be used in many manyways

bull Note electricity is not a primary source of energy Energy(from burning coal nat gas from hydro wind nuke orsolar) is used to pull of electrons and that energy can bemoved through wires and got back at will

31

And those are the majorplayershellip

bull Wersquove now seen most of the major energyplayersndash work as force times distancendash kinetic energy (wind ocean currents)ndash gravitational potential energy (hydroelectric tidal)ndash chemical energy (fossil fuels batteries food biomass)ndash heat energy (power plants space heating)ndash mass-energy (nuclear sources sunrsquos energy)ndash radiant energy (solar energy)ndash electrical energy (energy of electrons separated from

their atoms)

Conservation and Exchange ofEnergy

Nothing Comes for Free

32

Energy is Conservedbull Conservation of Energy is different from Energy

Conservation the latter being about using energywisely

bull Conservation of Energy means energy is neithercreated nor destroyed The amount of energy inthe Universe is constant

bull Donrsquot we create energy at a power plantndash Oh that this were truemdashno we simply transform

energy at our power plantsbull Doesnrsquot the sun create energy

ndash Nopemdashit exchanges mass for energybull Donrsquot batteries give us new energy

ndash Nope just convert stored chemical energy to electricalenergy Someone had to put that energy in there

height referenceh

Energy Exchangebull Though the total energy of a system is constant

the form of the energy can changebull A simple example is that of a simple pendulum in

which a continual exchange goes on betweenkinetic and potential energy

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

33

Perpetual Motion

bull Why wonrsquot the pendulum swing foreverbull Itrsquos hard to design a system free of energy pathsbull The pendulum slows down by several mechanisms

ndash Friction at the contact point requires force to opposeforce acts through distance rarr work is done

ndash Air resistance must push through air with a force(through a distance) rarr work is done

ndash Gets some air swirling puts kinetic energy into air (notreally fair to separate these last two)

bull Perpetual motion means no loss of energyndash solar system orbits come very close

Some Energy Chains

bull A coffee mug with some gravitational potentialenergy is dropped

bull potential energy turns into kinetic energybull kinetic energy of the mug goes into

ndash ripping the mug apart (chemical breaking bonds)ndash sending the pieces flying (kinetic)ndash into soundndash into heating the floor and pieces through friction as the

pieces slide to a stopbull In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored inthe potential energy)

34

Gasoline Examplebull Put gas in your car containing 9 Calgbull Combust gas turning 9 Calg into kinetic energy of

explosionbull Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a wholebull That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water andsurrounding air) and friction of transmission system(heat) and noise of engine (heating the air) etc

bull Much of energy goes into stirring the air (ends up as heat)bull Apply the brakes and convert kinetic energy into heatbull It all ends up as waste heat ultimately

Bouncing Ballbull Superball has gravitational potential energybull Drop the ball and this becomes kinetic energybull Ball hits ground and compresses (force times

distance) storing energy in the springbull Ball releases this mechanically stored energy

and it goes back into kinetic form (bouncesup)

bull Inefficiencies in ldquospringrdquo end up heating theball and the floor and stirring the air a bit

bull In the end all is heat

35

Why donrsquot we get hotter andhotter

bull If all these processes end up as heat why arenrsquotwe continually getting hotter

bull If earth retained all its heat we would get hotterbull All of earthrsquos heat is radiated away

F = σT4

bull If we dump more power the temperature goes upthe radiated power increases dramaticallyndash comes to equilibrium power dumped = power radiatedndash stable against perturbation T tracks power budget

Rough numbers

bull How much power does the earth radiatebull F = σT4 for T = 288ordmK = 15ordmC is 390 Wm2

bull Summed over entire surface area (4πR2 where R= 6378000 meters) is 20times1017 W

bull Global production is 3times1012 Wbull Solar radiation incident on earth is 18times1017 W

ndash just solar luminosity of 39times1026 W divided bygeometrical fraction that points at earth

bull Amazing coincidence of numbers (or is ithellip)

36

No Energy for Free

bull No matter what you canrsquot create energy out ofnothing it has to come from somewhere

bull We can transform energy from one form toanother we can store energy we can utilizeenergy being conveyed from natural sources

bull The net energy of the entire Universe is constantbull The best we can do is scrape up some useful

crumbs

Examplesbull Unit conversion

ndash 100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Calndash 100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 Jndash 100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWhndash 10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWhndash How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86Calorieshour About what average person eats

ndash Gasoline is $3gal Electricity if $015kWh Which is moreexpensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh)= $008kWh for gasoline Gasoline is cheap in the USA

37

Examplesbull Power vs Energy (P=Etime E = P t t = EP)

ndash Car goes 60 miles in one hour and uses 3 gal of gas What wastotal power in Watts P=Et Power = (3 gal1 hour) = 3galhr(366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W[Alternative method 3 galhr (132000000 J1 gal) (1 hr3600sec) = 110000 Jsec = 110000 W

ndash 1000 W space heater is on for 3 hours How much does it cost ifelectricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr(1kW1000W) = 3kWh ($15kWh) = $45 [Alternative methodE = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000J (1 kWh3600000J) = 3 kWh Again 45 cents

ndash AAA Battery contains 33 Calories of chemical energy How longcan it run a 2 Watt light bulb time = EP time = 33 Calories2W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1hr3600 sec) = 19 hours

QuestionThe US uses about 7 Gbarrels of oil each year This couldbe converted into which of the following units

A Joules B Watts C QBtus D Dollars $ E Any of the above

38

QuestionIf one barrel of oil contains 1700 kWh of energy how manyWatts is 7 Gbarrelyear

A 1400 GW (Giga Watts)

B 14 GW

C 11900 W

D 119 MW

E 1 x 1011 W

QuestionIf the total yearly oil use in the US is about 1400 GW howmany 1000 MW nuclear reactors will need to be built toreplace all oil use with electricity

A Only one will be needed

B Around 14

C Around 140

D Around 1400

E Cant convert Watts to reactors power vs energy

39

More Power Examplesbull How much power does it take to lift 10 kg up 2 meters in 2

secondsmgh = (10 kg)times(10 ms2)times(2 m) = 200J

200 J in 2 seconds rarr 100 Wattsbull If you want to heat the 3 m cubic room by 10ordmC with a

1000 W space heater how long will it takeWe know from before that the room needs to have 360000 J addedto it so at 1000 W = 1000 Js this will take 360 seconds or sixminutes

But the walls need to be warmed up too so it will actually takelonger (and depends on quality of insulation etc)

