ThermodynamicsThermodynamics

Chapter 14Chapter 14

Work in a Gas CylinderWork in a Gas Cylinder

nn A force is applied toA force is applied toslowly compress theslowly compress thegasgasnn The compression isThe compression is

slow enough for allslow enough for allthe system to remainthe system to remainessentially in thermalessentially in thermalequilibriumequilibrium

nn W = - P W = - P ΔΔVVnn This is the workThis is the work

done done onon the gas the gas

More about Work on a GasMore about Work on a GasCylinderCylinder

nn When the gas is compressedWhen the gas is compressednn ΔΔV is negativeV is negativenn The work done on the gas is positiveThe work done on the gas is positive

nn When the gas is allowed to expandWhen the gas is allowed to expandnn ΔΔV is positiveV is positivenn The work done on the gas is negativeThe work done on the gas is negative

nn When the volume remains constantWhen the volume remains constantnn No work is done on the gasNo work is done on the gas

Notes about the WorkNotes about the WorkEquationEquation

nn The pressure remains constant duringThe pressure remains constant duringthe expansion or compressionthe expansion or compressionnn This is called an This is called an isobaricisobaric process process

nn If the pressure changes, the averageIf the pressure changes, the averagepressure may be used to estimate thepressure may be used to estimate thework donework done

Other ProcessesOther Processes

nn IsovolumetricIsovolumetricnn Volume stays constantVolume stays constant

nn IsothermalIsothermalnn Temperature stays the sameTemperature stays the same

nn AdiabaticAdiabaticnn No heat is exchanged with theNo heat is exchanged with the

surroundingssurroundings

First Law of ThermodynamicsFirst Law of Thermodynamics

nn Terms in the equationTerms in the equationnn QQ

nn HeatHeatnn Positive if energy is transferred Positive if energy is transferred toto the system the system

nn WWnn WorkWorknn Positive if done Positive if done onon the system the system

nn UUnn Internal energyInternal energynn Positive if the temperature increasesPositive if the temperature increases

First Law of Thermodynamics,First Law of Thermodynamics,contcont

nn The relationship among U, W, and QThe relationship among U, W, and Qcan be expressed ascan be expressed asnn ΔΔU = UU = Uff –– U Uii = Q + W = Q + W

nn This means that the change in internalThis means that the change in internalenergy of a system is equal to the sumenergy of a system is equal to the sumof the energy transferred across theof the energy transferred across thesystem boundary by heat and thesystem boundary by heat and theenergy transferred by workenergy transferred by work

Additional Notes About theAdditional Notes About theFirst LawFirst Law

nn The First Law is a general equation ofThe First Law is a general equation ofConservation of EnergyConservation of Energy

nn There is no practical, macroscopic,There is no practical, macroscopic,distinction between the results ofdistinction between the results ofenergy transfer by heat and by workenergy transfer by heat and by work

nn Q and W are related to the properties ofQ and W are related to the properties ofstate for a systemstate for a system

The First Law and HumanThe First Law and HumanMetabolismMetabolism

nn The First Law can be applied to livingThe First Law can be applied to livingorganismsorganisms

nn The internal energy stored in humans goesThe internal energy stored in humans goesinto other forms needed by the organs andinto other forms needed by the organs andinto work and heatinto work and heat

nn The The metabolic ratemetabolic rate ( (ΔΔU / U / ΔΔT) is directlyT) is directlyproportional to the rate of oxygenproportional to the rate of oxygenconsumption by volumeconsumption by volumenn Basal metabolic rate (to maintain and run organs,Basal metabolic rate (to maintain and run organs,

etc.) is about 80 Wetc.) is about 80 W

Efficiency of the Human BodyEfficiency of the Human Body

nn Efficiency isEfficiency isthe ratio ofthe ratio ofthethemechanicalmechanicalpowerpowersupplied tosupplied tothethemetabolicmetabolicrate or totalrate or totalpower inputpower input F ig T p. 12.3, . 370

Sl id e 13

Heat EngineHeat Engine

nn A A heat engineheat engine is a device that converts is a device that convertsinternal energy to other useful forms,internal energy to other useful forms,such as electrical or mechanical energysuch as electrical or mechanical energy

nn A heat engine carries some workingA heat engine carries some workingsubstance through a cyclical processsubstance through a cyclical process

We’re heat engines!We’re heat engines!

