192ndLawofThermodynamics热力学第二定律课件

19.2ndLawofThermodynamics熱力學第二定律Reversibility&Irreversibility 1.可逆性和不可逆性The2ndLawofThermodynamics 2.熱力學第二定律Applicationsofthe2ndLaw 3.第二定律的應用Entropy&EnergyQuality 4.熵和能量品質19.2ndLawofThermodynamicsMostenergyextractedfromthefuelinpowerplantsisdumpedtotheenvironmentaswasteheat,hereusingalargecoolingtower.發電廠內從燃料抽取的能量，大部份都被當成廢熱而丟到環境裏；圖中用的是一個大型冷卻塔。Whyissomuchenergywasted?為甚麼浪費這麼多能量？2ndlaw:noQWwith100%efficiency第二定律：沒有QW可以達到100%効率。MostenergyextractedfromtheEfficiencies 効率Engine引擎Efficiency効率Gasoline汽油18~20%Diesel柴油upto可達40%Steam蒸氣~8%GasTurbine氣渦輪upto可達40%PowerPlant發電廠Efficiency効率Coal燃煤36%Nuclear核子30%Efficiencies 効率Engine引擎Effic19.1.Reversibility&Irreversibility可逆性和不可逆性Blocksloweddown 質塊因摩擦力byfriction: 而慢下來:Irreversible 不可逆Bouncingball: 彈跳的球:

reversible 可逆Examplesofirreversibleprocesses:不可逆程序範例:Beatinganegg,blendingyolk&white打一個蛋，蛋黄蛋白混成一團Cupsofcold&hotwaterincontact幾杯冷和熱水貼在一起Spontaneousprocess: 自發性程序:orderdisorder 有序無序(statisticallymoreprobable) (统計上較有可能)時間19.1.Reversibility&IrreversGOTIT?19.1.Whichoftheseprocessesareirreversible: 以下那些程序是不可逆的：stirringsugarintocoffee, (a)把糖攪進咖啡中，buildingahouse, (b)建一幢房子，demolishingahousewithawreckingball, (c)用鐵球撞毀一幢房子，demolishingahousebytakingitapartpiecebypiece, (d)把房子逐塊拆下，harnessingtheenergyoffallingwatertodrivemachinery,(e)利用水下墮的能量驅動機器，harnessingtheenergyoffallingwatertoheatahouse? (f)利用水下墮的能量加熱房子？GOTIT?19.1.Whichofthesep19.2.The2ndLawofThermodynamics熱力學第二定律Heatengineextractsworkfromheatreservoirs.熱引擎從熱庫取熱。gasoline&dieselengines 汽油和柴油引擎fossil-fueled&nuclearpowerplants 化石燃料和核子發電廠jetengines 噴射引擎2ndlawofthermodynamics(Kelvin-Planckversion):Thereisnoperfectheatengine.熱力學第二定律

(凱爾文-普朗克版)：沒有完美熱引擎。Perfectheatengine:covertsheattoworkdirectly.

完美熱引擎:把熱直接變成功。熱庫Heatdumped倒掉的廢熱Noprocessispossibleinwhichthesoleresultistheabsorptionofheatfromareservoiranditscompleteconversionintowork.沒有任何程序的淨効果可以是從單一個熱庫吸收熱量，然後把它全部變成功。19.2.The2ndLawofThermodynsimpleheatengine簡單熱引擎

cylindercompressedadiabatically氣缸絕熱地壓縮(TrisestoThadiabaticallyT絕熱地升至Th

)gasincontactwithTh,expandsisothermallytodowork;heatQh=Whabsorbed氣缸與Th接觸，氣體等温膨脹作工；吸進Qh=Wh的熱

cylinderexpandsadiabatically氣缸絕熱地膨脹(TdropstoTcadiabaticallyT絕熱地降至Tc

)cylinderincontactwithTc,gascompressedisothermallyheat

Qc=Wcdumped氣缸與Tc接觸，氣體等温壓縮；倒出Qc=Wc的熱Efficiency効率(anyengine)任何引擎(Simpleengine)簡單引擎(anycycle)任何循環simpleheatenginecylinderCarnotEngine(Cycle) 卡諾引擎(循環)Isothermalexpansion等温膨脹: T=Th,W1=Qh>0Adiabaticexpansion絕熱膨脹: Th