A note on arithmetic of unitsbull You should carry units in your calculations and multiply and divide them

as if they were numbersbull Example the force of air drag is given bybull Fdrag = frac12cDrAv2

bull cD is a dimensionless drag coefficientbull r is the density of air 13 kgm3

bull A is the cross-sectional area of the body in m2

bull v is the velocity in msbull units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) =

kgmiddotmiddotmm22middotmiddotmm22

m3middotmiddotss22kgmiddotmiddotmm44

m3middotmiddotss22= = kgmiddotmiddotmsms22 = = NewtonsNewtons

30

Radiant Energy continued

bull Example The sun is 5800ordmK on its surface soF = σT4 = (567times10-8)times(5800)4 = 64times107 Wm2

Summing over entire surface area of sun gives39times1026 W

bull Compare to total capacity of energy production onearth 33times1012 Wndash Single power plant typically 05ndash10 GW (109 W)

bull In earthly situations radiated power out partiallybalanced by radiated power in from other sourcesndash Not 523 Wm2 in 70ordmF room more like 100 Wm2

bull goes like σTh4 ndash σTc

4

Electrical Energybull Opposite charges attract so electrons are attracted to

protons This holds atoms togetherbull It takes energy to pull electrons off their atomsbull Electrons want to get back home to their protons They can

only travel through conductors like wires not throughinsulators like plastic paper or wood They will gothrough miles of wire to get home to their protons

bull This is how electricity works The electronrsquos energy canbe stolen as it goes home Can be used in many manyways

bull Note electricity is not a primary source of energy Energy(from burning coal nat gas from hydro wind nuke orsolar) is used to pull of electrons and that energy can bemoved through wires and got back at will

31

And those are the majorplayershellip

bull Wersquove now seen most of the major energyplayersndash work as force times distancendash kinetic energy (wind ocean currents)ndash gravitational potential energy (hydroelectric tidal)ndash chemical energy (fossil fuels batteries food biomass)ndash heat energy (power plants space heating)ndash mass-energy (nuclear sources sunrsquos energy)ndash radiant energy (solar energy)ndash electrical energy (energy of electrons separated from

their atoms)

Conservation and Exchange ofEnergy

Nothing Comes for Free

32

Energy is Conservedbull Conservation of Energy is different from Energy

Conservation the latter being about using energywisely

bull Conservation of Energy means energy is neithercreated nor destroyed The amount of energy inthe Universe is constant

bull Donrsquot we create energy at a power plantndash Oh that this were truemdashno we simply transform

energy at our power plantsbull Doesnrsquot the sun create energy

ndash Nopemdashit exchanges mass for energybull Donrsquot batteries give us new energy

ndash Nope just convert stored chemical energy to electricalenergy Someone had to put that energy in there

height referenceh

Energy Exchangebull Though the total energy of a system is constant

the form of the energy can changebull A simple example is that of a simple pendulum in

which a continual exchange goes on betweenkinetic and potential energy

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

33

Perpetual Motion

bull Why wonrsquot the pendulum swing foreverbull Itrsquos hard to design a system free of energy pathsbull The pendulum slows down by several mechanisms

ndash Friction at the contact point requires force to opposeforce acts through distance rarr work is done

ndash Air resistance must push through air with a force(through a distance) rarr work is done

ndash Gets some air swirling puts kinetic energy into air (notreally fair to separate these last two)

bull Perpetual motion means no loss of energyndash solar system orbits come very close

Some Energy Chains

bull A coffee mug with some gravitational potentialenergy is dropped

bull potential energy turns into kinetic energybull kinetic energy of the mug goes into

ndash ripping the mug apart (chemical breaking bonds)ndash sending the pieces flying (kinetic)ndash into soundndash into heating the floor and pieces through friction as the

pieces slide to a stopbull In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored inthe potential energy)

34

Gasoline Examplebull Put gas in your car containing 9 Calgbull Combust gas turning 9 Calg into kinetic energy of

explosionbull Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a wholebull That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water andsurrounding air) and friction of transmission system(heat) and noise of engine (heating the air) etc

bull Much of energy goes into stirring the air (ends up as heat)bull Apply the brakes and convert kinetic energy into heatbull It all ends up as waste heat ultimately

Bouncing Ballbull Superball has gravitational potential energybull Drop the ball and this becomes kinetic energybull Ball hits ground and compresses (force times

distance) storing energy in the springbull Ball releases this mechanically stored energy

and it goes back into kinetic form (bouncesup)

bull Inefficiencies in ldquospringrdquo end up heating theball and the floor and stirring the air a bit

bull In the end all is heat

35

Why donrsquot we get hotter andhotter

bull If all these processes end up as heat why arenrsquotwe continually getting hotter

bull If earth retained all its heat we would get hotterbull All of earthrsquos heat is radiated away

F = σT4

bull If we dump more power the temperature goes upthe radiated power increases dramaticallyndash comes to equilibrium power dumped = power radiatedndash stable against perturbation T tracks power budget

Rough numbers

bull How much power does the earth radiatebull F = σT4 for T = 288ordmK = 15ordmC is 390 Wm2

bull Summed over entire surface area (4πR2 where R= 6378000 meters) is 20times1017 W

bull Global production is 3times1012 Wbull Solar radiation incident on earth is 18times1017 W

ndash just solar luminosity of 39times1026 W divided bygeometrical fraction that points at earth

bull Amazing coincidence of numbers (or is ithellip)

36

No Energy for Free

bull No matter what you canrsquot create energy out ofnothing it has to come from somewhere

bull We can transform energy from one form toanother we can store energy we can utilizeenergy being conveyed from natural sources

bull The net energy of the entire Universe is constantbull The best we can do is scrape up some useful

crumbs

Examplesbull Unit conversion

ndash 100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Calndash 100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 Jndash 100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWhndash 10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWhndash How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86Calorieshour About what average person eats

ndash Gasoline is $3gal Electricity if $015kWh Which is moreexpensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh)= $008kWh for gasoline Gasoline is cheap in the USA

37

Examplesbull Power vs Energy (P=Etime E = P t t = EP)

ndash Car goes 60 miles in one hour and uses 3 gal of gas What wastotal power in Watts P=Et Power = (3 gal1 hour) = 3galhr(366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W[Alternative method 3 galhr (132000000 J1 gal) (1 hr3600sec) = 110000 Jsec = 110000 W

ndash 1000 W space heater is on for 3 hours How much does it cost ifelectricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr(1kW1000W) = 3kWh ($15kWh) = $45 [Alternative methodE = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000J (1 kWh3600000J) = 3 kWh Again 45 cents

ndash AAA Battery contains 33 Calories of chemical energy How longcan it run a 2 Watt light bulb time = EP time = 33 Calories2W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1hr3600 sec) = 19 hours

