梁新剛-2013-火積新理論基礎(chǔ)及進展

Entransy[

]:

ItsApplicationinHeatTransfer

and

ThermodynamicSystemXin-gangLiangSchoolofAerospace,TsinghuaUniversity1ContentPart1:

Whatisentransy?Part2:OptimizationofheatconductionPart3:ThedifferencebetweenentransyoptimizationandentropyoptimizationPart4:Applicationto

heatexchanger(HX)optimizationPart5:ApplicationtothermodynamicsystemPart6:Anattempt:entransyanalysisofthermodynamiccycle--entransylossPart7Arguments2Part1:

Whatisentransy?

[火積]？3Definition-entransyInternalenergySpecificheattemperatureBodymassZYGuoetal,Entransy–Aphysicalquantitydescribingheattransferability,Int.J.HeatMassTransfer,2007,50:2545–2556.4Physicalmeaning“Potentialenergy”ofheatinanobject;Theabilitytoreleaseheatfromanobject；Thelargestentransythatabodycouldreleaseis?UT.PotentialenergyofwaterinatankentransyHA56HotstonepotforcookingTemperatureHeatcapacityBothfactorsareimportant,notsingleone.PhysicalmeaningAnalogybetweenelectrical&heatconduction7Electricalcond.HeatconductionPotentialUe

[V]Uh=T

[K]FlowI

[C/s]Qh

[J/s]Flux

[C/m2s]

[J/m2s]Resistance

Re[

]Rh

[sK/J]Law

Uh=TElectricalCharge/storedheatQveQvh

=

McvTCapacity

Ce

=

Qve

/

Ue

Ch

=

Qvh

/

UhPotentialenergyEe=

QveUe

/2Potentialenergyofheat？PhysicalmeaningPotentialenergyofcharge8“Potentialenergy”ofheatinabodyatatemperaturePotentialenergyofchargeinacapacitance

ZYGuoetal,Entransy–Aphysicalquantitydescribingheattransferability,Int.J.HeatMassTransfer,2007,50:2545–2556.entransyInternalenergy

massPhysicalmeaningEe=QveUe

/2

Whyisthequantity,G, calledentransy?Clausiushadcoineden-tropy(熵)forS=

Q/Tbecauseitpossesboththenatureofenergyandtransformationability.en

---prefixofenergy;tropy---rootoftransformationEn-transyforwascoinedforGh=UT/2becauseitpossesboththenatureofenergyandtransferability.en

---prefixofenergy;transy--rootoftransportGh=UT/2

wascalledheattransportpotentialcapacity9Whathappenstoentransyifheatistransferred?ItcanbeprovedInitialstatesAfterequilibrium10EntransydissipationThetotalentransyisreducedwhenheatistransferredThechangeinentransyduetoheattransferiscalledentransydissipation

11EntransydissipationWhathappensifheatistransferred?Itcanbeproved:anyspontaneousheattransferwillresultinentransydecreaseforisolatedsystem.Hence,entransydissipationcouldbe

anthermeasureoftheirreversibilityforheattransport12孤立系統(tǒng)熵增原理Entransyflow13Qf:heatexchangeatconstanttemperatureTWhenQfistransferredfromTH

toTL,

theentransydissipationisEntransyflow:Whyentransy?Anyadvantage?Anyapplicationofconvenience?14Whyentransy?Enhancement(強化)Increasingheattransferratewithinputinpower,materials,etc.Optimization（優(yōu)化）BestheattransferperformanceunderfixedinputAnyprinciple?Howtooptimize？15Whyentransy?16Constructaltheory：ABejanGivingprescribedconstructandthenoptimizingaspectratio.Minimizingthelargesttemperaturedifference.Onedimensionconductionassumptionintheconstruct.Effectiveforsymmetricstructure.OptimizationmethodsHowtodoiftherearemorethantwooutlettemperaturesorifthedomainiscomplex?Whyentransy?17Entropygeneration(EG)MinimizationBelief:Lessentropygeneration,betterheattransfer;TheNewtoncoolinglawQ=AhTforfixedQ,Tbecomesmallerunderimprovement,thenlessentropygenerationManysuccessfulapplicationsOptimizationmethodsDifferentopinionson

entropygenerationminimizationoptimization18entropygenerationlossinheat-workconversion,orexergy[火用];focusonirreversibilityfromtheviewpointofheat-workconversion.Heatistransportednotfordoingworkinmanyapplications.However,thereareConflictson

entropygenerationminimizationoptimization19TheNewtoncoolinglawQ=

AhT：ifTfixed,enhancementoroptimizationwillmakeheatexchangeincreasedQ;EGwillincreaseeitherLargerEGcorrespondslargerheattransferrate?HoweverConflictson

