热学教学教程电子教案

HeatEngines,HeatPumps,andRefrigeratorsGettingsomethingusefulfromheatSpring20071HeatcanbeusefulNormallyheatistheend-productoftheflow/transformationofenergyrememberexamplesfromlecture#4(coffeemug,automobile,bouncingball)heatregardedaswaste:asuselessendresultSometimesheatiswhatwewant,thoughhotwater,cooking,spaceheatingHeatcanalsobecoercedintoperforming“useful”(e.g.,mechanical)workthisiscalleda“heatengine”Spring20072HeatEngineConceptAnytimeatemperaturedifferenceexistsbetweentwobodies,thereisapotentialforheatflowExamples:heatflowsoutofahotpotofsoupheatflowsintoacolddrinkheatflowsfromthehotsandintoyourfeetRateofheatflowdependsonnatureofcontactandthermalconductivityofmaterialsIfwe’reclever,wecanchannelsomeofthisflowofenergyintomechanicalworkSpring20073HeatWorkWecanseeexamplesofheatenergyproducingothertypesofenergyAiroverahotcarroofislofted,gainingkineticenergyThatsameairalsogainsgravitationalpotentialenergyAllofourwindisdrivenbytemperaturedifferencesWealreadyknowaboutradiative

heatenergytransferOurelectricitygenerationthrivesontemperaturedifferences:nosteamwouldcirculateifeverythingwasatthesametemperatureSpring20074PowerPlantArrangementHeatflowsfromTh

toTc,turningturbinealongthewaySpring20075HeatEngineNomenclatureThesymbolsweusetodescribetheheatengineare:Th

isthetemperatureofthehotobjectTc

isthetemperatureofthecoldobjectT=Th–Tc

isthetemperaturedifference

Qh

istheamountofheatthatflowsoutofthehotbodyQcistheamountofheatflowingintothecoldbodyWistheamountof“useful”mechanicalwork

Sh

isthechangeinentropyofthehotbodySc

isthechangeinentropyofthecoldbody

Stot

isthetotalchangeinentropy(entiresystem)EistheentireamountofenergyinvolvedintheflowSpring20076What’sthisEntropybusiness?Entropyisameasureofdisorder(andactuallyquantifiableonanatom-by-atombasis)Icehaslowentropy,liquidwaterhasmore,steamhasalotSpring20077TheLawsofThermodynamicsEnergyisconservedTotalsystementropycanneverdecreaseAsthetemperaturegoestozero,theentropyapproachesaconstantvalue—thisvalueiszeroforaperfectcrystallatticeTheconceptofthe“totalsystem”isveryimportant:entropycandecreaselocally,butitmustincreaseelsewherebyatleastasmuchnoenergyflowsintooroutofthe“totalsystem”:ifitdoes,there’smoretothesystemthanyouthoughtSpring20078QuantifyingheatenergyWe’vealreadyseenmanyexamplesofquantifyingheat1Calorieistheheatenergyassociatedwithraising1kg(1liter)ofwater1ºCIngeneral,Q=cpmT,wherecpistheheatcapacityWeneedtoalsopointoutthatachangeinheatenergyaccompaniesachangeinentropy:

Q=TSAddingheatincreasesentropymoreenergygoesintorandommotionsmorerandomness(entropy)Spring20079Howmuchworkcanbeextractedfromheat?Th

Qh

QcW=Qh

–

QcTcHotsourceofenergyColdsinkofenergyheatenergydeliveredfromsourceheatenergydeliveredtosinkexternallydeliveredwork:efficiency==W

workdone

Qh

heatsuppliedconservationofenergySpring200710Let’scrankuptheefficiencyTh

Qh

QcW=Qh

–

QcTcefficiency==W

workdone

Qh

heatsuppliedLet’sextractalotofwork,anddeliververylittleheattothesinkInfact,let’sdemand100%efficiencybysendingnoheattothesink:allconvertedtousefulworkSpring200711Notsofast…Thesecondlawofthermodynamicsimposesaconstraintonthisrecklessattitude:totalentropymustneverdecreaseTheentropyofthesourcegoesdown(heatextracted),andtheentropyofthesinkgoesup(heatadded):rememberthatQ=TSThegaininentropyinthesinkmustatleastbalancethelossofentropyinthesource

Stot

=Sh

+Sc=–

Qh/Th

+Qc/Tc

≥0

Qc≥(Tc/Th)

Qh

setsaminimumonQcSpring200712Whatdoesthisentropylimitmean?W=Qh

–Qc,soWcanonlybeasbigastheminimumQcwillallow

Wmax

=Qh

–Qc,min=Qh

–

Qh(Tc/Th)=

Qh(1–Tc/Th)Sothemaximumefficiencyis:maximumefficiency=Wmax/

Qh

=(1–

Tc/Th)=(Th

–Tc)/ThthisandsimilarformulasmusthavethetemperatureinKelvinSoperfectefficiencyisonlypossibleifTc

iszero(inºK)Ingeneral,thisisnottrueAsTc

Th,theefficiencydropstozero:noworkcanbeextractedSpring200713ExamplesofMaximumEfficiencyAcoalfireburningat825ºKdeliversheatenergytoareservoirat300ºKmaxefficiencyis(825–300)/825=525/825=64%thispowerstationcannotpossiblyachieveahigherefficiencybasedonthesetemperaturesAcarenginerunningat400ºKdeliversheatenergytotheambient290ºKairmaxefficiencyis(400–290)/400=110/400=27.5%nottoofarfromrealitySpring200714ExampleefficienciesofpowerplantsPowerplantsthesedays(almostallofwhichareheat-engines)typicallygetnobetterthan33%overallefficiencySpring200715Whattodowiththewasteheat(Qc)?Oneoption:useitforspace-heatinglocallySpring200716OverallefficiencygreatlyenhancedbycogenerationSpring200717HeatPumpsHeatPumpsprovideameanstoveryefficientlymoveheataround,andworkbothinthewinterandthesummerSpring200718HeatPumpDiagramSpring200719HeatPumpsandRefrigerators:ThermodynamicsTh

Qh

QcW=Qh

–

QcTcHotentity(indoorair)Coldentity(outsideairorrefrigerator)heatenergydeliveredheatenergyextracteddeliveredwork:conservationofenergyJustaheatenginerunbackwards…efficiency==W

workdone

Qh

heatdelivered(heatpump)efficiency==W

workdone

Qc

heatextracted(refrigerator)Spring200720HeatPump/RefrigeratorEfficienciesCanworkthroughsamesortoflogicasbeforetoseethat:heatpumpefficiencyis:Th/(Th

–Tc)=Th/T

inºKrefrigeratorefficiencyis:Tc/(Th

–

Tc)=Tc/T

inºKNotethatheatpumpsandrefrigeratorsaremostefficientforsmalltemperaturedifferenceshardonheatpumpsinverycoldclimateshardonrefrigeratorsinhotsettingsSpring200721ExampleEfficiencies