QuestionThe US uses about 7 Gbarrels of oil each year This couldbe converted into which of the following units

A Joules B Watts C QBtus D Dollars $ E Any of the above

38

QuestionIf one barrel of oil contains 1700 kWh of energy how manyWatts is 7 Gbarrelyear

A 1400 GW (Giga Watts)

B 14 GW

C 11900 W

D 119 MW

E 1 x 1011 W

QuestionIf the total yearly oil use in the US is about 1400 GW howmany 1000 MW nuclear reactors will need to be built toreplace all oil use with electricity

A Only one will be needed

B Around 14

C Around 140

D Around 1400

E Cant convert Watts to reactors power vs energy

39

More Power Examplesbull How much power does it take to lift 10 kg up 2 meters in 2

secondsmgh = (10 kg)times(10 ms2)times(2 m) = 200J

200 J in 2 seconds rarr 100 Wattsbull If you want to heat the 3 m cubic room by 10ordmC with a

1000 W space heater how long will it takeWe know from before that the room needs to have 360000 J addedto it so at 1000 W = 1000 Js this will take 360 seconds or sixminutes

But the walls need to be warmed up too so it will actually takelonger (and depends on quality of insulation etc)

A note on arithmetic of unitsbull You should carry units in your calculations and multiply and divide them

as if they were numbersbull Example the force of air drag is given bybull Fdrag = frac12cDrAv2

bull cD is a dimensionless drag coefficientbull r is the density of air 13 kgm3

bull A is the cross-sectional area of the body in m2

bull v is the velocity in msbull units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) =

kgmiddotmiddotmm22middotmiddotmm22

m3middotmiddotss22kgmiddotmiddotmm44

m3middotmiddotss22= = kgmiddotmiddotmsms22 = = NewtonsNewtons

31

And those are the majorplayershellip

bull Wersquove now seen most of the major energyplayersndash work as force times distancendash kinetic energy (wind ocean currents)ndash gravitational potential energy (hydroelectric tidal)ndash chemical energy (fossil fuels batteries food biomass)ndash heat energy (power plants space heating)ndash mass-energy (nuclear sources sunrsquos energy)ndash radiant energy (solar energy)ndash electrical energy (energy of electrons separated from

their atoms)

Conservation and Exchange ofEnergy

Nothing Comes for Free

32

Energy is Conservedbull Conservation of Energy is different from Energy

Conservation the latter being about using energywisely

bull Conservation of Energy means energy is neithercreated nor destroyed The amount of energy inthe Universe is constant

bull Donrsquot we create energy at a power plantndash Oh that this were truemdashno we simply transform

energy at our power plantsbull Doesnrsquot the sun create energy

ndash Nopemdashit exchanges mass for energybull Donrsquot batteries give us new energy

ndash Nope just convert stored chemical energy to electricalenergy Someone had to put that energy in there

height referenceh

Energy Exchangebull Though the total energy of a system is constant

the form of the energy can changebull A simple example is that of a simple pendulum in

which a continual exchange goes on betweenkinetic and potential energy

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

33

Perpetual Motion

bull Why wonrsquot the pendulum swing foreverbull Itrsquos hard to design a system free of energy pathsbull The pendulum slows down by several mechanisms

ndash Friction at the contact point requires force to opposeforce acts through distance rarr work is done

ndash Air resistance must push through air with a force(through a distance) rarr work is done

ndash Gets some air swirling puts kinetic energy into air (notreally fair to separate these last two)

bull Perpetual motion means no loss of energyndash solar system orbits come very close

Some Energy Chains

bull A coffee mug with some gravitational potentialenergy is dropped

bull potential energy turns into kinetic energybull kinetic energy of the mug goes into

ndash ripping the mug apart (chemical breaking bonds)ndash sending the pieces flying (kinetic)ndash into soundndash into heating the floor and pieces through friction as the

pieces slide to a stopbull In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored inthe potential energy)

34

Gasoline Examplebull Put gas in your car containing 9 Calgbull Combust gas turning 9 Calg into kinetic energy of

explosionbull Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a wholebull That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water andsurrounding air) and friction of transmission system(heat) and noise of engine (heating the air) etc

bull Much of energy goes into stirring the air (ends up as heat)bull Apply the brakes and convert kinetic energy into heatbull It all ends up as waste heat ultimately

Bouncing Ballbull Superball has gravitational potential energybull Drop the ball and this becomes kinetic energybull Ball hits ground and compresses (force times

distance) storing energy in the springbull Ball releases this mechanically stored energy

and it goes back into kinetic form (bouncesup)

bull Inefficiencies in ldquospringrdquo end up heating theball and the floor and stirring the air a bit

bull In the end all is heat

35

Why donrsquot we get hotter andhotter

bull If all these processes end up as heat why arenrsquotwe continually getting hotter

bull If earth retained all its heat we would get hotterbull All of earthrsquos heat is radiated away

F = σT4

bull If we dump more power the temperature goes upthe radiated power increases dramaticallyndash comes to equilibrium power dumped = power radiatedndash stable against perturbation T tracks power budget

Rough numbers

bull How much power does the earth radiatebull F = σT4 for T = 288ordmK = 15ordmC is 390 Wm2

bull Summed over entire surface area (4πR2 where R= 6378000 meters) is 20times1017 W

bull Global production is 3times1012 Wbull Solar radiation incident on earth is 18times1017 W

ndash just solar luminosity of 39times1026 W divided bygeometrical fraction that points at earth

bull Amazing coincidence of numbers (or is ithellip)

36

No Energy for Free

bull No matter what you canrsquot create energy out ofnothing it has to come from somewhere

bull We can transform energy from one form toanother we can store energy we can utilizeenergy being conveyed from natural sources

bull The net energy of the entire Universe is constantbull The best we can do is scrape up some useful

crumbs

Examplesbull Unit conversion

ndash 100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Calndash 100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 Jndash 100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWhndash 10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWhndash How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86Calorieshour About what average person eats

ndash Gasoline is $3gal Electricity if $015kWh Which is moreexpensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh)= $008kWh for gasoline Gasoline is cheap in the USA