Minimumentropygeneration(EG)optimization20TheparadoxinHeatexchangeroptimizationBejan:effectivenessdoesnotalwaysincreaseswithdecreasingEGmonotonicallyShah:18typesofHXs,notmonotonicrelationbetweenEGandeffectiveness.HoweverConflictson

Minimumentropygeneration(EG)optimization21TheparadoxinheatexchangeroptimizationHoweverEffectivenessisnotamonotonicfunctionofEGCounterflowHXEntransycouldbeahelpondealingwithheattransferoptimization?22Part2

Optimizationofheatconduction

23EntransybalanceequationEnergyeq.HeatsourceHeatfluxMultipleTintegrateoverthewholevolume24EntransybalanceequationForconstantcvEntransyperunitvolumeFromtheGausstheorem25EntransybalanceequationEntransyvariationwithtime-EntransydissipationEntransyvariationduetoboundaryheatexchange

Entransyproductionduetoheatsource

26Entransybalanceequationentransyvariationwithtime=netentransyflowintovolumethroughboundary+netentransyduetoheatsource+entransydissipation27Entransybalanceequation28Atsteadystate,withoutheatsource00orEntransydissipationrate=entransyflowintothevolumethroughboundary

-entransyflowoutofthevolumethroughboundaryGin-Gout=

GRelationbetweenheattransfer&entransydissipationNetheatexchangethoughboundaryisrelatedtotheentransydissipationinthevolume!EntransydissipationNetentransyflowintoVthoughboundary2930Steadystatewithoutheatsourcewhereboundaryflux-weightedtemperaturedifferenceQ0：totalnetheattransportbetweenthesourceandsinkboundaryForgivenboundaryflowRelationbetweenheattransfer&entransydissipationqin:heatfluxintoboundaryareaSqin

qout:heatfluxoutofboundaryareaSqout

31SteadystatewithoutheatsourceMinimumentransydissipation

smallesttemperaturedifferenceForgivenboundaryflowRelationbetweenheattransfer&entransydissipation32SteadystatewithoutheatsourceForgivenboundarytemperatureRelationbetweenheattransfer&entransydissipationMaximumentransydissipation

largestheatexchange33MaximumentransydissipationprincipleforgiventemperatureMinimumentransydissipationprincipleforgivenheatfluxEntransydissipationextremumprinciplesforheatconductionRelationbetweenheattransfer&entransydissipationOptimizationapplicationHowtodistributegoodconductingmaterialstoobtainlowestaveragetemperature?Volumetopointheatconduction,steadysateUniformheatsourceThereisonlyoneoutletattemperatureT0Limitedgoodconductivity34OptimizationapplicationEntransybalanceeq.VolumetopointheatconductionQisthetotalheatgeneratedinV,whichisgiven35OptimizationapplicationEntransybalanceeq.VolumetopointheatconductionEntransydissipationinVNetentransyflowintoVSmallerentransydissipation,loweraveragetemperature.Howtofindtheoptimaltemperaturedistributionwithlimitationongoodconductingmaterials?36MinimumConstraintPurpose:findtheminimumentransydissipationundertheconstraint37OptimizationapplicationVolumetopointheatconductionRequirementsPurpose:findtheminimumentransydissipationundertheconstraint38OptimizationapplicationVolumetopointheatconductionConstituteaLagrangefunctionwiththeconstraintoflimitinggoodconductingmaterialsPursuingacalculusofvariation,takingconductivitykasafunction.39OptimizationapplicationVolumetopointheatconductionWehaveThisistherule/principletodistributegoodconductingHowtousethisrule?40OptimizationapplicationVolumetopointheatconductionHowtousetherule(4)Returntostep(2)untilallthegoodconductingmaterialsareusedup.(1)Fillinthedomainwithbasematerials,lowconductivity;(2)Solvetheenergyequationtoobtainthetemperaturefieldandheatfluxfield;(3)Putagoodconductingmaterialsattheplacewherethetemperaturegradientislargest;Thereareotherimprovedmethodsofputtinggoodconductingmaterials41OptimizationapplicationVolumetopointheatconductionThestructuredependsontheconductivityratio,fractionofgoodconductingmaterialsnon-uniformheatsourceQQ12.5%oftotalVolumeOptimizationapplicationVolumetopointheatconduction42Thestructuredependsontheconductivityratio,fractionofgoodconductingmaterialsYoucanusedifferentprocedurebasedontheruleandcouldobtaindifferentstructuresOptimizationapplicationVolumetopointheatconduction43Entransydissipation-basedthermalresistanceTheentransydissipationextremumprinciplesdivideintotwocases,complex.MaximumentransydissipationprincipleforgiventemperatureMinimumentransydissipationprincipleforgivenheatfluxEntransydissipationextremumprinciplesforheatconductionCouldwemakeanimprovementandexpressthemmoresimply?44ThermalresistanceConventionaldefinitionofthermalResistance:

R=

T/Q

Withentransydissipation,wecandefinedeffectiveresistanceforx-DsystemT1T2adiabaticT3?Itcanonlybedefinedfor1-Dsystem

Ifmanytemperatures?45Resistancewasdefinedbasedonentransydissipationandthetotalnetheatexchange.WeightedTdifferenceEntransyDissipationNetheatexchangebetweensource&sinkboundariesEntransy-dissipation-basedthermalresistanceEntransydissipation-basedthermalresistance46Entransybalanceeq.atsteadystateForfixedT,largerentransydissipation,largerheatexchange,smallerthermalresistance.ForfixedQ,smallerentransydissipation,smallertemperaturedifference,smallerthermalresistance.47Entransydissipation-basedthermalresistanceMinimumresistanceprincipleMaximumentransydissipationprinciple(forgiventemperature)Minimumentransydissipationprinciple(forgivenheatflux）Heatalwaysconductsviaminimumthermalresistance!48Part3

Thedifferencebetweenentransyoptimizationandentropyoptimization

49EntropyForanyreversiblecycleentropyEntropychangeforanyprocessfromstate1tostate2Entropygeneration50Entropybalanceeq.forheattransferEntropychangerateInternalentropygenerationEntropyflowthoughboundaryandheatsourceAtsteadystateWithoutheatsource51Entropybalanceeq.forheattransferForheatconductionthenEntropychangerateentropygenerationEntropyflowthoughboundaryEntropyduetoheatsource52Entropygenerationandheattransfer53qistheheatfluxthoughboundaryqisthatinnormaldirectionFromentropybalanceeq.QnetisthenetheatflowbetweenheatsourceandsinkboundaryEntropygenerationandheattransfer54EntropyoptimizationEntransyoptimizationForprescribedheatflowSmallerentropygeneration,SmallerentransydissipationSmallerSmallerEntropygenerationandheattransfer55EntropyoptimizationEntransyoptimizationForprescribedboundarytemperaturelargerentropygeneration,largerentransydissipationLargerQnet

LargerQnetEntropygenerationoptimizationForgivenboundaryheatflowminimizingentropygenerationistoreduce(1/T)(objective),notT;minimizingentransydissipationistoreduce

T(objective).Forgivenboundarytemperaturesmaximizing(notminimizing)entropygenerationistoincreaseheattransferrate,notT;minimizingentransydissipationistoreduceT.56Heattransferprocesscanbedividedintotwocategoriesaccordingtotheir

purposes:ClassificationofheattransferprocessOneisforheat-workconversionanditsirreversibilityismeasuredbytheentropygenerationrate.Anotherisforheatingorcoolingobjects

anditsirreversibilityismeasuredbytheentransydissipationrate57Correspondingtotwopurposesofheattransfer,therearetwokindsofoptimizationprinciplesforheattransferTheprincipleofminimumentropygenerationforoptimizationofheattransferforheat-workconversion.Theprinciple

ofminimumentransydissipation-basedthermalresistanceforoptimizationofheattransferforobjectheating.5859EntropyoptimizationFormaLagrangefunctionwiththeconstraintoflimitinggoodconductingmaterialsVariationwithrespecttoTRulestoarrangegoodconductingmaterialsResultcomparisonVariationwithrespecttokEntransyoptimizationResultcomparison<

averageT:150.8K

AverageT：

51.6

K

Min.entropygeneration：increaseT,reduce

(1/T);Min.entransydissipation：reduce

T.Entropyoptimization60TemperaturedistributionReduceentropygenerationreducetheabilitylossindoingworkResultcomparisonEntransyopt.Entropyopt.<averageT:150.8K

AverageT：

51.6

K

61優(yōu)化結(jié)果比較

resultΦh

/(W?K)Sgen/(W/K)Tm/KTmax/K/(1/K)Entransydissipationopt5.5×104100.751.683.02.2×10-2Entropymini.Opt.1.58×10581.7150.8194.97.1×10-3TheoptimizationobjectivesaredifferentforentransydissipationoptimizationandentropygenerationoptimizationResultcomparison62purposeheat-workconv.heating/coolingirreversibilityentropygenerationentransydissipationopt.objectiveconver.Efficiency

(1/T)transferperformance

Topt.principleminimumentropygenerationrateminimumthermalresistanceprocesstendency

dS>0

dG<0criterionofequi.