Heat Pumps and RefrigeratorsHeat Pumps and Refrigerators

nn Heat engines can run in reverseHeat engines can run in reversenn Send in energySend in energynn Energy is extracted from the cold reservoirEnergy is extracted from the cold reservoirnn Energy is transferred to the hot reservoirEnergy is transferred to the hot reservoir

nn This process means the heat engine isThis process means the heat engine isrunning as a heat pumprunning as a heat pumpnn A refrigerator is a common type of heat pumpA refrigerator is a common type of heat pumpnn An air conditioner is another example of a heatAn air conditioner is another example of a heat

pumppump

Second Law ofSecond Law ofThermodynamicsThermodynamics

nn It is impossible to construct a heatIt is impossible to construct a heatengine that, operating in a cycle,engine that, operating in a cycle,produces no other effect than theproduces no other effect than theabsorption of energy from a reservoirabsorption of energy from a reservoirand the performance of an equaland the performance of an equalamount of workamount of worknn Kelvin – Planck statementKelvin – Planck statementnn Means that QMeans that Qcc cannot equal 0 cannot equal 0

nn Some QSome Qcc must be expelled to the environment must be expelled to the environmentnn Means that e cannot equal 100%Means that e cannot equal 100%

Summary of the First andSummary of the First andSecond LawsSecond Laws

nn First LawFirst Lawnn We cannot get a greater amount of energyWe cannot get a greater amount of energy

out of a cyclic process than we put inout of a cyclic process than we put in

nn Second LawSecond Lawnn We cannot break evenWe cannot break even

Reversible and IrreversibleReversible and IrreversibleProcessesProcesses

nn A A reversiblereversible process is one in which every process is one in which everystate along some path is an equilibrium statestate along some path is an equilibrium statenn And one for which the system can be returned toAnd one for which the system can be returned to

its initial state along the same pathits initial state along the same path

nn An An irreversibleirreversible process does not meet these process does not meet theserequirementsrequirementsnn Most natural processes are irreversibleMost natural processes are irreversiblenn Reversible process are an idealization, but someReversible process are an idealization, but some

real processes are good approximationsreal processes are good approximations

EntropyEntropy

nn A state variable related to the SecondA state variable related to the SecondLaw of Thermodynamics, the entropyLaw of Thermodynamics, the entropy

nn The change in entropy, The change in entropy, ΔΔS, betweenS, betweentwo equilibrium states is given by thetwo equilibrium states is given by theenergy, Q, divided by the absoluteenergy, Q, divided by the absolutetemperature, T, of the system in thistemperature, T, of the system in thisintervalinterval

More About EntropyMore About Entropy

nn Note, the equation defines the Note, the equation defines the change inchange inentropyentropy

nn The entropy of the Universe increases in allThe entropy of the Universe increases in allnatural processesnatural processesnn This is another way of expressing the Second Law ofThis is another way of expressing the Second Law of

ThermodynamicsThermodynamics

nn There are processes in which the entropy of aThere are processes in which the entropy of asystem decreasessystem decreasesnn If the entropy of one system, A, decreases it will beIf the entropy of one system, A, decreases it will be

accompanied by the increase of entropy of another system,accompanied by the increase of entropy of another system,B.B.

nn The change in entropy in system B will be greater than thatThe change in entropy in system B will be greater than thatof system A.of system A.