37

Examplesbull Power vs Energy (P=Etime E = P t t = EP)

ndash Car goes 60 miles in one hour and uses 3 gal of gas What wastotal power in Watts P=Et Power = (3 gal1 hour) = 3galhr(366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W[Alternative method 3 galhr (132000000 J1 gal) (1 hr3600sec) = 110000 Jsec = 110000 W

ndash 1000 W space heater is on for 3 hours How much does it cost ifelectricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr(1kW1000W) = 3kWh ($15kWh) = $45 [Alternative methodE = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000J (1 kWh3600000J) = 3 kWh Again 45 cents

ndash AAA Battery contains 33 Calories of chemical energy How longcan it run a 2 Watt light bulb time = EP time = 33 Calories2W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1hr3600 sec) = 19 hours

QuestionThe US uses about 7 Gbarrels of oil each year This couldbe converted into which of the following units

A Joules B Watts C QBtus D Dollars $ E Any of the above

38

QuestionIf one barrel of oil contains 1700 kWh of energy how manyWatts is 7 Gbarrelyear

A 1400 GW (Giga Watts)

B 14 GW

C 11900 W

D 119 MW

E 1 x 1011 W

QuestionIf the total yearly oil use in the US is about 1400 GW howmany 1000 MW nuclear reactors will need to be built toreplace all oil use with electricity

A Only one will be needed

B Around 14

C Around 140

D Around 1400

E Cant convert Watts to reactors power vs energy

39

More Power Examplesbull How much power does it take to lift 10 kg up 2 meters in 2

secondsmgh = (10 kg)times(10 ms2)times(2 m) = 200J

200 J in 2 seconds rarr 100 Wattsbull If you want to heat the 3 m cubic room by 10ordmC with a

1000 W space heater how long will it takeWe know from before that the room needs to have 360000 J addedto it so at 1000 W = 1000 Js this will take 360 seconds or sixminutes

But the walls need to be warmed up too so it will actually takelonger (and depends on quality of insulation etc)

A note on arithmetic of unitsbull You should carry units in your calculations and multiply and divide them

as if they were numbersbull Example the force of air drag is given bybull Fdrag = frac12cDrAv2

bull cD is a dimensionless drag coefficientbull r is the density of air 13 kgm3

bull A is the cross-sectional area of the body in m2

bull v is the velocity in msbull units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) =

kgmiddotmiddotmm22middotmiddotmm22

m3middotmiddotss22kgmiddotmiddotmm44

m3middotmiddotss22= = kgmiddotmiddotmsms22 = = NewtonsNewtons

32

Energy is Conservedbull Conservation of Energy is different from Energy

Conservation the latter being about using energywisely

bull Conservation of Energy means energy is neithercreated nor destroyed The amount of energy inthe Universe is constant

bull Donrsquot we create energy at a power plantndash Oh that this were truemdashno we simply transform

energy at our power plantsbull Doesnrsquot the sun create energy

ndash Nopemdashit exchanges mass for energybull Donrsquot batteries give us new energy

ndash Nope just convert stored chemical energy to electricalenergy Someone had to put that energy in there

height referenceh

Energy Exchangebull Though the total energy of a system is constant

the form of the energy can changebull A simple example is that of a simple pendulum in

which a continual exchange goes on betweenkinetic and potential energy

pivot

KE = 0 P E = mgh KE = 0 P E = mgh

PE = 0 KE = mgh

33

Perpetual Motion

bull Why wonrsquot the pendulum swing foreverbull Itrsquos hard to design a system free of energy pathsbull The pendulum slows down by several mechanisms

ndash Friction at the contact point requires force to opposeforce acts through distance rarr work is done

ndash Air resistance must push through air with a force(through a distance) rarr work is done

ndash Gets some air swirling puts kinetic energy into air (notreally fair to separate these last two)

bull Perpetual motion means no loss of energyndash solar system orbits come very close

Some Energy Chains

bull A coffee mug with some gravitational potentialenergy is dropped

bull potential energy turns into kinetic energybull kinetic energy of the mug goes into

ndash ripping the mug apart (chemical breaking bonds)ndash sending the pieces flying (kinetic)ndash into soundndash into heating the floor and pieces through friction as the

pieces slide to a stopbull In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored inthe potential energy)

34

Gasoline Examplebull Put gas in your car containing 9 Calgbull Combust gas turning 9 Calg into kinetic energy of

explosionbull Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a wholebull That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water andsurrounding air) and friction of transmission system(heat) and noise of engine (heating the air) etc

bull Much of energy goes into stirring the air (ends up as heat)bull Apply the brakes and convert kinetic energy into heatbull It all ends up as waste heat ultimately

Bouncing Ballbull Superball has gravitational potential energybull Drop the ball and this becomes kinetic energybull Ball hits ground and compresses (force times

distance) storing energy in the springbull Ball releases this mechanically stored energy

and it goes back into kinetic form (bouncesup)

bull Inefficiencies in ldquospringrdquo end up heating theball and the floor and stirring the air a bit

bull In the end all is heat

35

Why donrsquot we get hotter andhotter

bull If all these processes end up as heat why arenrsquotwe continually getting hotter

bull If earth retained all its heat we would get hotterbull All of earthrsquos heat is radiated away

F = σT4

bull If we dump more power the temperature goes upthe radiated power increases dramaticallyndash comes to equilibrium power dumped = power radiatedndash stable against perturbation T tracks power budget

Rough numbers

bull How much power does the earth radiatebull F = σT4 for T = 288ordmK = 15ordmC is 390 Wm2

bull Summed over entire surface area (4πR2 where R= 6378000 meters) is 20times1017 W

bull Global production is 3times1012 Wbull Solar radiation incident on earth is 18times1017 W

ndash just solar luminosity of 39times1026 W divided bygeometrical fraction that points at earth

bull Amazing coincidence of numbers (or is ithellip)

36

No Energy for Free

bull No matter what you canrsquot create energy out ofnothing it has to come from somewhere

bull We can transform energy from one form toanother we can store energy we can utilizeenergy being conveyed from natural sources

bull The net energy of the entire Universe is constantbull The best we can do is scrape up some useful

crumbs

Examplesbull Unit conversion

ndash 100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Calndash 100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 Jndash 100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWhndash 10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWhndash How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86Calorieshour About what average person eats

ndash Gasoline is $3gal Electricity if $015kWh Which is moreexpensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh)= $008kWh for gasoline Gasoline is cheap in the USA

