英文版大学物理 第八章

TheFirstLawofThermodynamicsChapter8Chapter8TheFirstLawofThermodynamics

8-1ChangesinThermodynamicSystems8-2HeatandWorkDonebyThermodynamicSystems8-3TheFirstLawofThermodynamics8-4SomeSpecialCasesoftheFirstlawofThermodynamics8-5TheMolarSpecificHeatsofanIdealGas8-6TheAdiabaticExpansionofanIdealGas8-7HeatTransferMechanisms8-1ChangesinThermodynamicSystemsThermodynamicsystemsinequilibrium,suchasabottleofhotsteam,aredescribedbyonlyafewthermodynamicvariables.Foragasthesevariablesare

p,V,T,

(orN).Foranidealgas,pV=

RT=

NkT.Assumethat

isfixed,thenitisenoughtodescribethe(equilibrium)stateonatwo-dimensionalplot,suchasap

Vdiagram,ap

Tdiagram,oraV

Tdiagram.ThermodynamicprocessWhenthesurroundingischanged,asystemwilldeviatefromequilibrium.Afteratime

,thesystemwillreachanewequilibriumstate(ifexists).Wesaythatthesystemundergoesathermodynamicprocess.Thetime

iscalledrelaxationtime.

Quasi-staticprocess

Tomaintainthermalequilibriumateachstepinathermalprocess,changesmustbemadesuchslowlythatthetimetakenbythethermalprocessismuchlongerthanrelaxationtime.Suchaprocessiscalled

quasi-staticprocess,whichcanberepresentedasacurveonap

Vdiagram,ap

Tdiagram,oraV

Tdiagram.Unlesswestateotherwise,weconsideronlyquasi-staticprocess.Thermodynamicsisbasedonourabilitytotreatquasi-staticprocess.Therearesituations(suchasfreeexpansion)inwhichprocessesoccurtoofastforequilibriumthermodynamicstoapply.Somequasi-staticprocessesiVp(a)(b)(d)(c)pconstantpressure(isobaric)process;isothermalprocess;isentropic(adiabatic)process;constantvolume(isochoric)process.8-2HeatandWorkDonebyThermodynamicSystemsTESystemTSQEnvironmentTS>TE

Q<0

TESystemTSEnvironmentTS=TE

Q=0

TESystemTSQEnvironmentTS<TE

Q>0

HeatHeatistheenergythatistransferredbetweenasystemanditsenvironmentbecauseofatemperaturedifferencethatexistsbetweenthem.HeatislostbythesystemtotheenvironmentQ<0.HeatisabsorbedbythesystemfromtheenvironmentQ>0.HeatisneitherreleasednorabsorbedQ=0.WorkDonebyThermodynamicSystemsdsApConsiderapistonofareaApushedoutbythepressurepofthegascontainedinthecylinder.TheinfinitesimalworkdonebythegasinmovingthepistondsisThevolumechangesfromVi

toVf:Duringthechangeinvolume,thepressureandtemperaturemayalsochange.Thereareactuallymanywaystotakethegasfromstateitostatef.0pW>0Vifahp0VifcgWnet

>00VpifThermodynamiccycleW<00VpifcompressedW>0Process0VpifexpandedDiscussionW>00VpifcAsystemcanbetakenfromagiveninitialstatetoagivenfinalstatebyaninfinitenumberofprocesses.Heatmayormaynotbeinvolved,andingeneral,theworkWandtheheatQwillhavedifferentvaluesfordifferentprocess.Wesaythatheatandworkarepath-dependentquantitiesCheckpoint18-3TheFirstLawofThermodynamicsIfanamountofheatQentersathermodynamicsystem,itcouldmanifestitselfaseitheranincreaseininternalenergyoraresultingquantityofworkperformedbythesystemonthesurroundings,orabitofboth.Then

