A2Physics物理出國英語ThermodynamicsMS

1.

Question:Agasisheatedatconstantvolume.Whathappenstotheinternalenergyofthegas?

Answer:Accordingtothefirstlawofthermodynamics,$DeltaU=Q+W$.Atconstantvolume,$W=0$(since$W=PDeltaV$and$DeltaV=0$).Whenthegasisheated,$Q>0$.So,$DeltaU=Q$.Theinternalenergyofthegasincreasesasheatisaddedtothegasatconstantvolume.

2.

Question:Asystemundergoesanadiabaticprocess.Iftheworkdoneonthesystemis50J,whatisthechangeininternalenergy?

Answer:Foranadiabaticprocess,$Q=0$.Fromthefirstlawofthermodynamics$DeltaU=Q+W$.Substituting$Q=0$and$W=50J$,weget$DeltaU=50J$.Theinternalenergyofthesystemincreasesby50Jbecauseworkisdoneonthesystem.

3.

Question:Explainwhythetemperatureofagasdecreasesduringanadiabaticexpansion.

Answer:Inanadiabaticexpansion,$Q=0$.Thegasexpands,soitdoesworkonthesurroundings,i.e.,$W>0$.Fromthefirstlawofthermodynamics$DeltaU=Q+W$,with$Q=0$,wehave$DeltaU=W$.Since$W>0$,$DeltaU<0$.Theinternalenergyofanidealgasisdirectlyproportionaltoitstemperature($U=frac{3}{2}nRT$foramonoatomicidealgas).Adecreaseininternalenergyimpliesadecreaseintemperature.

4.

Question:Agasexpandsisothermally.Whatcanbesaidabouttheheattransferandworkdone?

Answer:Foranisothermalprocessofanidealgas,$DeltaU=0$(becauseinternalenergyofanidealgasdependsonlyontemperature,andtemperatureisconstant).Fromthefirstlawofthermodynamics$DeltaU=Q+W$,so$0=Q+W$,whichmeans$Q=W$.Thegasdoesworkonthesurroundings($W>0$asthevolumeincreases),andheatmustbeaddedtothegas($Q>0$)tomaintainaconstanttemperature.

5.

Question:Twodifferentgases,heliumandnitrogen,areatthesametemperature.Comparetheiraveragekineticenergiespermolecule.

Answer:Theaveragekineticenergypermoleculeofanidealgasisgivenby$overline{E_k}=frac{3}{2}kT$,where$k$istheBoltzmannconstantand$T$isthetemperature.Sincebothheliumandnitrogenareatthesametemperature,theiraveragekineticenergiespermoleculeareequal.

6.

Question:Agasiscompressedisobarically.Doestheinternalenergyofthegasincreaseordecrease?

Answer:Inanisobariccompression,thevolumedecreases($DeltaV<0$),sotheworkdoneonthegas$W=PDeltaV<0$(negativeworkisdoneonthegas).Heatisusuallyreleasedfromthegasduringcompression.Fromthefirstlawofthermodynamics$DeltaU=Q+W$.Theheatreleased$Q<0$.Also,theworkdoneonthegasisnegative.Theinternalenergyofthegasusuallydecreasesbecausebothheatlossandworkdoneonthegascontributetoadecreaseininternalenergy.

7.

Question:Whatisthedifferencebetweenanisothermalandanadiabaticprocessintermsofheattransfer?

Answer:Inanisothermalprocess,thetemperatureofthesystemremainsconstant.Heatcanbetransferredtoorfromthesystemtomaintaintheconstanttemperature.Forexample,whenagasexpandsisothermally,heatisaddedtothegas.Inanadiabaticprocess,thereisnoheattransferbetweenthesystemandthesurroundings,i.e.,$Q=0$.

8.

Question:Agasinacontainerisheatedatconstantpressure.Whatfractionoftheheatsuppliedisusedtodoworkandwhatfractionisusedtoincreasetheinternalenergyforamonoatomicidealgas?