Tc,W2>0Isothermalcompression等温壓縮: T=Tc,W3=Qc<04.Adiabaticcompression絕熱壓縮: Tc

Th,W4=W2<0Idealgas理想氣體：Adiabaticprocesses絕熱程序：AB:Heatabs.吸收了熱CD:Heatrej.排出熱BC:Workd.做了功DA:Workd.被做了功CarnotEngine(Cycle) 卡諾引擎(循環Example19.1.CarnotEngine卡諾引擎ACarnotengineextracts240JfromitshighTreservoirduringeachcycle,&rejects100Jtotheenvironmentat15C.一部卡諾引擎每週期從它的高T熱庫提取240J，再於15C向外丟出100J。Howmuchworkdoestheenginedoineachcycle?引擎每週期作功多少？What’sitsefficiency? 它的功率為何？What’stheTofthehotreservoir? 高温熱庫的T為何？workdone所作功Efficiency功率Example19.1.CarnotEngineEngines,Refrigerators,&the2ndLaw

引擎，冷凍機，和第二定律Carnot’stheorem卡諾定理:AllCarnotenginesoperatingbetweentemperaturesTh&Tchavethesameefficiency.所有在温度Th&Tc

之間運作的卡諾引擎都有同樣的効率。NootherengineoperatingbetweenTh&Tccanhaveagreaterefficiency.沒有其他在温度Th&Tc

之間運作的引擎可以有更大的効率。Refrigerator:extractsheatfromcoolreservoirintoahotone.冷凍機:從冷庫抽送熱量到一個熱庫。workrequired所需功Engines,Refrigerators,&th2ndlawofthermodynamics(Clausiusversion):Thereisnoperfectrefrigerator.熱力學第二定律

(克勞修斯版)：沒有完美冷凍機。perfectrefrigerator:movesheatfromcooltohotreservoirwithoutworkbeingdoneonit.完美冷凍機：不用對它作功就可以把熱量從低移到高温熱庫。Noprocessispossiblewhosesoleresultisthetransferofheatfromabodyoflowertemperaturetoabodyofhighertemperature.沒有任何程序的淨効果可以是把熱從一個較低温的物體送到一個較高温的物體。2ndlawofthermodynamics(ClPerfectrefrigerator

Perfectheatengine完美冷凍機

完美熱引擎 ClausiusKelvin-Planck

克勞修斯

凱爾文-普朗克完美冷凍機完美熱引擎實在的熱引擎PerfectrefrigeratorPerf

Carnotengineismostefficient

卡諾引擎效率最高eCarnot=thermodynamicefficiency

熱力效率eCarnot

erev>eirrevCarnotrefrigerator卡諾冷凍機,e=60%Hypotheticalengine

假想引擎,e=70%完美熱引擎Carnotengineismostef19.3.Applicationsofthe2ndLaw第二定律的應用Powerplant發電廠fossil-fuel化石燃料:Th=650K

Nuclear核能:Th=570K

Tc=310KActualvalues實在數值:efossil~40% enuclear

~34% ecar~20%Prob54&55Heatsource熱源Boiler鍋爐Turbine渦輪機Generator發電機Electricity電Condenser冷凝器Wastewater廢水Coolingwater冷卻用水温度温度温度水蒸氣水入出19.3.Applicationsofthe2ndApplication:Combined-CyclePowerPlant

應用:聯合-循環發電廠Turbineengines:highTh(1000K2000K)&Tc(800K)…notefficient.渦輪機:高Th(1000K2000K)&Tc(800K)…無効率。Steamengines:Tc~ambient300K.蒸氣機:Tc~周圍的300K.Combined-cycle聯合-循環:Th(1000K2000K)&Tc(300K)…e~60%Application:Combined-CyclePExample19.2.Combined-CyclePowerPlant

聯合-循環發電廠Thegasturbineinacombined-cyclepowerplantoperatesat1450C.一個聯合-循環發電廠內的氣渦輪機在1450C下運作。Itswasteheatat500Cistheinputforaconventionalsteamcycle,withitscondenserat8C.它的500C廢熱輸入另一個冷凝器在8C的傳统蒸氣循環。Findeofthecombined-cycle,&compareitwiththoseoftheindividualcomponents.求此聯合-循環的e，並與其個別組件的值比較。氣渦輪機燃燒温度氣渦輪機蒸氣循環中介温度冷卻水温度Example19.2.Combined-CycleRefrigerators冷凍機Coefficientofperformance(COP)forrefrigerators:冷凍機的績效系數COPishighifTh