Q

=

Eint

W，where

Eintisthechangeinthesystem’sinternalenergy,Wisthenetworkdonebythesystem.Notethatbeforethischapter,thetermwork

meantthattheworkdoneonasystemandissymbolizedW.However,inthischapterandthenext,wedefinethe

workandthesymbolWastheworkdonebyasystem.Ifthethermodynamicsystemundergoesonlyadifferentialprocess,dQ

=

dEint

dW.Checkpoint28-4SomeSpecialCasesoftheFirstlawofThermodynamics1.Constant-volumeprocessesiVpfpfpiOVIfV=constant,W=0.Suchaprocessiscalledanisochoricprocess,

Q

=

Eint

W

Eint

=

Q

Because

Eint=Q

=,ThenNotethat

Eintisafunctionofstateonly,and

Eintisindependentofprocesses,butQdependsonthepath.Therefore,thisequationholdsonlyforconstant-volumeprocess.2.Constant-pressureprocessesW>0ifOpVpVi

Vf

Anisobaricprocessisoneinwhichthepressureiskeptconstant.IfthevolumechangesfromVi

toVf

whilethepressureofthegasisheldconstantp,theworkdonebythegasisgivenby=

p(Vf

Vi)

Eintisindependentofprocesses,foranyprocessQ=

Eint

W=p(Vf

Vi)Fromthefirstlawofthermodynamics,heattransferinanisobaricprocessisgivenby3.Isothermalprocesses.

W>0TOVpifpipfViVfSupposethatweallowanidealgastoexpandfromaninitialvolumeVitoafinalvolumeVf

whilewekeepthetemperatureTofthegasconstant.isothermalexpansion:Vi<Vf

isothermalcompression:Vi>VfForanidealgas,theinternalenergyisthefunctionoftemperature,thusforanisothermalprocess

Eint=0Q=W

Fromthefirstlawofthermodynamics,workdonebyanidealgasduringanisothermalexpansion8-5TheMolarSpecificHeatsofanIdealGasHeatcapacityproportionalityconstantbetweentheheatdQthattheobjectabsorbsorlosesandtheresultingtemperaturechangedToftheobjectTheheatcapacityCofanobjectistheBecauseheatisapath-dependentquantity,theheatcapacityforagivenbodywillhavedifferentvaluesfordifferentprocesses.Forconstantvolume:Forconstantpressure:

MolarSpecificHeatatConstantVolumeSupposethat

molesofanidealgasundergoaninfinitesimalprocess,absorbasmallamountofheat

dQ,andthegastemperaturerisesasmallamountof

dT，ForanidealgasForaconstantvolumeprocess,dV=

0,(holdsforanyprocess)FromthedefinitionforheatcapacityatconstantvolumeThemolarspecificheatatconstantvolumeofanidealgasMolarSpecificHeatatConstantPressureForaconstantpressureprocess,dW=

pdV=

RdT

FromthedefinitionforheatcapacitySubstitutingdWanddEintintoForanyprocess,ThemolarspecificheatatconstantvolumeofanidealgasorSummary(anyidealgas).(idealgas,anyprocess).AchangeintheinternalenergyEintofaconfinedidealgasdependsonthechangeinthegastemperatureonly;itdoesnotdependonwhattypeofprocessproducesthechangeinthetemperature.IntermsofCV,m,EintcanberewrittenasCheckpoint3Example8-2Abubbleof5.00molofheliumatacertaindepthinliquidwaterwhenthewater(andthusthehelium)undergoesatemperatureincrease

Tof20.0C

atconstantpressure.Asaresult,thebubbleexpands.Theheliumismonatomicandideal.(a)Howmuchenergyisaddedaheattotheheliumduringtheincreaseandexpansion?Solution:BecausethepressurepisheldconstantduringtheadditionofenergyBecause=(5.00)(2.5)(8.31)(20)=2077.5J

2078J.(b)Whatisthechange

Eintintheinternalenergyoftheheliumduringthetemperatureincrease?Solution:Foranyprocessofanyidealgas,

Eintdependsonlyonthechangeintemperatu