Answer:Foramonoatomicidealgas,$C_p=frac{5}{2}R$and$C_v=frac{3}{2}R$.Atconstantpressure,$Q=nC_pDeltaT$and$DeltaU=nC_vDeltaT$.Theworkdone$W=QDeltaU=n(C_pC_v)DeltaT$.Since$C_pC_v=R$,thefractionofheatusedforworkis$frac{W}{Q}=frac{nRDeltaT}{nC_pDeltaT}=frac{R}{frac{5}{2}R}=frac{2}{5}$,andthefractionusedtoincreaseinternalenergyis$frac{DeltaU}{Q}=frac{nC_vDeltaT}{nC_pDeltaT}=frac{frac{3}{2}R}{frac{5}{2}R}=frac{3}{5}$.

9.

Question:Explaintheconceptofentropyintermsofdisorder.

Answer:Entropyisameasureofthedegreeofdisorderinasystem.Asystemwithhighentropyismoredisordered.Forexample,whenagasexpandsintoalargervolume,themoleculeshavemorepossiblepositionsandvelocities,sothedisorderofthesystemincreases,andtheentropyofthegasincreases.Inaspontaneousprocess,thetotalentropyoftheuniversealwaysincreases.

10.

Question:Aheatengineoperatesbetweentworeservoirsattemperatures$T_1$and$T_2$($T_1>T_2$).Whatisthemaximumefficiencyoftheheatengine?

Answer:ThemaximumefficiencyofaheatengineisgivenbytheCarnotefficiency,$eta=1frac{T_2}{T_1}$,where$T_1$isthetemperatureofthehotreservoirand$T_2$isthetemperatureofthecoldreservoir.ThisefficiencyisachievedbyaCarnotengine,whichisanidealizedreversibleheatengine.

11.

Question:Whycan'taheatenginehave100%efficiency?

Answer:Accordingtothesecondlawofthermodynamics,itisimpossibletoconvertalltheheatabsorbedfromahotreservoirintowork.Someheatmustberejectedtoacoldreservoir.Inaheatengine,theworkdone$W=Q_1Q_2$,where$Q_1$istheheatabsorbedfromthehotreservoirand$Q_2$istheheatrejectedtothecoldreservoir.Theefficiency$eta=frac{W}{Q_1}=1frac{Q_2}{Q_1}$.Since$Q_2>0$,theefficiencyisalwayslessthan100%.

12.

Question:Arefrigeratorhasacoefficientofperformance(COP).Whatdoesitrepresentandhowisitcalculated?

Answer:Thecoefficientofperformanceofarefrigeratorrepresentstheratiooftheheatremovedfromthecoldreservoirtotheworkinput.Forarefrigerator,$COP=frac{Q_2}{W}$,where$Q_2$istheheatremovedfromthecoldreservoirand$W$istheworkdoneontherefrigerator.

13.

Question:Agasistakenthroughacyclicprocess.Whatisthenetchangeininternalenergy?

Answer:Sincetheinternalenergyofasystemisastatefunction,andinacyclicprocess,thesystemreturnstoitsinitialstate.Thenetchangeininternalenergy$DeltaU=0$.Fromthefirstlawofthermodynamics$DeltaU=Q+W$,so$Q=W$.Thenetheattransfertothesystemisequaltothenetworkdonebythesystem.

14.

Question:Comparethespecificheatcapacitiesatconstantvolumeandconstantpressureforanidealgas.

Answer:Foranidealgas,thespecificheatcapacityatconstantvolume$C_v$isrelatedtotheinternalenergychangeofthegas.Thespecificheatcapacityatconstantpressure$C_p$isrelatedtotheheattransferatconstantpressure.Therelationshipbetweenthemis$C_pC_v=R$,where$R$istheuniversalgasconstant.Since$R>0$,$C_p>C_v$.

15.

Question:Agasisexpandinginsuchawaythat$PV=$constant.Whattypeofprocessisthis?

Answer:Aprocessinwhich$PV=$constantisanisothermalprocessforanidealgas.Fromtheidealgaslaw$PV=nRT$,if$PV$isconstant,thenthetemperature$T$isconstant.