37

Examplesbull Power vs Energy (P=Etime E = P t t = EP)

ndash Car goes 60 miles in one hour and uses 3 gal of gas What wastotal power in Watts P=Et Power = (3 gal1 hour) = 3galhr(366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W[Alternative method 3 galhr (132000000 J1 gal) (1 hr3600sec) = 110000 Jsec = 110000 W

ndash 1000 W space heater is on for 3 hours How much does it cost ifelectricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr(1kW1000W) = 3kWh ($15kWh) = $45 [Alternative methodE = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000J (1 kWh3600000J) = 3 kWh Again 45 cents

ndash AAA Battery contains 33 Calories of chemical energy How longcan it run a 2 Watt light bulb time = EP time = 33 Calories2W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1hr3600 sec) = 19 hours

QuestionThe US uses about 7 Gbarrels of oil each year This couldbe converted into which of the following units

A Joules B Watts C QBtus D Dollars $ E Any of the above

38

QuestionIf one barrel of oil contains 1700 kWh of energy how manyWatts is 7 Gbarrelyear

A 1400 GW (Giga Watts)

B 14 GW

C 11900 W

D 119 MW

E 1 x 1011 W

QuestionIf the total yearly oil use in the US is about 1400 GW howmany 1000 MW nuclear reactors will need to be built toreplace all oil use with electricity

A Only one will be needed

B Around 14

C Around 140

D Around 1400

E Cant convert Watts to reactors power vs energy

39

More Power Examplesbull How much power does it take to lift 10 kg up 2 meters in 2

secondsmgh = (10 kg)times(10 ms2)times(2 m) = 200J

200 J in 2 seconds rarr 100 Wattsbull If you want to heat the 3 m cubic room by 10ordmC with a

1000 W space heater how long will it takeWe know from before that the room needs to have 360000 J addedto it so at 1000 W = 1000 Js this will take 360 seconds or sixminutes

But the walls need to be warmed up too so it will actually takelonger (and depends on quality of insulation etc)

A note on arithmetic of unitsbull You should carry units in your calculations and multiply and divide them

as if they were numbersbull Example the force of air drag is given bybull Fdrag = frac12cDrAv2

bull cD is a dimensionless drag coefficientbull r is the density of air 13 kgm3

bull A is the cross-sectional area of the body in m2

bull v is the velocity in msbull units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) =

kgmiddotmiddotmm22middotmiddotmm22

m3middotmiddotss22kgmiddotmiddotmm44

m3middotmiddotss22= = kgmiddotmiddotmsms22 = = NewtonsNewtons

33

Perpetual Motion

bull Why wonrsquot the pendulum swing foreverbull Itrsquos hard to design a system free of energy pathsbull The pendulum slows down by several mechanisms

ndash Friction at the contact point requires force to opposeforce acts through distance rarr work is done

ndash Air resistance must push through air with a force(through a distance) rarr work is done

ndash Gets some air swirling puts kinetic energy into air (notreally fair to separate these last two)

bull Perpetual motion means no loss of energyndash solar system orbits come very close

Some Energy Chains

bull A coffee mug with some gravitational potentialenergy is dropped

bull potential energy turns into kinetic energybull kinetic energy of the mug goes into

ndash ripping the mug apart (chemical breaking bonds)ndash sending the pieces flying (kinetic)ndash into soundndash into heating the floor and pieces through friction as the

pieces slide to a stopbull In the end the room is slightly warmer (heated by

exactly the number of Calories originally stored inthe potential energy)

34

Gasoline Examplebull Put gas in your car containing 9 Calgbull Combust gas turning 9 Calg into kinetic energy of

explosionbull Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a wholebull That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water andsurrounding air) and friction of transmission system(heat) and noise of engine (heating the air) etc

bull Much of energy goes into stirring the air (ends up as heat)bull Apply the brakes and convert kinetic energy into heatbull It all ends up as waste heat ultimately

Bouncing Ballbull Superball has gravitational potential energybull Drop the ball and this becomes kinetic energybull Ball hits ground and compresses (force times

distance) storing energy in the springbull Ball releases this mechanically stored energy

and it goes back into kinetic form (bouncesup)

bull Inefficiencies in ldquospringrdquo end up heating theball and the floor and stirring the air a bit

bull In the end all is heat

35

Why donrsquot we get hotter andhotter

bull If all these processes end up as heat why arenrsquotwe continually getting hotter

bull If earth retained all its heat we would get hotterbull All of earthrsquos heat is radiated away

F = σT4

bull If we dump more power the temperature goes upthe radiated power increases dramaticallyndash comes to equilibrium power dumped = power radiatedndash stable against perturbation T tracks power budget

Rough numbers

bull How much power does the earth radiatebull F = σT4 for T = 288ordmK = 15ordmC is 390 Wm2

bull Summed over entire surface area (4πR2 where R= 6378000 meters) is 20times1017 W

bull Global production is 3times1012 Wbull Solar radiation incident on earth is 18times1017 W

ndash just solar luminosity of 39times1026 W divided bygeometrical fraction that points at earth

bull Amazing coincidence of numbers (or is ithellip)

36

No Energy for Free

bull No matter what you canrsquot create energy out ofnothing it has to come from somewhere

bull We can transform energy from one form toanother we can store energy we can utilizeenergy being conveyed from natural sources

bull The net energy of the entire Universe is constantbull The best we can do is scrape up some useful

crumbs

Examplesbull Unit conversion

ndash 100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Calndash 100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 Jndash 100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWhndash 10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWhndash How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86Calorieshour About what average person eats

ndash Gasoline is $3gal Electricity if $015kWh Which is moreexpensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh)= $008kWh for gasoline Gasoline is cheap in the USA

37

Examplesbull Power vs Energy (P=Etime E = P t t = EP)

ndash Car goes 60 miles in one hour and uses 3 gal of gas What wastotal power in Watts P=Et Power = (3 gal1 hour) = 3galhr(366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W[Alternative method 3 galhr (132000000 J1 gal) (1 hr3600sec) = 110000 Jsec = 110000 W

ndash 1000 W space heater is on for 3 hours How much does it cost ifelectricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr(1kW1000W) = 3kWh ($15kWh) = $45 [Alternative methodE = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000J (1 kWh3600000J) = 3 kWh Again 45 cents

ndash AAA Battery contains 33 Calories of chemical energy How longcan it run a 2 Watt light bulb time = EP time = 33 Calories2W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1hr3600 sec) = 19 hours

QuestionThe US uses about 7 Gbarrels of oil each year This couldbe converted into which of the following units

A Joules B Watts C QBtus D Dollars $ E Any of the above

38

QuestionIf one barrel of oil contains 1700 kWh of energy how manyWatts is 7 Gbarrelyear

A 1400 GW (Giga Watts)