Entropy and DisorderEntropy and Disorder

nn Entropy can be described in terms ofEntropy can be described in terms ofdisorderdisorder

nn A disorderly arrangement is much moreA disorderly arrangement is much moreprobable than an orderly one if the lawsprobable than an orderly one if the lawsof nature are allowed to act withoutof nature are allowed to act withoutinterferenceinterferencenn This comes from a statistical mechanicsThis comes from a statistical mechanics

developmentdevelopment

Chapter 15Chapter 15

WavesWaves

Simple Harmonic Motion andSimple Harmonic Motion andUniform Circular MotionUniform Circular Motion

nn A ball is attached to theA ball is attached to therim of a turntable of radiusrim of a turntable of radiusAA

nn The focus is on theThe focus is on theshadow that the ball castsshadow that the ball castson the screenon the screen

nn When the turntable rotatesWhen the turntable rotateswith a constant angularwith a constant angularspeed, the shadow movesspeed, the shadow movesin simple harmonic motionin simple harmonic motion

FrequencyFrequency

nn The angular frequency is related to theThe angular frequency is related to thefrequencyfrequency

ƒ2πω =

nn PeriodPeriod

nn FrequencyFrequency

nn Units are cycles/second or Hertz, HzUnits are cycles/second or Hertz, Hz

T

T1ƒ =

Motion as a Function of TimeMotion as a Function of Time

nn Use of a Use of a referencereferencecirclecircle allows a allows adescription of thedescription of themotionmotion

nn x = A cos (2x = A cos (2ππƒƒt)t)nn x is the position atx is the position at

time ttime tnn x varies between +Ax varies between +A

and -Aand -A

Graphical Representation ofGraphical Representation ofMotionMotion

nn When x is a maximumWhen x is a maximumor minimum, velocity isor minimum, velocity iszerozero

nn When x is zero, theWhen x is zero, thevelocity is a maximumvelocity is a maximum

nn When x is a maximumWhen x is a maximumin the positive direction,in the positive direction,a is a maximum in thea is a maximum in thenegative directionnegative direction

Verification of SinusoidalVerification of SinusoidalNatureNature

nn This experimentThis experimentshows the sinusoidalshows the sinusoidalnature of simplenature of simpleharmonic motionharmonic motion

nn The spring massThe spring masssystem oscillates insystem oscillates insimple harmonicsimple harmonicmotionmotion

nn The attached penThe attached pentraces out thetraces out thesinusoidal motionsinusoidal motion

Simple PendulumSimple Pendulum

nn The simpleThe simplependulum is anotherpendulum is anotherexample of simpleexample of simpleharmonic motionharmonic motion

nn The force is theThe force is thecomponent of thecomponent of theweight tangent toweight tangent tothe path of motionthe path of motionnn F = - m g sin F = - m g sin θθ

Pendulum, Pendulum, contcont

Period of Simple PendulumPeriod of Simple Pendulum

nn This shows that the period isThis shows that the period isindependent of of the amplitudeindependent of of the amplitude

nn The period depends on the length ofThe period depends on the length ofthe pendulum and the acceleration ofthe pendulum and the acceleration ofgravity at the location of the pendulumgravity at the location of the pendulum

gLT π2=

Damped OscillationsDamped Oscillations

nn Only ideal systems oscillate indefinitelyOnly ideal systems oscillate indefinitelynn In real systems, friction retards theIn real systems, friction retards the

motionmotionnn Friction reduces the total energy of theFriction reduces the total energy of the

system and the oscillation is said to besystem and the oscillation is said to bedampeddamped

Damped Oscillations, cont.Damped Oscillations, cont.

nn Damped motion variesDamped motion variesdepending on the fluiddepending on the fluidusedused

nn With a low viscosityWith a low viscosityfluid, the vibratingfluid, the vibratingmotion is preserved,motion is preserved,but the amplitude ofbut the amplitude ofvibration decreases invibration decreases intime and the motiontime and the motionultimately ceasesultimately ceases

Wave MotionWave Motion

nn A wave is the motion of a disturbanceA wave is the motion of a disturbancenn Mechanical waves requireMechanical waves requirenn Some source of disturbanceSome source of disturbancenn A medium that can be disturbedA medium that can be disturbednn Some physical connection between orSome physical connection between or

mechanism though which adjacent portionsmechanism though which adjacent portionsof the medium influence each otherof the medium influence each other

nn All waves carry energy and momentumAll waves carry energy and momentum

Waves and energyWaves and energy

Types of Waves -- TransverseTypes of Waves -- Transverse

nn In a transverse wave, each element that isIn a transverse wave, each element that isdisturbed moves perpendicularly to the wavedisturbed moves perpendicularly to the wavemotionmotion