16.

Question:WhatisthesignificanceoftheBoltzmannconstantinthermodynamics?

Answer:TheBoltzmannconstant$k$relatesthemacroscopicpropertiesofagas(suchastemperature)tothemicroscopicpropertiesofitsmolecules.Forexample,theaveragekineticenergyofamoleculeofanidealgasisgivenby$overline{E_k}=frac{3}{2}kT$.Italsoappearsinthestatisticaldefinitionofentropy$S=klnOmega$,where$Omega$isthenumberofmicrostatesofthesystem.

17.

Question:Agasiscompressedrapidly.Isthisprocessmorelikelytobeadiabaticorisothermal?

Answer:Thisprocessismorelikelytobeadiabatic.Whenagasiscompressedrapidly,thereisnotenoughtimeforsignificantheattransfertooccurbetweenthegasandthesurroundings.Inanadiabaticprocess,$Q=0$.Incontrast,foranisothermalprocess,heattransfermustoccurtomaintainaconstanttemperature,whichisnotpossibleinarapidcompression.

18.

Question:Anidealgasisheatedatconstantvolumeuntilitspressuredoubles.Bywhatfactordoestheinternalenergychange?

Answer:Fromtheidealgaslaw$PV=nRT$,atconstantvolume$V$,$frac{P_1}{T_1}=frac{P_2}{T_2}$.If$P_2=2P_1$,then$T_2=2T_1$.Theinternalenergyofanidealgas$U=frac{3}{2}nRT$(foramonoatomicidealgas).So,$frac{U_2}{U_1}=frac{frac{3}{2}nRT_2}{frac{3}{2}nRT_1}=frac{T_2}{T_1}=2$.Theinternalenergydoubles.

19.

Question:Explaintheconceptofareversibleprocessinthermodynamics.

Answer:Areversibleprocessisanidealizedprocessinwhichthesystemanditssurroundingscanberestoredtotheirinitialstateswithoutleavinganytraceontheuniverse.Inareversibleprocess,thesystemisalwaysinequilibriumwithitssurroundingsateverystageoftheprocess.Forexample,aCarnotcycleconsistsofreversibleisothermalandadiabaticprocesses.

20.

Question:Aheatpumpisusedtoheatahouse.Howdoesitworkandwhatisitsadvantageoverasimpleheater?

Answer:Aheatpumpextractsheatfromacoldreservoir(suchastheoutsideair)andtransfersittoahotreservoir(theinsideofthehouse).Itusesworkinputtoachievethisheattransfer.Theadvantageoverasimpleheateristhattheheatpumpcantransfermoreheattothehotreservoirthantheworkinput.Thecoefficientofperformanceofaheatpump$COP=frac{Q_1}{W}$,where$Q_1$istheheatdeliveredtothehotreservoirand$W$istheworkinput.Foraheatpump,$COP>1$,soitcanbemoreenergyefficientthanasimpleheaterthatconvertsallelectricalenergyintoheat.

21.

Question:Agasisallowedtoexpandfreelyintoavacuum.Whatisthechangeininternalenergyandtemperature?

Answer:Whenagasexpandsfreelyintoavacuum,noworkisdoneonorbythegas($W=0$)becausethereisnoexternalpressure.Also,sincetheexpansionisrapidandthereisnoheattransfer($Q=0$).Fromthefirstlawofthermodynamics$DeltaU=Q+W$,so$DeltaU=0$.Foranidealgas,sinceinternalenergydependsonlyontemperatureand$DeltaU=0$,thetemperatureofthegasremainsconstant.

22.

Question:Inarealgas,howdoesthebehaviordeviatefromanidealgasathighpressures?

Answer:Athighpressures,thevolumeofthegasmoleculesthemselvesbecomessignificantcomparedtothetotalvolumeofthegas.Also,theintermolecularforcesbetweenthegasmoleculescannotbeneglected.Inanidealgas,themoleculesareassumedtohavenovolumeandnointermolecularforces.Arealgaswillhaveasmallervolumethanpredictedbytheidealgaslawathighpressuresduetothefinitevolumeofthemoleculesandtheattractiveintermolecularforces.