B 14 GW

C 11900 W

D 119 MW

E 1 x 1011 W

QuestionIf the total yearly oil use in the US is about 1400 GW howmany 1000 MW nuclear reactors will need to be built toreplace all oil use with electricity

A Only one will be needed

B Around 14

C Around 140

D Around 1400

E Cant convert Watts to reactors power vs energy

39

More Power Examplesbull How much power does it take to lift 10 kg up 2 meters in 2

secondsmgh = (10 kg)times(10 ms2)times(2 m) = 200J

200 J in 2 seconds rarr 100 Wattsbull If you want to heat the 3 m cubic room by 10ordmC with a

1000 W space heater how long will it takeWe know from before that the room needs to have 360000 J addedto it so at 1000 W = 1000 Js this will take 360 seconds or sixminutes

But the walls need to be warmed up too so it will actually takelonger (and depends on quality of insulation etc)

A note on arithmetic of unitsbull You should carry units in your calculations and multiply and divide them

as if they were numbersbull Example the force of air drag is given bybull Fdrag = frac12cDrAv2

bull cD is a dimensionless drag coefficientbull r is the density of air 13 kgm3

bull A is the cross-sectional area of the body in m2

bull v is the velocity in msbull units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) =

kgmiddotmiddotmm22middotmiddotmm22

m3middotmiddotss22kgmiddotmiddotmm44

m3middotmiddotss22= = kgmiddotmiddotmsms22 = = NewtonsNewtons

34

Gasoline Examplebull Put gas in your car containing 9 Calgbull Combust gas turning 9 Calg into kinetic energy of

explosionbull Transfer kinetic energy of gas to piston to crankshaft to

drive shaft to wheel to car as a wholebull That which doesnrsquot go into kinetic energy of the car goes

into heating the engine block (and radiator water andsurrounding air) and friction of transmission system(heat) and noise of engine (heating the air) etc

bull Much of energy goes into stirring the air (ends up as heat)bull Apply the brakes and convert kinetic energy into heatbull It all ends up as waste heat ultimately

Bouncing Ballbull Superball has gravitational potential energybull Drop the ball and this becomes kinetic energybull Ball hits ground and compresses (force times

distance) storing energy in the springbull Ball releases this mechanically stored energy

and it goes back into kinetic form (bouncesup)

bull Inefficiencies in ldquospringrdquo end up heating theball and the floor and stirring the air a bit

bull In the end all is heat

35

Why donrsquot we get hotter andhotter

bull If all these processes end up as heat why arenrsquotwe continually getting hotter

bull If earth retained all its heat we would get hotterbull All of earthrsquos heat is radiated away

F = σT4

bull If we dump more power the temperature goes upthe radiated power increases dramaticallyndash comes to equilibrium power dumped = power radiatedndash stable against perturbation T tracks power budget

Rough numbers

bull How much power does the earth radiatebull F = σT4 for T = 288ordmK = 15ordmC is 390 Wm2

bull Summed over entire surface area (4πR2 where R= 6378000 meters) is 20times1017 W

bull Global production is 3times1012 Wbull Solar radiation incident on earth is 18times1017 W

ndash just solar luminosity of 39times1026 W divided bygeometrical fraction that points at earth

bull Amazing coincidence of numbers (or is ithellip)

36

No Energy for Free

bull No matter what you canrsquot create energy out ofnothing it has to come from somewhere

bull We can transform energy from one form toanother we can store energy we can utilizeenergy being conveyed from natural sources

bull The net energy of the entire Universe is constantbull The best we can do is scrape up some useful

crumbs

Examplesbull Unit conversion

ndash 100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Calndash 100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 Jndash 100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWhndash 10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWhndash How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86Calorieshour About what average person eats

ndash Gasoline is $3gal Electricity if $015kWh Which is moreexpensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh)= $008kWh for gasoline Gasoline is cheap in the USA

37

Examplesbull Power vs Energy (P=Etime E = P t t = EP)

ndash Car goes 60 miles in one hour and uses 3 gal of gas What wastotal power in Watts P=Et Power = (3 gal1 hour) = 3galhr(366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W[Alternative method 3 galhr (132000000 J1 gal) (1 hr3600sec) = 110000 Jsec = 110000 W

ndash 1000 W space heater is on for 3 hours How much does it cost ifelectricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr(1kW1000W) = 3kWh ($15kWh) = $45 [Alternative methodE = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000J (1 kWh3600000J) = 3 kWh Again 45 cents

ndash AAA Battery contains 33 Calories of chemical energy How longcan it run a 2 Watt light bulb time = EP time = 33 Calories2W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1hr3600 sec) = 19 hours

QuestionThe US uses about 7 Gbarrels of oil each year This couldbe converted into which of the following units

A Joules B Watts C QBtus D Dollars $ E Any of the above

38

QuestionIf one barrel of oil contains 1700 kWh of energy how manyWatts is 7 Gbarrelyear

A 1400 GW (Giga Watts)

B 14 GW

C 11900 W

D 119 MW

E 1 x 1011 W

QuestionIf the total yearly oil use in the US is about 1400 GW howmany 1000 MW nuclear reactors will need to be built toreplace all oil use with electricity

A Only one will be needed

B Around 14

C Around 140

D Around 1400

E Cant convert Watts to reactors power vs energy

39

More Power Examplesbull How much power does it take to lift 10 kg up 2 meters in 2

secondsmgh = (10 kg)times(10 ms2)times(2 m) = 200J

200 J in 2 seconds rarr 100 Wattsbull If you want to heat the 3 m cubic room by 10ordmC with a

1000 W space heater how long will it takeWe know from before that the room needs to have 360000 J addedto it so at 1000 W = 1000 Js this will take 360 seconds or sixminutes

But the walls need to be warmed up too so it will actually takelonger (and depends on quality of insulation etc)

A note on arithmetic of unitsbull You should carry units in your calculations and multiply and divide them

as if they were numbersbull Example the force of air drag is given bybull Fdrag = frac12cDrAv2

bull cD is a dimensionless drag coefficientbull r is the density of air 13 kgm3

bull A is the cross-sectional area of the body in m2

bull v is the velocity in msbull units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) =

kgmiddotmiddotmm22middotmiddotmm22

m3middotmiddotss22kgmiddotmiddotmm44

m3middotmiddotss22= = kgmiddotmiddotmsms22 = = NewtonsNewtons

35

Why donrsquot we get hotter andhotter

bull If all these processes end up as heat why arenrsquotwe continually getting hotter

bull If earth retained all its heat we would get hotterbull All of earthrsquos heat is radiated away

