What happens when we place a hot bowl of soup in a cool room?

ice water at 5 oC

air trappedfrom outsideat 25 0C

water at 15 0C

air at 15 0C

Why the difference in the two scenarios?Different number of molecules involved in energy exchange

Once the temperature equalizes there is no further NET transfer ofthermal energy. This condition (no NET transfer) is called Thermal Equilibrium

somethingwarm

somethingcool

two some things at an“intermediate” temperature

make thermal contact

Thermal Equilibrium

air = 25 C

soup = 95 C

What happens over a period of time?

There is a net transfer of thermal from the soup to the air. As a result,the temperature of the soup and thetemperature of the air become thesame. (i.e. reach Thermal Equilibrium)

airsoup

more KinEmore momentum

more KinEmore momentum

some KinE lostsome momentum lost

what can we say aboutthe average kE of the soup molecules compared to the air molecules? ..how iskE related to temp?

The zero th law of Thermodynamics: (i.e. the transitive property)

If A is in thermal equilibrium with B (Temp A = Temp B)

And B is in thermal equilibrium with C (Temp B = Temp C)

Then A is also in thermal equilibrium with C (Temp A = Temp C)

A B C

A B C

Thermal equilibrium

Consider once again the Bowl of Soup example……..

At first less averagethermal energy

more averagethermal energy

same average thermal energy everywhere

In which situation is the energy of the system (bowl of soup + air in room)more organized ?

Later that day

At First

you could easily select a molecule with largerthermal (kE) energy……. just scoop out some of the “hot” soup

Later thatday

molecules of various energiesevenly distributed throughoutthe soup and air…who knows where to find one with a lot ofenergy

As a general rule, the disorganization of the energy of the UniverseNEVER DECREASES as a result of a process. And, the disorganizationof the energy of the Universe could only stay the same as a result ofan IDEAL process (which never actually occurs)

NOTE: Over time, things run down…but the universe does not lose energy!!

Remember the track and ball example:“later”“start”

hAhE

“IDEAL CASE”

“later”“start”

hAhE < hA

all organized

thermaldisorganized

“REAL CASE”

At the “start” the energy is in an organized state, at point E the energy is still all in just as organized a state

not allorganized

We use the word Entropy to describe the quantitative measure ofdisorganization of energy.

1. The soup and the air have higher entropy after coming to the same temperature than before

2. The ball and the track along with the surroundings have more

entropy when the ball is at point E than at point A in the “REAL CASE”

The 4 laws of Thermodynamics:zero: If two systems are in thermal equilibrium with a third system, then then they are also in thermal equilibrium with one another

one: energy can neither be created nor destroyed, only transformed into another type of Energy

two: Entropy NEVER decreases and only stays the same in IDEAL processes

three: there is a lowest possible temperature (= -273 C) it is not attainable due to a number of irreversible energy transfer

play

Tin

Tex

measure thesein Kelvin, K,K = C + 273.15

somewhatdisorganized

organized

highly disorganized

“exhaust”“waste”

2nd Law: Any process that usesthermal energy to do work must alsohave a thermal energy output orexhaust. In otherwords, heat enginesare always less than100% efficient.

3rd Law: It is notpossible for Tex tobe at or lower thanabsolute zero (0 K)

Flow of thermal energy is essential to heat engines.

Summary:1. Every heat engine has at least some thermal energy as output.

2. even an “ideal” heat engine (which does not exist) is less 100% efficient

The Ideal Efficiency (IE) of a heat engine is computed using:

%100

in

exin

TTT

IE

Note: Tin and Tex must be expressed in Kelvin (K)

For any real heat engine, the Actual Efficiency is less than the Ideal Efficiency: AE < IE

Exponential Growth

thermodynamics: 1. Energy quality runs down as time proceeds 2. Useful energy is needed to do work and thus support human civilization

history: Human populations grow at nearly an exponential rate

problem: Will we run out of high quality energy resources?

Solution: 1. Renewable energy resources? 2. Slow down the exponential population growth?

Linear GrowthStart a new job and work for free the 1st day with the agreementthat you get a fixed $10,000 raise each day.

Exponential Growth

Start a new job and work for $1 the 1st day with the agreement thatyou get a fixed 1% raise each day.

Which job would you take (assuming each involves the same set of responsibilities?

A. job #1 – LinearB. job #2 – Exponential

Does the length of the contract affect your decision?

0 500 1000 1500 20000

10000000

20000000

30000000

40000000

50000000Exponential Growthat 1% /day

Linear Growth at $10,000/day

Da

ily W

ag

e

Days

Linear Exp

0 70 140 2100

1

2

3

4

5

6

7

8

double

double

double

T = 70/PT = 70/PT = 70/P

Da

ily W

ag

e

Days

0 35 70 105 1400

2

4

6

8

10

12

14

16

18

20

T = 70/1% = 70 years

Exponential growthat 1%/year

Exponential growth at 2% / year

T = 70/2% = 35 years

Pop

ula

tion

of B

ass

et H

oun

ds

Years

For exponential growth at rate P%, the population DOUBLES ina time:

%70P

T

If P% is P%/year then T is in yearsIf P% is P%/day then T is in days…etc…

NOTE: this approximation only works for P% < 10%!!