Chapter-10--The-Second--Law-of--Thermodynamics

thermodynamiccycle热力学循环heatengine热机efficiencyofheatengine热机效率refrigerator制冷机heatpump热泵coefficientofperformance制冷系数reversible(irreversible)process可逆（不可逆）过程entropy熵KeywordsandTerms10.1Cycle10.2SecondLawofThermodynamics10.3EntropyChapter10SecondLawofThermodynamics10.1Cycle1.CycleThesystemreturnsrepeatedlytoitsstartingpoint.若系统经历了一系列准静态过程之后又回到初态，则称这个系统经历了一个热力学循环过程，简称循环pVoWABAVBVcdFeature:0UThenetworkdoneinacyclicprocessistheareaenclosedbythecurverepresentingtheprocessonaPVdiagram.WpVoABAVBVcdCategoriesofcycle(1)Clockwisecycle(正循环)：Heatenginecycle(2)Anticlockwisecycle(逆循环):CoolingdevicecycleWpVoABAVBVcdW0W0HeatEngine（热机）Aheatengineisanydevicethatchangesenergyintomechanicalwork,suchassteamenginesandautomobileEngines.2.HeatengineefficiencyandcoefficientofperformanceCoolingdevice(制冷机）Acoolingdeviceistotransformheatoutofacoolenvironmentintoawarmenvironment.HeatengineEnvironmentathightemperatureEnvironmentatlowertemperatureHQLQWHeatengineefficiency:||||1||||||||||HLHLHHQQQQQQWeWpVoABAVBVcd(1)Heatengineefficiencyeeenergyweget(mechanicalwork)energywepayfor(energytransferathightemperature)(2)CoefficientofPerformanceCPCoolingdeviceEnvironmentathightemperatureHQLQWEnvironmentatlowtemperatureWpVoABAVBVcdCoefficientofPerformance:whatwewantCPwhatwepayfor||||||||HHHLQQCPWQQEnergytransferredathightemperatureCP(K)[heatingmode]=WorkdonebypumpTheeffectivenessofaheatpump||||||||LLHLQQCPWQQTheeffectivenessofarefrigeratorEnergyremovedfromthecoldreservoirCP(K)[coolingmode]=Workdonebyrefrigerator3.CarnotCycleSadiCarnot(萨迪.卡诺)(1796-1832)ACarnotcycleconsistsoftwoisothermalandtwoadiabaticprocesses.VopLTWHTabcd1p2p4p3p1V4V2V3VHQLQCarnotEngineEnvironmentatlowertemperatureHQLQWEnvironmentathightemperatureVopLTWHTabcd1p2p4p3p1V4V2V3VHQLQ(1)Carnotheatengineefficiency卡诺热机效率VopLTWHTabcd1p2p4p3p1V4V2V3VHQLQa-bIsothermalexpansionQ012ln||VVnRTQHHb-cAdiabaticexpansionW0c-dIsothermalcompressionQ04334lnln||VVnRTVVnRTQLLLd-aAdiabaticcompressionW0b-c,d-aareadiabaticprocesses:LHTVTV1411LHTVTV13124312VVVVCarnotCycleHLHLHLTTVVVVTTQQe1lnln1||||11243TheefficiencyofaCarnotcycle:卡诺热机效率与工作物质无关，只与两个热源的温度有关，两热源的温差越大，则卡诺循环的效率越高.TheefficiencyofaCarnotenginedependsonlyonthetemperaturesand.LTHT(2)CPofaCarnotcycle(heatpumporrefrigerator)||||coolingmode)||||LLHLQQCPWQQ（LHLTCPTT||||(heatingmode)||||HHHLQQCPWQQHHLTCPTTQuestion:ACarnotheatenginerunsbetweenacoldreservoirattemperatureTCandahotreservoirattemperatureTH.Youwanttoincreaseitsefficiency.Ofthefollowing,whichchangeresultsinthegreatestincreaseinefficiency?ThevalueofTisthesameforallchanges.A.RaisethetemperatureofthehotreservoirbyTB.RaisethetemperatureofthecoldreservoirbyTC.LowerthetemperatureofthehotreservoirbyTD.LowerthetemperatureofthecoldreservoirbyTE.Lowerthetemperatureofthehotreservoirby1/2Tandraisethetemperatureofthecoldreservoirby1/2TQuestion:ACarnotcoolingdevicerunsbetweenacoldreservoirattemperatureTCandahotreservoirattemperatureTH.Youwanttoincreaseitscoefficientofperformance.Ofthefollowing,whichchangeresultsinthegreatestincreaseincoefficient?ThevalueofTisthesameforallchanges.A.RaisethetemperatureofthehotreservoirbyTB.RaisethetemperatureofthecoldreservoirbyTC.LowerthetemperatureofthehotreservoirbyTD.LowerthetemperatureofthecoldreservoirbyTE.Lowerthetemperatureofthehotreservoirby1/2Tandraisethetemperatureofthecoldreservoirby1/2TExample：AnidealdiatomicgasofvolumeV1atapleasureofP1variesalongthecurvedpathshowninthefigure.IfP2=2P1,V2=2V1Finde=?1P12P()PPaVo1V12VSolution:111111(2)(2)WPPVVPV12341221111111()2(2)22VfQnCTnRTTffPVPVPVBA1P12P()PPaVo1V12V1234423211111112()22(222)(2)2pfQnCTnRTTfPVPVfPV111111(2)222210.6%3435419PVWefQfPVPVfExampleAnidealmonatomicgas,originallyatpointA,undergoesthefollowingcycleasshown.Calculate(a)thechangeininternalenergy,theworkdonebythegasandtheheataddedtothegasforeachprocess;(b)theefficiencyofthiscycleV(10-3m3)1312p(105Pa)ABC0A—BJ200))((21ABBAABVVppWSolution:()3()23()750J2ABVBABABBAAUnCTTnRTTpVpVΔU950JABABABQWV(10-3m3)1312p(105Pa)ABC0B—Cisochoric0BCW3()2600JBCCCBBUpVpVC600JBCBBCQUWV(10-3m3)1312p(105Pa)ABC0J100)(CAACAVVpWC—Aisobaric3()2150JCAAACCUpVpVΔ250JCACACAQUWV(10-3m3)1312p(105Pa)ABC010010.5%950ABWWeQQHTwomolesdiatomicidealgastakesthefollowingcycle.Inthiscycleprocess2-3isadiabatic,and3-1isisothermal.T1,V1isknownandT2＝3T1，V3＝8V1.Find：(a)heatinthethreeprocesses,(b)theefficiencyofthiscycle（ln2=0.6931）Ans：65.3%PP2O123P1V1VV2V3Example:1212221121111()()222WPVPVnRTnRTRT1221111(3)1022ffUnRTnRTTfnRTRT121212112QWURTPP2O123P1V1VV2V3230Q131313131113ln6ln2VQWUWnRTRTV21116ln2ln211165.3%122QRTeQRT23adiabatic31isotheormalPP2O123P1V1VV2V3TheOttoCycle.PathsADandBCareadiabatic,andpathsbdanddaareatconstantvolume.Find：e=？Solution:1()1()1dabcvdavcbdacbQeQCTTCTTTTTTPVQHQLcdbaVbVaoExample:abandcdareadiabaticprocesses1,abbaTVTV1dccdTVTVadbcTTTTSo11111daadcbbcbaTTTTeTTTTVVPVQHQLcdbaVbVaoabcdPV