F = σT4

bull If we dump more power the temperature goes upthe radiated power increases dramaticallyndash comes to equilibrium power dumped = power radiatedndash stable against perturbation T tracks power budget

Rough numbers

bull How much power does the earth radiatebull F = σT4 for T = 288ordmK = 15ordmC is 390 Wm2

bull Summed over entire surface area (4πR2 where R= 6378000 meters) is 20times1017 W

bull Global production is 3times1012 Wbull Solar radiation incident on earth is 18times1017 W

ndash just solar luminosity of 39times1026 W divided bygeometrical fraction that points at earth

bull Amazing coincidence of numbers (or is ithellip)

36

No Energy for Free

bull No matter what you canrsquot create energy out ofnothing it has to come from somewhere

bull We can transform energy from one form toanother we can store energy we can utilizeenergy being conveyed from natural sources

bull The net energy of the entire Universe is constantbull The best we can do is scrape up some useful

crumbs

Examplesbull Unit conversion

ndash 100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Calndash 100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 Jndash 100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWhndash 10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWhndash How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86Calorieshour About what average person eats

ndash Gasoline is $3gal Electricity if $015kWh Which is moreexpensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh)= $008kWh for gasoline Gasoline is cheap in the USA

37

Examplesbull Power vs Energy (P=Etime E = P t t = EP)

ndash Car goes 60 miles in one hour and uses 3 gal of gas What wastotal power in Watts P=Et Power = (3 gal1 hour) = 3galhr(366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W[Alternative method 3 galhr (132000000 J1 gal) (1 hr3600sec) = 110000 Jsec = 110000 W

ndash 1000 W space heater is on for 3 hours How much does it cost ifelectricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr(1kW1000W) = 3kWh ($15kWh) = $45 [Alternative methodE = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000J (1 kWh3600000J) = 3 kWh Again 45 cents

ndash AAA Battery contains 33 Calories of chemical energy How longcan it run a 2 Watt light bulb time = EP time = 33 Calories2W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1hr3600 sec) = 19 hours

QuestionThe US uses about 7 Gbarrels of oil each year This couldbe converted into which of the following units

A Joules B Watts C QBtus D Dollars $ E Any of the above

38

QuestionIf one barrel of oil contains 1700 kWh of energy how manyWatts is 7 Gbarrelyear

A 1400 GW (Giga Watts)

B 14 GW

C 11900 W

D 119 MW

E 1 x 1011 W

QuestionIf the total yearly oil use in the US is about 1400 GW howmany 1000 MW nuclear reactors will need to be built toreplace all oil use with electricity

A Only one will be needed

B Around 14

C Around 140

D Around 1400

E Cant convert Watts to reactors power vs energy

39

More Power Examplesbull How much power does it take to lift 10 kg up 2 meters in 2

secondsmgh = (10 kg)times(10 ms2)times(2 m) = 200J

200 J in 2 seconds rarr 100 Wattsbull If you want to heat the 3 m cubic room by 10ordmC with a

1000 W space heater how long will it takeWe know from before that the room needs to have 360000 J addedto it so at 1000 W = 1000 Js this will take 360 seconds or sixminutes

But the walls need to be warmed up too so it will actually takelonger (and depends on quality of insulation etc)

A note on arithmetic of unitsbull You should carry units in your calculations and multiply and divide them

as if they were numbersbull Example the force of air drag is given bybull Fdrag = frac12cDrAv2

bull cD is a dimensionless drag coefficientbull r is the density of air 13 kgm3

bull A is the cross-sectional area of the body in m2

bull v is the velocity in msbull units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) =

kgmiddotmiddotmm22middotmiddotmm22

m3middotmiddotss22kgmiddotmiddotmm44

m3middotmiddotss22= = kgmiddotmiddotmsms22 = = NewtonsNewtons

36

No Energy for Free

bull No matter what you canrsquot create energy out ofnothing it has to come from somewhere

bull We can transform energy from one form toanother we can store energy we can utilizeenergy being conveyed from natural sources

bull The net energy of the entire Universe is constantbull The best we can do is scrape up some useful

crumbs

Examplesbull Unit conversion

ndash 100 Btu into Calories 100 Btu (1 Calorie396 Btu) = 25 Calndash 100 Btu into Joules 100Btu (1055 J1 Btu) = 105500 J = 1 x 105 Jndash 100 Btu into kWh 100Btu (1 kWh 3413 Btu) = 0029 kWhndash 10 gallons of gasoline into kWh 10 gals (132000000 J1 gal) (1

kWh3600000 J) = 366 kWhndash How many calories per hour does 100 W bulb use 100 W = 100

Joulesec (1 Cal4184 J) (60 sec 1 min) (60 min 1 hour) = 86Calorieshour About what average person eats

ndash Gasoline is $3gal Electricity if $015kWh Which is moreexpensive Convert $3gal to $ per kWh $3gal (1 gal366 kWh)= $008kWh for gasoline Gasoline is cheap in the USA

37

Examplesbull Power vs Energy (P=Etime E = P t t = EP)

ndash Car goes 60 miles in one hour and uses 3 gal of gas What wastotal power in Watts P=Et Power = (3 gal1 hour) = 3galhr(366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W[Alternative method 3 galhr (132000000 J1 gal) (1 hr3600sec) = 110000 Jsec = 110000 W

ndash 1000 W space heater is on for 3 hours How much does it cost ifelectricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr(1kW1000W) = 3kWh ($15kWh) = $45 [Alternative methodE = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000J (1 kWh3600000J) = 3 kWh Again 45 cents

ndash AAA Battery contains 33 Calories of chemical energy How longcan it run a 2 Watt light bulb time = EP time = 33 Calories2W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1hr3600 sec) = 19 hours

QuestionThe US uses about 7 Gbarrels of oil each year This couldbe converted into which of the following units

A Joules B Watts C QBtus D Dollars $ E Any of the above

38

QuestionIf one barrel of oil contains 1700 kWh of energy how manyWatts is 7 Gbarrelyear

A 1400 GW (Giga Watts)

B 14 GW

C 11900 W

D 119 MW

E 1 x 1011 W

QuestionIf the total yearly oil use in the US is about 1400 GW howmany 1000 MW nuclear reactors will need to be built toreplace all oil use with electricity

A Only one will be needed

B Around 14

C Around 140

D Around 1400

E Cant convert Watts to reactors power vs energy

39

More Power Examplesbull How much power does it take to lift 10 kg up 2 meters in 2

secondsmgh = (10 kg)times(10 ms2)times(2 m) = 200J

200 J in 2 seconds rarr 100 Wattsbull If you want to heat the 3 m cubic room by 10ordmC with a

1000 W space heater how long will it takeWe know from before that the room needs to have 360000 J addedto it so at 1000 W = 1000 Js this will take 360 seconds or sixminutes