Tc.Th

Tc時COP高Max.theoreticalvalue(Carnotcycle)理論最大值(卡諾循環)1stlawW=0(COP=)formovingQwhenTh

=Tc.若Th

=Tc

，移動Q時W=0(COP=)。Refrigerators冷凍機CoefficientoExample19.3.HomeFreezer家用冰箱AtypicalhomefreezeroperatesbetweenTc=18CtoTh=30C.家用冰箱通常都在Tc=18C到Th=30C之間運作。What’sitsmaximumpossibleCOP? 它可能的最大COP值為何？WiththisCOP,howmuchelectricalenergywouldittaketofreeze500gofwaterinitiallyat0C?在這COP值之下，需要多少電能才可以把500g在0C的水凝固？Table17.12ndlaw:onlyafractionofQcanbecomeWinheatengines.第二定律：熱引擎中祇有一部份Q能變成W。 alittleWcanmovealotofQinrefrigerators.

冷凍機內一點W可以產生很多Q。Example19.3.HomeFreezerHeatPumps熱泵HeatpumpasAC:以熱泵作冷氣機Heatpumpasheater:以熱泵作暖爐Groundtemp~10Cyearround土地温度整年都~10CHeatpump:movesheatfromTctoTh.HeatPumps熱泵HeatpumpasAGOTIT?19.2.AcleverengineerdecidestoincreasetheefficiencyofaCarnotenginebycoolingthelow-TreservoirusingarefrigeratorwiththemaximumpossibleCOP.一個聰明的工程師决定要提高卡諾引擎的効率，方法是用一部具有最大COP可能值的冷凍機來冷卻低温熱庫。Willtheoverallefficiencyofthissystem這系統的整體效率會exceed 超過，belessthan 低於，equalthatof 等於theoriginalenginealone 原來引擎本身的值？seeProb32forproof證明可參考Prob32GOTIT?19.2.Acleverenginee19.4.Entropy&EnergyQuality 熵和能量品質EnergyqualityQmeasurestheversatilityofdifferentenergyforms.能量品質

Q衡量各種能量的可用性。2ndlaw:Energyofhigherqualitycanbeconvertedcompletelyintolowerqualityform.第二定律：高質能量可以完全變成較低質能量Butnotviceversa.反之卻不成。最高質最低質機械，電能高温低温19.4.Entropy&EnergyQualityConceptualExample19.1.EnergyQuality,EndUse,&Cogeneration

能量品質，終端使用，和共發電Youneedanewwaterheater,&you’retryingtodecidebetweengas&electric.你需要一個新的熱水器；現正在瓦斯和電熱兩者之間作一選擇。Thegasheateris85%efficient,meaning85%ofthefuelenergygoesintoheatingwater.瓦斯熱水器的効率是85%，亦即85%的燃料能可以用來熱水。Theelectricheaterisessentially100%efficient. 電熱水器的効率可說是100%。Thermodynamically,whichheatermakesthemostsense? 從熱力學來看，那一個熱水器比較值得用?Cogeneration共發電:WasteheatfromelectricitygenerationusedforlowQneeds.發電時產生的廢熱用在低Q的需求上。Ans. 答Only1/3offuelenergyisconvertedtoelectricityatapowerplant.發電廠祗把燃料能的1/3轉成電能。Withthisinmind,thegasheaterisabetterchoice.在這考量下，瓦斯熱水器是較佳選擇。ConceptualExample19.1.EnerMakingtheConnection 連起來Iftheelectricitycomesfromamoreefficientgas-firedpowerplantwithe=48%,假設電力來自効率較佳，e=48%，的天然氣發電廠，comparethegasconsumptionofyourtwoheaterchoices.比較上述兩種熱水器的瓦斯消耗。Gasheater: 1unitoffuelenergybecomes0.85unitofheat.瓦斯熱水器: 1單位的燃料能可變成0.85單位的熱。Electricheater: 1unitoffuelenergybecomes0.48unitofelectricenergy,電熱水器: 1單位的燃料能可變成0.48單位的電能， thenbecomes0.48unitofheat.