23.

Question:AgasistakenfromstateAtostateBalongtwodifferentpaths.Comparethechangeininternalenergyandtheheattransferforthetwopaths.

Answer:Thechangeininternalenergy$DeltaU$isthesameforbothpathsbecauseinternalenergyisastatefunction,whichdependsonlyontheinitialandfinalstates.However,theheattransfer$Q$andtheworkdone$W$canbedifferentforthetwopaths.Fromthefirstlawofthermodynamics$DeltaU=Q+W$.Differentpathscanhavedifferentcombinationsofheattransferandworkdonetoachievethesamechangeininternalenergy.

24.

Question:Whatistheeffectofincreasingthetemperatureontherootmeansquare(rms)speedofgasmolecules?

Answer:Therootmeansquarespeedofgasmoleculesisgivenby$v_{rms}=sqrt{frac{3RT}{M}}$,where$R$istheuniversalgasconstant,$T$isthetemperature,and$M$isthemolarmassofthegas.Asthetemperature$T$increases,thermsspeedofthegasmoleculesincreases.

25.

Question:Agasiscompressedadiabatically.Whatistherelationshipbetweentheinitialandfinalpressuresandvolumes?

Answer:Foranadiabaticprocessofanidealgas,$PV^{gamma}=$constant,where$gamma=frac{C_p}{C_v}$.Iftheinitialstateis$(P_1,V_1)$andthefinalstateis$(P_2,V_2)$,then$P_1V_1^{gamma}=P_2V_2^{gamma}$.

26.

Question:Explainwhyaheatenginecannotoperatewithoutacoldreservoir.

Answer:Accordingtothesecondlawofthermodynamics,aheatengineneedstorejectsomeheattoacoldreservoirtocompletethecycle.Ifthereisnocoldreservoir,alltheheatabsorbedfromthehotreservoirwouldhavetobeconvertedintowork,whichisimpossible.Theheatrejectedtothecoldreservoirallowstheenginetoreturntoitsinitialstateandcontinuethecyclicoperation.

27.

Question:Agashasacertainnumberofdegreesoffreedom.Howdoesitaffectthespecificheatcapacityatconstantvolume?

Answer:Thespecificheatcapacityatconstantvolumeofanidealgasisgivenby$C_v=frac{f}{2}R$,where$f$isthenumberofdegreesoffreedomofthegasmoleculesand$R$istheuniversalgasconstant.Asthenumberofdegreesoffreedomincreases,thespecificheatcapacityatconstantvolumeincreases.Forexample,amonoatomicgashas$f=3$and$C_v=frac{3}{2}R$,whileadiatomicgashas$f=5$(atnormaltemperatures)and$C_v=frac{5}{2}R$.

28.

Question:Asystemundergoesaprocessinwhichtheentropydecreases.Isthisprocesspossible?

Answer:Aprocessinwhichtheentropyofasystemdecreasesispossibleiftheentropyofthesurroundingsincreasesbyagreateramountsuchthatthetotalentropyoftheuniverseincreases.Accordingtothesecondlawofthermodynamics,thetotalentropyoftheuniversealwaysincreasesinaspontaneousprocess.Forexample,inarefrigerator,theentropyofthecoldreservoirdecreasesasheatisremovedfromit,buttheentropyofthesurroundingsincreasesduetotheheatreleasedandtheworkdone,resultinginanoverallincreaseintheentropyoftheuniverse.

29.

Question:Agasisheatedatconstantpressure.Howdoesthevolumeofthegaschangewithtemperature?

Answer:Fromtheidealgaslaw$PV=nRT$,atconstantpressure$P$,$V=frac{nR}{P}T$.Thisisalinearrelationship,sothevolumeofthegasisdirectlyproportionaltothetemperature.Asthetemperatureincreases,thevolumeofthegasincreases.