But the walls need to be warmed up too so it will actually takelonger (and depends on quality of insulation etc)

A note on arithmetic of unitsbull You should carry units in your calculations and multiply and divide them

as if they were numbersbull Example the force of air drag is given bybull Fdrag = frac12cDrAv2

bull cD is a dimensionless drag coefficientbull r is the density of air 13 kgm3

bull A is the cross-sectional area of the body in m2

bull v is the velocity in msbull units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) =

kgmiddotmiddotmm22middotmiddotmm22

m3middotmiddotss22kgmiddotmiddotmm44

m3middotmiddotss22= = kgmiddotmiddotmsms22 = = NewtonsNewtons

37

Examplesbull Power vs Energy (P=Etime E = P t t = EP)

ndash Car goes 60 miles in one hour and uses 3 gal of gas What wastotal power in Watts P=Et Power = (3 gal1 hour) = 3galhr(366 kWhr 1 gal) = 109 kW (1000W 1 kW) = 109000 W[Alternative method 3 galhr (132000000 J1 gal) (1 hr3600sec) = 110000 Jsec = 110000 W

ndash 1000 W space heater is on for 3 hours How much does it cost ifelectricity is $15kWh E= P t E = (1000 W)(3 hr) = 3000 W hr(1kW1000W) = 3kWh ($15kWh) = $45 [Alternative methodE = (1000 W)(3 hr) (3600 sec1hr) = 10800000 Ws = 10800000J (1 kWh3600000J) = 3 kWh Again 45 cents

ndash AAA Battery contains 33 Calories of chemical energy How longcan it run a 2 Watt light bulb time = EP time = 33 Calories2W = 165 Cal secJoule (4184 J1 Cal) = 6900 seconds (1hr3600 sec) = 19 hours

QuestionThe US uses about 7 Gbarrels of oil each year This couldbe converted into which of the following units

A Joules B Watts C QBtus D Dollars $ E Any of the above

38

QuestionIf one barrel of oil contains 1700 kWh of energy how manyWatts is 7 Gbarrelyear

A 1400 GW (Giga Watts)

B 14 GW

C 11900 W

D 119 MW

E 1 x 1011 W

QuestionIf the total yearly oil use in the US is about 1400 GW howmany 1000 MW nuclear reactors will need to be built toreplace all oil use with electricity

A Only one will be needed

B Around 14

C Around 140

D Around 1400

E Cant convert Watts to reactors power vs energy

39

More Power Examplesbull How much power does it take to lift 10 kg up 2 meters in 2

secondsmgh = (10 kg)times(10 ms2)times(2 m) = 200J

200 J in 2 seconds rarr 100 Wattsbull If you want to heat the 3 m cubic room by 10ordmC with a

1000 W space heater how long will it takeWe know from before that the room needs to have 360000 J addedto it so at 1000 W = 1000 Js this will take 360 seconds or sixminutes

But the walls need to be warmed up too so it will actually takelonger (and depends on quality of insulation etc)

A note on arithmetic of unitsbull You should carry units in your calculations and multiply and divide them

as if they were numbersbull Example the force of air drag is given bybull Fdrag = frac12cDrAv2

bull cD is a dimensionless drag coefficientbull r is the density of air 13 kgm3

bull A is the cross-sectional area of the body in m2

bull v is the velocity in msbull units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) =

kgmiddotmiddotmm22middotmiddotmm22

m3middotmiddotss22kgmiddotmiddotmm44

m3middotmiddotss22= = kgmiddotmiddotmsms22 = = NewtonsNewtons

38

QuestionIf one barrel of oil contains 1700 kWh of energy how manyWatts is 7 Gbarrelyear

A 1400 GW (Giga Watts)

B 14 GW

C 11900 W

D 119 MW

E 1 x 1011 W

QuestionIf the total yearly oil use in the US is about 1400 GW howmany 1000 MW nuclear reactors will need to be built toreplace all oil use with electricity

A Only one will be needed

B Around 14

C Around 140

D Around 1400

E Cant convert Watts to reactors power vs energy

39

More Power Examplesbull How much power does it take to lift 10 kg up 2 meters in 2

secondsmgh = (10 kg)times(10 ms2)times(2 m) = 200J

200 J in 2 seconds rarr 100 Wattsbull If you want to heat the 3 m cubic room by 10ordmC with a

1000 W space heater how long will it takeWe know from before that the room needs to have 360000 J addedto it so at 1000 W = 1000 Js this will take 360 seconds or sixminutes

But the walls need to be warmed up too so it will actually takelonger (and depends on quality of insulation etc)

A note on arithmetic of unitsbull You should carry units in your calculations and multiply and divide them

as if they were numbersbull Example the force of air drag is given bybull Fdrag = frac12cDrAv2

bull cD is a dimensionless drag coefficientbull r is the density of air 13 kgm3

bull A is the cross-sectional area of the body in m2

bull v is the velocity in msbull units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) =

kgmiddotmiddotmm22middotmiddotmm22

m3middotmiddotss22kgmiddotmiddotmm44

m3middotmiddotss22= = kgmiddotmiddotmsms22 = = NewtonsNewtons

39

More Power Examplesbull How much power does it take to lift 10 kg up 2 meters in 2

secondsmgh = (10 kg)times(10 ms2)times(2 m) = 200J

200 J in 2 seconds rarr 100 Wattsbull If you want to heat the 3 m cubic room by 10ordmC with a

1000 W space heater how long will it takeWe know from before that the room needs to have 360000 J addedto it so at 1000 W = 1000 Js this will take 360 seconds or sixminutes

But the walls need to be warmed up too so it will actually takelonger (and depends on quality of insulation etc)

A note on arithmetic of unitsbull You should carry units in your calculations and multiply and divide them

as if they were numbersbull Example the force of air drag is given bybull Fdrag = frac12cDrAv2

bull cD is a dimensionless drag coefficientbull r is the density of air 13 kgm3

bull A is the cross-sectional area of the body in m2

bull v is the velocity in msbull units (kgm3)(m2)(ms)2 = (kgm2m3) (m2s2) =

kgmiddotmiddotmm22middotmiddotmm22

m3middotmiddotss22kgmiddotmiddotmm44

m3middotmiddotss22= = kgmiddotmiddotmsms22 = = NewtonsNewtons