再變成0.48單位的熱。Electricheaterconsumes0.85/0.48=1.8timesthefuelconsumedbygasheater.電熱水器消耗0.85/0.48=1.8倍瓦斯熱水器所需的燃料。MakingtheConnection 連起來IfthEntropy 熵lukewarm:can’tdoW,Q

微温：不能作功，Q

Carnotcycle(reversibleprocesses):卡諾循環(可逆程序)Qh=heatabsorbed所吸熱Qc=heatrejected所排熱Qh,Qc=heatabsorbed 所吸熱C=anyclosedpath任何閉口路徑S=entropy

熵[S]=J/KIrreversibleprocessescan’tberepresentedbyapath.不可逆程序不能以路徑表達。等温線體積壓力絕熱線C=Carnotcycle卡諾循環Contour=sumofCarnotcycles.路徑=所有卡諾循環之和Entropy 熵lukewarm:can’tdoW,Entropy 熵lukewarm:can’tdoW,Q

微温：不能作功，Q

Carnotcycle(reversibleprocesses):卡諾循環(可逆程序)Qh=heatabsorbed所吸熱Qc=heatrejected所排熱Qh,Qc=heatabsorbed 所吸熱C=anyclosedpath任何閉口路徑S=entropy

熵[S]=J/KIrreversibleprocessescan’tberepresentedbyapath.不可逆程序不能以路徑表達。等温線體積壓力絕熱線C=Carnotcycle卡諾循環Entropy 熵lukewarm:can’tdoW,Entropychangeispath-independent.熵變量與路徑無關。(Sisathermodynamicvariable)(S是一個熱力變數)S=0overanyclosedpath任何閉口路徑上，S=0

S21

+

S12=0

S21

=

S21

Entropychangeispath-indepenEntropyinCarnotCycle 卡諾循環的熵Idealgas理想氣體：Adiabaticprocesses絕熱程序：Heatabsorbed:吸收的熱Heatrejected:排出的熱EntropyinCarnotCycle 卡諾循環的熵IrreversibleHeatTransfer 不可逆熱傳遞Cold&hotwatercanbemixedreversiblyusingextraheatbaths.冷和熱水可以用額外的熱庫來達成可逆性混合。Actualmixing,irreversibleprocesses原來的混合，不可逆程序reversibleprocesses可逆程序T1=somemediumT.某個中介T。T2=somemediumT.某個中介T。IrreversibleHeatTransfer 不可逆AdiabaticFreeExpansion 絕熱性自由膨脹Adiabatic 絕熱Qad.exp.=0Scanbecalculatedbyanyreversibleprocessbetweenthesamestates.p=const. p=定值Can’tdowork 不能作功Qdegraded. Q被貶。

S可從兩態之間任何可逆程序計算真空提取功拿走隔板氣隔板isothermal等温

AdiabaticFreeExpansion 絕熱性自由Entropy&AvailabilityofWork熵與可用的功Beforeadiabaticexpansion,gascandoworkisothermally絕熱膨脹之前，氣體可以在等温下作功Afteradiabaticexpansion,gascannotdowork,whileitsentropyincreasesby絕熱膨脹之後，氣體不能作功，它的熵則增加了Inageneralirreversibleprocess在一個廣泛的不可逆程序中CoolestTinsystemEntropy&AvailabilityofWorkExample19.4.

LossofQ Q的損耗A2.0Lcylindercontains5.0molofcompressedgasat300K.一個2.0L氣筒灌了5.0mol在300K的壓縮氣體。Ifthecylinderisdischargedintoa150Lvacuumchamber&itstemperatureremainsat300K,如果氣筒往一個150L真空倉放氣，而且它的温度保持在300K，howmuchenergybecomesunavailabletodowork?有多少能量變成不能作功？閥打開之前氣閥關上真空之後Example19.4.LossofQ Q的損耗AStatisticalInterpretationofEntropy 熵的統計詮釋Gasof2distinguishablemoleculesoccupying2sidesofabox由可存在盒子兩邊的兩個可分辨分子所組成的氣體Microstates微觀態Macrostates巨觀態probabilityofmacrostate巨觀態的或然率

1/42¼=½1/4AStatisticalInterpretationoGasof4distinguishablemoleculesoccupying2sidesofabox由可存在盒子兩邊的4個可分辨分子所組成的氣體Microstates微觀態Macrostates巨觀態probabilityofmacrostate巨觀態的或然率