30.

Question:ACarnotengineoperatesbetweentemperatures$T_1=600K$and$T_2=300K$.Ifitabsorbs1000Jofheatfromthehotreservoir,howmuchworkdoesitdo?

Answer:TheefficiencyofaCarnotengine$eta=1frac{T_2}{T_1}=1frac{300}{600}=0.5$.Theefficiencyisalsogivenby$eta=frac{W}{Q_1}$,where$Q_1$istheheatabsorbedfromthehotreservoirand$W$istheworkdone.Given$Q_1=1000J$,then$W=etaQ_1=0.5times1000=500J$.

31.

Question:Comparetheentropychangeinareversibleandanirreversibleprocessbetweenthesametwostates.

Answer:Forareversibleprocess,theentropychangeoftheuniverseiszero.Theentropychangeofthesystem$DeltaS_{sys}$andtheentropychangeofthesurroundings$DeltaS_{surr}$areequalinmagnitudeandoppositeinsign,i.e.,$DeltaS_{univ}=DeltaS_{sys}+DeltaS_{surr}=0$.Inanirreversibleprocessbetweenthesametwostates,theentropychangeoftheuniverseispositive.Theentropychangeofthesystemisthesameasinthereversibleprocess(sinceentropyisastatefunction),buttheentropychangeofthesurroundingsisdifferent,resultingin$DeltaS_{univ}>0$.

32.

Question:Agasiscompressedisothermally.Howdoesthepressurechangewithvolume?

Answer:Fromtheidealgaslaw$PV=nRT$.Foranisothermalprocess,$T$isconstant.So,$P=frac{nRT}{V}$.Thepressureisinverselyproportionaltothevolume.Asthevolumedecreasesduringisothermalcompression,thepressureincreases.

33.

Question:Aheatenginehasanefficiencyof40%.Ifitrejects600Jofheattothecoldreservoir,howmuchheatdoesitabsorbfromthehotreservoir?

Answer:Theefficiencyofaheatengine$eta=1frac{Q_2}{Q_1}$,where$Q_1$istheheatabsorbedfromthehotreservoirand$Q_2$istheheatrejectedtothecoldreservoir.Given$eta=0.4$and$Q_2=600J$.Wecanrewritetheefficiencyformulaas$0.4=1frac{600}{Q_1}$.Solvingfor$Q_1$,weget$frac{600}{Q_1}=10.4=0.6$,so$Q_1=frac{600}{0.6}=1000J$.

34.

Question:Agashasamolarspecificheatcapacityatconstantvolume$C_v$.Howisitrelatedtotheinternalenergychangeof$n$molesofthegas?

Answer:Theinternalenergychangeofanidealgasatconstantvolumeisgivenby$DeltaU=nC_vDeltaT$,where$n$isthenumberofmolesofthegas,$C_v$isthemolarspecificheatcapacityatconstantvolume,and$DeltaT$isthechangeintemperature.

35.

Question:ArefrigeratorhasaCOPof3.Ifitremoves300Jofheatfromthecoldreservoir,howmuchworkisdoneontherefrigerator?

Answer:Thecoefficientofperformanceofarefrigerator$COP=frac{Q_2}{W}$,where$Q_2$istheheatremovedfromthecoldreservoirand$W$istheworkdoneontherefrigerator.Given$COP=3$and$Q_2=300J$,then$W=frac{Q_2}{COP}=frac{300}{3}=100J$.

36.

Question:Agasistakenthroughaprocesswherethepressureandvolumebothincrease.Whatcanbesaidaboutthetemperatureandinternalenergy?

Answer:Fromtheidealgaslaw$PV=nRT$,ifboth$P$and$V$increase,thenthetemperature$T$mustincrease.Sincetheinternalenergyofanidealgasdependsonlyontemperature($U=frac{3}{2}nRT$foramonoatomicidealgas),theinternalenergyofthegasalsoincreases.

37.

Question:Explaintheconceptofequipartitionofenergy.