Types of Waves --Types of Waves --LongitudinalLongitudinal

nn In a longitudinal wave, the elements of theIn a longitudinal wave, the elements of themedium undergo displacements parallel tomedium undergo displacements parallel tothe motion of the wavethe motion of the wave

nn A longitudinal wave is also called aA longitudinal wave is also called acompression wavecompression wave

EarthquakesEarthquakes

Waveform – A Picture of aWaveform – A Picture of aWaveWave

nn The red curve is aThe red curve is a“snapshot” of the“snapshot” of thewave at somewave at someinstant in timeinstant in time

nn The blue curve isThe blue curve islater in timelater in time

nn A is a A is a crestcrest of the of thewavewave

nn B is a B is a troughtrough of the of thewavewave

Longitudinal WaveLongitudinal WaveRepresented as a Sine CurveRepresented as a Sine Curve

nn A longitudinal wave can also be representedA longitudinal wave can also be representedas a sine curveas a sine curve

nn Compressions correspond to crests andCompressions correspond to crests andstretches correspond to troughsstretches correspond to troughs

Description of a WaveDescription of a Wave

nn Amplitude is theAmplitude is themaximum displacementmaximum displacementof string above theof string above theequilibrium positionequilibrium position

nn Wavelength, Wavelength, λλ, is the, is thedistance between twodistance between twosuccessive points thatsuccessive points thatbehave identicallybehave identically

Speed of a WaveSpeed of a Wavenn v = ƒ v = ƒ λλnn Is derived from the basic speed equation ofIs derived from the basic speed equation of

distance/timedistance/time

nn This is a general equation that can beThis is a general equation that can beapplied to many types of wavesapplied to many types of waves

nn Example: Example: The speed on a wave stretchedThe speed on a wave stretchedunder some tension, under some tension, FF

LmFv == µ

µwhere

Interference of WavesInterference of Waves

nn Two traveling waves can meet and passTwo traveling waves can meet and passthrough each other without being destroyedthrough each other without being destroyedor even alteredor even altered

nn Waves obey the Waves obey the Superposition PrincipleSuperposition Principlenn If two or more traveling waves are movingIf two or more traveling waves are moving

through a medium, the resulting wave is found bythrough a medium, the resulting wave is found byadding together the displacements of theadding together the displacements of theindividual waves point by pointindividual waves point by point

nn Actually only true for waves with small amplitudesActually only true for waves with small amplitudes

Interference of Waves, Interference of Waves, contcont..

Constructive InterferenceConstructive Interference

nn Two waves, a and b,Two waves, a and b,have the samehave the samefrequency andfrequency andamplitudeamplitudenn Are Are in phasein phase

nn The combined wave,The combined wave,c, has the samec, has the samefrequency and afrequency and agreater amplitudegreater amplitude

Destructive InterferenceDestructive Interference

nn Two waves, a and b,Two waves, a and b,have the samehave the sameamplitude andamplitude andfrequencyfrequency

nn They are 180° out ofThey are 180° out ofphasephase

nn When they combine,When they combine,the waveforms cancelthe waveforms cancel

Chapter 16Chapter 16

SoundSound

Using a Tuning Fork toUsing a Tuning Fork toProduce a Sound WaveProduce a Sound Wave

nn A tuning fork will produce a pureA tuning fork will produce a puremusical notemusical note

nn As the tines vibrate, they disturbAs the tines vibrate, they disturbthe air near themthe air near them

nn As the tine swings to the right, itAs the tine swings to the right, itforces the air molecules near itforces the air molecules near itcloser togethercloser together

nn This produces a high densityThis produces a high densityarea in the airarea in the airnn This is an area of compressionThis is an area of compression

Using a Tuning Fork, cont.Using a Tuning Fork, cont.