1/16=0.0641/16=¼=0.2541/16=¼=0.251/16=0.0661/16=3/8=0.38Gasof4distinguishablemolecGasof100molecules100個分子的氣體Gasof1023molecules1023個分子的氣體Equaldistributionofmolecules分子平均分佈或然率Statisticaldefinitionofentropy:熵的统計定義：#ofmicrostates=微觀態數目Gasof100moleculesGasof102Entropy&the2ndLawofThermodynamics

熵與熱力學第二定律2ndLawofThermodynamics:熱力學第二定律inanyclosedsystem任何密閉系統中Scandecreaseinanopensystembyoutsideworkonit.S可以在一個開放系統中因外界對它作功而減少。However,S0forcombinedsystem.不過，如果把”外界”也算進來，整個系统還是S0。 S0intheuniverse 整個宇宙S0 Universetendstodisorder 宇宙趨向混亂Life生命?Entropy&the2ndLawofThermGOTIT?19.3.Ineachofthefollowingprocesses,doestheentropyofthenamedsystem increase,decrease,orstaythesame?在下列每個程序中，熵在提到的系统裏是增加，減少，或是不變？aballooninflates 氣球充氣cellsdifferentiateinagrowingembryo,formingdifferentorgans細胞在成長中的胚胎裏分化，形成各種器官ananimaldies,itsremainsgraduallydecays 一個動物死了，它的遺體慢慢腐爛anearthquakedemolishesabuilding 一場地震把一幢建築物毁了aplantutilizesunlight,CO2,&watertomanufacturesugar一棵植物用陽光，CO2

，和水來制做糖apowerplantburnscoal&produceselectricalenergy 一所發電廠燒煤來產生電能acar’sfrictionbasedbrakesstopthecar. 以摩擦力為主的剎車把車子停下來。GOTIT?19.3.Ineachofthef19.2ndLawofThermodynamics熱力學第二定律Reversibility&Irreversibility 1.可逆性和不可逆性The2ndLawofThermodynamics 2.熱力學第二定律Applicationsofthe2ndLaw 3.第二定律的應用Entropy&EnergyQuality 4.熵和能量品質19.2ndLawofThermodynamicsMostenergyextractedfromthefuelinpowerplantsisdumpedtotheenvironmentaswasteheat,hereusingalargecoolingtower.發電廠內從燃料抽取的能量，大部份都被當成廢熱而丟到環境裏；圖中用的是一個大型冷卻塔。Whyissomuchenergywasted?為甚麼浪費這麼多能量？2ndlaw:noQWwith100%efficiency第二定律：沒有QW可以達到100%効率。MostenergyextractedfromtheEfficiencies 効率Engine引擎Efficiency効率Gasoline汽油18~20%Diesel柴油upto可達40%Steam蒸氣~8%GasTurbine氣渦輪upto可達40%PowerPlant發電廠Efficiency効率Coal燃煤36%Nuclear核子30%Efficiencies 効率Engine引擎Effic19.1.Reversibility&Irreversibility可逆性和不可逆性Blocksloweddown 質塊因摩擦力byfriction: 而慢下來:Irreversible 不可逆Bouncingball: 彈跳的球:

reversible 可逆Examplesofirreversibleprocesses:不可逆程序範例:Beatinganegg,blendingyolk&white打一個蛋，蛋黄蛋白混成一團Cupsofcold&hotwaterincontact幾杯冷和熱水貼在一起Spontaneousprocess: 自發性程序:orderdisorder 有序無序(statisticallymoreprobable) (统計上較有可能)時間19.1.Reversibility&IrreversGOTIT?19.1.Whichoftheseprocessesareirreversible: 以下那些程序是不可逆的：stirringsugarintocoffee, (a)把糖攪進咖啡中，buildingahouse, (b)建一幢房子，demolishingahousewithawreckingball, (c)用鐵球撞毀一幢房子，demolishingahousebytakingitapartpiecebypiece, (d)把房子逐塊拆下，harnessingtheenergyoffallingwatertodrivemachinery,(e)利用水下墮的能量驅動機器，harnessingtheenergyoffallingwatertoheatahouse? (f)利用水下墮的能量加熱房子？GOTIT?19.1.Whichofthesep19.2.The2ndLawofThermodynamics熱力學第二定律Heatengineextractsworkfromheatreservoirs.熱引擎從熱庫取熱。gasoline&dieselengines 汽油和柴油引擎fossil-fueled&nuclearpowerplants 化石燃料和核子發電廠jetengines 噴射引擎2ndlawofthermodynamics(Kelvin-Planckversion):Thereisnoperfectheatengine.熱力學第二定律

(凱爾文-普朗克版)：沒有完美熱引擎。Perfectheatengine:covertsheattoworkdirectly.