Answer:Theequipartitionofenergystatesthateachdegreeoffreedomofamoleculeinagasatthermalequilibriumhasanaverageenergyof$frac{1}{2}kT$,where$k$istheBoltzmannconstantand$T$isthetemperature.Forexample,amonoatomicgasmoleculehas3translationaldegreesoffreedom,soitsaveragekineticenergyis$frac{3}{2}kT$.

38.

Question:Agasisexpandingadiabatically.Howdoesthepressurechangewithvolume?

Answer:Foranadiabaticprocessofanidealgas,$PV^{gamma}=$constant,where$gamma=frac{C_p}{C_v}$.Asthevolume$V$increasesduringadiabaticexpansion,thepressure$P$decreasesaccordingtotherelationship$P=frac{constant}{V^{gamma}}$.

39.

Question:Aheatengineoperatesbetweentworeservoirs.Ifthetemperatureofthehotreservoirisincreasedwhilethetemperatureofthecoldreservoirremainsthesame,howdoestheefficiencychange?

Answer:Theefficiencyofaheatengineisgivenby$eta=1frac{T_2}{T_1}$,where$T_1$isthetemperatureofthehotreservoirand$T_2$isthetemperatureofthecoldreservoir.If$T_1$isincreasedand$T_2$isconstant,thevalueof$frac{T_2}{T_1}$decreases,andtheefficiency$eta$increases.

40.

Question:Agasisheatedatconstantvolume.Howdoesthepressurechangewithtemperature?

Answer:Fromtheidealgaslaw$PV=nRT$,atconstantvolume$V$,$P=frac{nR}{V}T$.Thepressureisdirectlyproportionaltothetemperature.Asthetemperatureincreases,thepressureofthegasincreases.

41.

Question:Asystemhasanentropychangeof$DeltaS$.Whatdoesapositive$DeltaS$imply?

Answer:Apositiveentropychange$DeltaS$impliesanincreaseinthedisorderofthesystem.Itcanoccurduetoprocessessuchasexpansionofagas,meltingofasolid,ormixingofsubstances.Inaspontaneousprocess,thetotalentropychangeoftheuniverseispositive,andapositiveentropychangeofasystemcancontributetothisoverallincrease.

42.

Question:Agasiscompressedisothermally.Howmuchworkisdoneonthegasiftheinitialvolumeis$V_1$,thefinalvolumeis$V_2$($V_2<V_1$),andthepressureis$P$?

Answer:Foranisothermalprocessofanidealgas,theworkdoneonthegas$W=nRTlnfrac{V_1}{V_2}$.Fromtheidealgaslaw$PV=nRT$,wecanalsowrite$W=P_1V_1lnfrac{V_1}{V_2}$(usingtheinitialstatevalues).Since$V_2<V_1$,$lnfrac{V_1}{V_2}>0$,andworkisdoneonthegas.

43.

Question:ACarnotrefrigeratoroperatesbetweentemperatures$T_1$and$T_2$($T_1>T_2$).Whatisitscoefficientofperformance?

Answer:ThecoefficientofperformanceofaCarnotrefrigeratorisgivenby$COP=frac{T_2}{T_1T_2}$,where$T_2$isthetemperatureofthecoldreservoirand$T_1$isthetemperatureofthehotreservoir.

44.

Question:Agashasaspecificheatcapacityatconstantpressure$C_p$andatconstantvolume$C_v$.Whatisthephysicalsignificanceofthedifference$C_pC_v$?

Answer:Thedifference$C_pC_v=R$,where$R$istheuniversalgasconstant.Atconstantpressure,whenheatisaddedtothegas,partoftheheatisusedtoincreasetheinternalenergyofthegasandpartisusedtodoworkasthegasexpands.Atconstantvolume,alltheheatisusedtoincreasetheinternalenergy.Thedifference$C_pC_v$representstheworkdonebythegaspermoleperunittemperatureincreaseatconstantpressure.

45.

Question:Agasistakenthroughacyclicprocessinaclockwisedirectionona$PV$diagram.Whatisthenet