nn As the tine moves towardAs the tine moves towardthe left, the air moleculesthe left, the air moleculesto the right of the tineto the right of the tinespread outspread out

nn This produces an area ofThis produces an area oflow densitylow densitynn This area is called aThis area is called a

rarefactionrarefaction

Using a Tuning Fork, finalUsing a Tuning Fork, final

nn As the tuning fork continues to vibrate, a successionAs the tuning fork continues to vibrate, a successionof compressions and rarefactions spread out from theof compressions and rarefactions spread out from theforkfork

nn A sinusoidal curve can be used to represent theA sinusoidal curve can be used to represent thelongitudinallongitudinal wave wavenn Crests correspond to compressions and troughs toCrests correspond to compressions and troughs to

rarefactionsrarefactions

Categories of Sound WavesCategories of Sound Waves

nn Audible wavesAudible wavesnn Lay within the normal range of hearing ofLay within the normal range of hearing of

the human earthe human earnn Normally between 20 Hz to 20,000 HzNormally between 20 Hz to 20,000 Hz

nn Infrasonic wavesInfrasonic wavesnn Frequencies are below the audible rangeFrequencies are below the audible range

nn Ultrasonic wavesUltrasonic wavesnn Frequencies are above the audible rangeFrequencies are above the audible range

Applications of UltrasoundApplications of Ultrasound

nn Can be used to produce images of smallCan be used to produce images of smallobjectsobjects

nn Widely used as a diagnostic and treatmentWidely used as a diagnostic and treatmenttool in medicinetool in medicinenn Ultrasonic flow meter to measure blood flowUltrasonic flow meter to measure blood flownn May use May use piezoelectricpiezoelectric devices that transform devices that transform

electrical energy into mechanical energyelectrical energy into mechanical energynn Reversible: mechanical to electricalReversible: mechanical to electrical

nn Ultrasounds to observe babies in the wombUltrasounds to observe babies in the wombnn Cavitron Ultrasonic Surgical Aspirator (CUSA) usedCavitron Ultrasonic Surgical Aspirator (CUSA) used

to surgically remove brain tumorsto surgically remove brain tumorsnn Ultrasonic ranging unit for camerasUltrasonic ranging unit for cameras

Speed of Sound in a LiquidSpeed of Sound in a Liquid

nn In a liquid, the speed depends on the liquid’sIn a liquid, the speed depends on the liquid’scompressibility and inertiacompressibility and inertia

nn B is the Bulk Modulus of the liquidB is the Bulk Modulus of the liquidnn ρρ is the density of the liquid is the density of the liquidnn Compares with the equation for a transverse waveCompares with the equation for a transverse wave

on a stringon a string

VVPBBv/∆

∆−== where

ρ

Speed of Sound in AirSpeed of Sound in Air

nn 331 m/s is the speed of sound at 0° C331 m/s is the speed of sound at 0° Cnn T is the absolute temperatureT is the absolute temperature

K273T)

sm331(v =

Interference of Sound WavesInterference of Sound Waves

nn Sound waves interfereSound waves interferenn Constructive interference occurs when theConstructive interference occurs when the

path difference between two waves’path difference between two waves’motion is zero or some integer multiple ofmotion is zero or some integer multiple ofwavelengthswavelengthsnn path difference = npath difference = nλλ

nn Destructive interference occurs when theDestructive interference occurs when thepath difference between two waves’path difference between two waves’motion is an odd half wavelengthmotion is an odd half wavelengthnn path difference = (n + path difference = (n + ½½))λλ

Standing WavesStanding Waves

nn When a traveling wave reflects back onWhen a traveling wave reflects back onitself, it creates traveling waves in bothitself, it creates traveling waves in bothdirectionsdirections

nn The wave and its reflection interfereThe wave and its reflection interfereaccording to the superposition principleaccording to the superposition principle

nn With exactly the right frequency, theWith exactly the right frequency, thewave will appear to stand stillwave will appear to stand stillnn This is called a This is called a standing wavestanding wave

Standing Waves, Standing Waves, contcont..