完美熱引擎:把熱直接變成功。熱庫Heatdumped倒掉的廢熱Noprocessispossibleinwhichthesoleresultistheabsorptionofheatfromareservoiranditscompleteconversionintowork.沒有任何程序的淨効果可以是從單一個熱庫吸收熱量，然後把它全部變成功。19.2.The2ndLawofThermodynsimpleheatengine簡單熱引擎

cylindercompressedadiabatically氣缸絕熱地壓縮(TrisestoThadiabaticallyT絕熱地升至Th

)gasincontactwithTh,expandsisothermallytodowork;heatQh=Whabsorbed氣缸與Th接觸，氣體等温膨脹作工；吸進Qh=Wh的熱

cylinderexpandsadiabatically氣缸絕熱地膨脹(TdropstoTcadiabaticallyT絕熱地降至Tc

)cylinderincontactwithTc,gascompressedisothermallyheat

Qc=Wcdumped氣缸與Tc接觸，氣體等温壓縮；倒出Qc=Wc的熱Efficiency効率(anyengine)任何引擎(Simpleengine)簡單引擎(anycycle)任何循環simpleheatenginecylinderCarnotEngine(Cycle) 卡諾引擎(循環)Isothermalexpansion等温膨脹: T=Th,W1=Qh>0Adiabaticexpansion絕熱膨脹: Th

Tc,W2>0Isothermalcompression等温壓縮: T=Tc,W3=Qc<04.Adiabaticcompression絕熱壓縮: Tc

Th,W4=W2<0Idealgas理想氣體：Adiabaticprocesses絕熱程序：AB:Heatabs.吸收了熱CD:Heatrej.排出熱BC:Workd.做了功DA:Workd.被做了功CarnotEngine(Cycle) 卡諾引擎(循環Example19.1.CarnotEngine卡諾引擎ACarnotengineextracts240JfromitshighTreservoirduringeachcycle,&rejects100Jtotheenvironmentat15C.一部卡諾引擎每週期從它的高T熱庫提取240J，再於15C向外丟出100J。Howmuchworkdoestheenginedoineachcycle?引擎每週期作功多少？What’sitsefficiency? 它的功率為何？What’stheTofthehotreservoir? 高温熱庫的T為何？workdone所作功Efficiency功率Example19.1.CarnotEngineEngines,Refrigerators,&the2ndLaw

引擎，冷凍機，和第二定律Carnot’stheorem卡諾定理:AllCarnotenginesoperatingbetweentemperaturesTh&Tchavethesameefficiency.所有在温度Th&Tc

之間運作的卡諾引擎都有同樣的効率。NootherengineoperatingbetweenTh&Tccanhaveagreaterefficiency.沒有其他在温度Th&Tc

之間運作的引擎可以有更大的効率。Refrigerator:extractsheatfromcoolreservoirintoahotone.冷凍機:從冷庫抽送熱量到一個熱庫。workrequired所需功Engines,Refrigerators,&th2ndlawofthermodynamics(Clausiusversion):Thereisnoperfectrefrigerator.熱力學第二定律

(克勞修斯版)：沒有完美冷凍機。perfectrefrigerator:movesheatfromcooltohotreservoirwithoutworkbeingdoneonit.完美冷凍機：不用對它作功就可以把熱量從低移到高温熱庫。Noprocessispossiblewhosesoleresultisthetransferofheatfromabodyoflowertemperaturetoabodyofhighertemperature.沒有任何程序的淨効果可以是把熱從一個較低温的物體送到一個較高温的物體。2ndlawofthermodynamics(ClPerfectrefrigerator

Perfectheatengine完美冷凍機

完美熱引擎 ClausiusKelvin-Planck

克勞修斯

凱爾文-普朗克完美冷凍機完美熱引擎實在的熱引擎PerfectrefrigeratorPerf

Carnotengineismostefficient

卡諾引擎效率最高eCarnot=thermodynamicefficiency

熱力效率eCarnot

erev>eirrevCarnotrefrigerator卡諾冷凍機,e=60%Hypotheticalengine

假想引擎,e=70%完美熱引擎Carnotengineismostef19.3.Applicationsofthe2ndLaw第二定律的應用Powerplant發電廠fossil-fuel化石燃料:Th=650K

Nuclear核能:Th=570K

Tc=310KActualvalues實在數值:efossil~40% enuclear

~34% ecar~20%Prob54&55Heatsource熱源Boiler鍋爐Turbine渦輪機Generator發電機Electricity電Condenser冷凝器Wastewater廢水Coolingwater冷卻用水温度温度温度水蒸氣水入出19.3.Applicationsofthe2ndApplication:Combined-CyclePowerPlant

應用:聯合-循環發電廠Turbineengines:highTh(1000K2000K)&Tc(800K)…notefficient.渦輪機:高Th(1000K2000K)&Tc(800K)…無効率。Steamengines:Tc~ambient300K.蒸氣機:Tc~周圍的300K.Combined-cycle聯合-循環:Th(1000K2000K)&Tc(300K)…e~60%Application:Combined-CyclePExample19.2.Combined-CyclePowerPlant

聯合-循環發電廠Thegasturbineinacombined-cyclepowerplantoperatesat1450C.一個聯合-循環發電廠內的氣渦輪機在1450C下運作。Itswasteheatat500Cistheinputforaconventionalsteamcycle,withitscondenserat8C.它的500C廢熱輸入另一個冷凝器在8C的傳统蒸氣循環。Findeofthecombined-cycle,&compareitwiththoseoftheindividualcomponents.求此聯合-循環的e，並與其個別組件的值比較。氣渦輪機燃燒温度氣渦輪機蒸氣循環中介温度冷卻水温度Example19.2.Combined-CycleRefrigerators冷凍機Coefficientofperformance(COP)forrefrigerators:冷凍機的績效系數COPishighifTh

Tc.Th

Tc時COP高Max.theoreticalvalue(Carnotcycle)理論最大值(卡諾循環)1stlawW=0(COP=)formovingQwhenTh

=Tc.若Th

=Tc

，移動Q時W=0(COP=)。Refrigerators冷凍機CoefficientoExample19.3.HomeFreezer家用冰箱AtypicalhomefreezeroperatesbetweenTc=18CtoTh=30C.家用冰箱通常都在Tc=18C到Th=30C之間運作。What’sitsmaximumpossibleCOP? 它可能的最大COP值為何？WiththisCOP,howmuchelectricalenergywouldittaketofreeze500gofwaterinitiallyat0C?在這COP值之下，需要多少電能才可以把500g在0C的水凝固？Table17.12ndlaw:onlyafractionofQcanbecomeWinheatengines.第二定律：熱引擎中祇有一部份Q能變成W。 alittleWcanmovealotofQinrefrigerators.

冷凍機內一點W可以產生很多Q。Example19.3.HomeFreezerHeatPumps熱泵HeatpumpasAC:以熱泵作冷氣機Heatpumpasheater:以熱泵作暖爐Groundtemp~10Cyearround土地温度整年都~10CHeatpump:movesheatfromTctoTh.HeatPumps熱泵HeatpumpasAGOTIT?19.2.AcleverengineerdecidestoincreasetheefficiencyofaCarnotenginebycoolingthelow-TreservoirusingarefrigeratorwiththemaximumpossibleCOP.一個聰明的工程師决定要提高卡諾引擎的効率，方法是用一部具有最大COP可能值的冷凍機來冷卻低温熱庫。Willtheoverallefficiencyofthissystem這系統的整體效率會exceed 超過，belessthan 低於，equalthatof 等於theoriginalenginealone 原來引擎本身的值？seeProb32forproof證明可參考Prob32GOTIT?19.2.Acleverenginee19.4.Entropy&EnergyQuality 熵和能量品質EnergyqualityQmeasurestheversatilityofdifferentenergyforms.能量品質