Standing Waves, contStanding Waves, cont

nn A A nodenode occurs where the two traveling occurs where the two travelingwaves have the same magnitude ofwaves have the same magnitude ofdisplacement, but the displacementsdisplacement, but the displacementsare in opposite directionsare in opposite directionsnn Net displacement is zero at that pointNet displacement is zero at that pointnn The distance between two nodes is The distance between two nodes is ½½λλ

nn An An antinodeantinode occurs where the standing occurs where the standingwave vibrates at maximum amplitudewave vibrates at maximum amplitude

Standing Waves on a StringStanding Waves on a String

nn Nodes must occur atNodes must occur atthe ends of thethe ends of thestring because thesestring because thesepoints are fixedpoints are fixed

F ig p 14.16, . 442

Sl ide 18

Standing Waves on a String,Standing Waves on a String,cont.cont.

nn The lowestThe lowestfrequency offrequency ofvibration (b) isvibration (b) iscalled thecalled thefundamentalfundamentalfrequencyfrequency

F ig p 14.18, . 443

Sl i de 25µ

==F

L2nƒnƒ 1n

Standing Waves on a StringStanding Waves on a String

nn ƒƒ11, ƒ, ƒ22, ƒ, ƒ33 form a harmonic series form a harmonic seriesnn ƒƒ1 1 is the fundamental and also the first is the fundamental and also the first

harmonicharmonicnn ƒƒ22 is the second harmonic is the second harmonic

nn Waves in the string that are not in theWaves in the string that are not in theharmonic series are quickly damped outharmonic series are quickly damped outnn In effect, when the string is disturbed, itIn effect, when the string is disturbed, it

“selects” the standing wave frequencies“selects” the standing wave frequencies

Forced VibrationsForced Vibrations

nn A system with a driving force will forceA system with a driving force will forcea vibration at its frequencya vibration at its frequency

nn When the frequency of the driving forceWhen the frequency of the driving forceequals the natural frequency of theequals the natural frequency of thesystem, the system is said to be insystem, the system is said to be inresonanceresonance

nn Examples:Examples:nn Child on a swingChild on a swingnn Shattering glassesShattering glasses

Resonance, Resonance, contcont..

Resonance, Resonance, contcont..

Standing Waves in AirStanding Waves in AirColumnsColumns

nn If one end of the air column is closed, aIf one end of the air column is closed, anode must exist at this end since thenode must exist at this end since themovement of the air is restrictedmovement of the air is restricted

nn If the end is open, the elements of theIf the end is open, the elements of theair have complete freedom ofair have complete freedom ofmovement and an antinode existsmovement and an antinode exists

Standing waves,Standing waves,exampleexample

Tube Open at Both EndsTube Open at Both Ends

Resonance in Air ColumnResonance in Air ColumnOpen at Both EndsOpen at Both Ends

nn In a pipe open at both ends, the naturalIn a pipe open at both ends, the naturalfrequency of vibration forms a seriesfrequency of vibration forms a serieswhose harmonics are equal to integralwhose harmonics are equal to integralmultiples of the fundamental frequencymultiples of the fundamental frequency

,3,2,1nL2vnƒn ==

Tube Closed at One EndTube Closed at One End

Resonance in an Air ColumnResonance in an Air ColumnClosed at One EndClosed at One End

nn The closed end must be a nodeThe closed end must be a nodenn The open end is an antinodeThe open end is an antinode

,5,3,1nL4vnfn ==

Resonance, ExampleResonance, Example

BeatsBeats

nn BeatsBeats are alternations in loudness, due to are alternations in loudness, due tointerferenceinterference

nn Waves have slightly different frequencies and theWaves have slightly different frequencies and thetime between constructive and destructivetime between constructive and destructiveinterference alternatesinterference alternates

The EarThe Ear

nn The outer ear consistsThe outer ear consistsof the ear canal thatof the ear canal thatterminates at theterminates at theeardrumeardrum

nn Just behind theJust behind theeardrum is the middleeardrum is the middleearear

nn The bones in the middleThe bones in the middleear transmit sounds toear transmit sounds tothe inner earthe inner ear

F ig p 14.27, . 452

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