Q衡量各種能量的可用性。2ndlaw:Energyofhigherqualitycanbeconvertedcompletelyintolowerqualityform.第二定律：高質能量可以完全變成較低質能量Butnotviceversa.反之卻不成。最高質最低質機械，電能高温低温19.4.Entropy&EnergyQualityConceptualExample19.1.EnergyQuality,EndUse,&Cogeneration

能量品質，終端使用，和共發電Youneedanewwaterheater,&you’retryingtodecidebetweengas&electric.你需要一個新的熱水器；現正在瓦斯和電熱兩者之間作一選擇。Thegasheateris85%efficient,meaning85%ofthefuelenergygoesintoheatingwater.瓦斯熱水器的効率是85%，亦即85%的燃料能可以用來熱水。Theelectricheaterisessentially100%efficient. 電熱水器的効率可說是100%。Thermodynamically,whichheatermakesthemostsense? 從熱力學來看，那一個熱水器比較值得用?Cogeneration共發電:WasteheatfromelectricitygenerationusedforlowQneeds.發電時產生的廢熱用在低Q的需求上。Ans. 答Only1/3offuelenergyisconvertedtoelectricityatapowerplant.發電廠祗把燃料能的1/3轉成電能。Withthisinmind,thegasheaterisabetterchoice.在這考量下，瓦斯熱水器是較佳選擇。ConceptualExample19.1.EnerMakingtheConnection 連起來Iftheelectricitycomesfromamoreefficientgas-firedpowerplantwithe=48%,假設電力來自効率較佳，e=48%，的天然氣發電廠，comparethegasconsumptionofyourtwoheaterchoices.比較上述兩種熱水器的瓦斯消耗。Gasheater: 1unitoffuelenergybecomes0.85unitofheat.瓦斯熱水器: 1單位的燃料能可變成0.85單位的熱。Electricheater: 1unitoffuelenergybecomes0.48unitofelectricenergy,電熱水器: 1單位的燃料能可變成0.48單位的電能， thenbecomes0.48unitofheat.

再變成0.48單位的熱。Electricheaterconsumes0.85/0.48=1.8timesthefuelconsumedbygasheater.電熱水器消耗0.85/0.48=1.8倍瓦斯熱水器所需的燃料。MakingtheConnection 連起來IfthEntropy 熵lukewarm:can’tdoW,Q

微温：不能作功，Q

Carnotcycle(reversibleprocesses):卡諾循環(可逆程序)Qh=heatabsorbed所吸熱Qc=heatrejected所排熱Qh,Qc=heatabsorbed 所吸熱C=anyclosedpath任何閉口路徑S=entropy

熵[S]=J/KIrreversibleprocessescan’tberepresentedbyapath.不可逆程序不能以路徑表達。等温線體積壓力絕熱線C=Carnotcycle卡諾循環Contour=sumofCarnotcycles.路徑=所有卡諾循環之和Entropy 熵lukewarm:can’tdoW,Entropy 熵lukewarm:can’tdoW,Q

微温：不能作功，Q

Carnotcycle(reversibleprocesses):卡諾循環(可逆程序)Qh=heatabsorbed所吸熱Qc=heatrejected所排熱Qh,Qc=heatabsorbed 所吸熱C=anyclosedpath任何閉口路徑S=entropy

熵[S]=J/KIrreversibleprocessescan’tberepresentedbyapath.不可逆程序不能以路徑表達。等温線體積壓力絕熱線C=Carnotcycle卡諾循環Entropy 熵lukewarm:can’tdoW,Entropychangeispath-independent.熵變量與路徑無關。(Sisathermodynamicvariable)(S是一個熱力變數)S=0overanyclosedpath任何閉口路徑上，S=0

S21

+

S12=0

S21

=

S21

Entropychangeispath-indepenEntropyinCarnotCycle 卡諾循環的熵Idealgas理想氣體：Adiabaticprocesses絕熱程序：Heatabsorbed:吸收的熱Heatrejected:排出的熱EntropyinCarnotCycle 卡諾循環的熵IrreversibleHeatTransfer 不可逆熱傳遞Cold&hotwatercanbemixedreversiblyusingextraheatbaths.冷和熱水可以用額外的熱庫來達成可逆性混合。Actualmixing,irreversibleprocesses原來的混合，不可逆程序reversibleprocesses可逆程序T1=somemediumT.某個中介T。T2=somemediumT.某個中介T。Irre