dS=0

dG=0HeattransferentropyentransyComparison:entropyandentransy63Whatdoyouthinkifentropyflowandgenerationiswroteinthisway?EntropygenerationEntropyflowEntransyflowEntransydissipation64Part4

Applicationto

heatexchanger(HX)optimization

65SomeconceptsforheatexchangerParallelflowheatexchangerCounterflowheatexchangerΔtmaxΔtmin0AtΔtmaxΔtmin0At66SomeconceptsforheatexchangerCrossflowheatexchanger67SomeconceptsforheatexchangerTheLog-MeanTemperatureDifferenceMethodΔtmaxΔtmin0AtΔtmaxΔtmin0AtHeatexchangedbetweenhotandcoldstreams(counter/parallel)K

isheattransfercoefficient,Aisareabetweenhotandcoldstream68Someconceptsforheatexchanger(HX)EffectivenessHeatexchangedxMaxpossibleheatexchange

NTU:NumberofTransferUnitsC=mc,Heatcapacityflowrateforhotandcoldstreams;mismassflowrate,cisspecificheat,h—hotstream,c—coldone.69ConventionalmethodsforthedesignofheatexchangersParallelandcounter-flowheatexchangersConvient!ConventionalHXdesigningmethodLog-MeanTemperatureDifferenceMethod(LMTD)Cross-flowandmultipassheatexchangersCorrectionfactor

isunavoidable!70ConventionalmethodsforthedesignofheatexchangersConventionalHXdesigningmethodTheEffectiveness---NTUmethodComplexexpressionsofNTUParallel:Counter-flow:71Couldwedosomethingwiththeconceptofentransy?72EntransyDissipationinheatexchangersEntransydissipationinaheatexchangerEntransydissipationestimatestheirreversibilityofheattransferinHXs.Local/totalentransydissipationrateforheattransferEntransydissipationforHX73TemperaturevariationsindifferentheatexchangersParallelflowHXCounterflowHXΔtmaxΔtmin0AtΔtmaxΔtmin0AtNonlineartemperaturedistributionalongtheheattransfersurface.TemperaturedistributioninHXHotstreamHotstreamcoldstreamcoldstream74ΔtmaxΔtmin0Qt0LineartemperaturevariationversusthetotalheattransferrateΔtmaxΔtminQtT-QdiagramandthermalresistancetemperaturevariationsvstotalheattransferrateParallelflowHXCounterflowHXEntransyDissipationEntransyDissipationThermalresistancehighlightedarea75TheinfluencefactorsonHXefficiency76

UnbalancedflowdifferentheatcapacityrateIfthesame

Non-optimalflowarrangementNon-counterflowForparallelflow,thereisalimitifonlyincreasearea.Counterflow:largerTalongflowdirection,lessarea

FiniteNTU(KA/Cmin)IncreasingareaanotherlimitTThTcQTThTcQTheentransydissipation(areasurroundedbyTcurves)becomeslesswithimprovingheatexchangeforgiveinletparameters77Applicationindatacentercoolinganalysis10121416182022242628-0.2500.250.50.7511.251.5Temperature/CHeatq/WTh,inQ0.5QTh,outTc,inTc,outTm,hTm,cToreducepowerconsumption,heatpipecanbeusedtoreplacetheinterloopcirculationIndoorairoutdoorairwaterHowtouseheatpipe?OneheatpipeTQTwoheatpipesatdifferenttemperature？Bettermatchinflowarrangement,betterperformanceorlessarea.78FlowarrangementisnotsatisfactoryIndoorairoutdoorairHeatpipeOutdoorairIndoorairHeatpipecondenserevaporatorDividetheindoor&outdoorHXsintotwoparts,usingtwoheatpipesworkingatdifferenttemperaturedatacentercoolinganalysis79Howtofindthekeypointofoptimizationforathermalsystemiftheinputheatisfixed?FindthedissipationdistributionbyT-QplotornumericalsimulationDeterminewheretheentransydissipationisdominantandtrytoreduceit:Betterarrangement,avoidingmixing,etc.80Aninstance:Xian-Yangairport81ConventionalairsupplyNo!Aninstance:Xian-Yangairport82Floorcooling:sunradiationisdirectlyremoved,avoidingmixingwithair;departurehall:coolairissuppliedatgroundlevel,hotairgoesoutatroofEntransydissipationbasedthermalresistance(EDTR)fordifferentHXParallelHXCounter-flowHXTEMAE-typeheatexchanger83TheinfluencefactorsofheatexchangerefficiencyInfluencefactorsRelatedquantitiesTypeofHeatexchangerThermalconductanceofheatexchangersHeatcapacitiesofhotandcoldfluidAllthefactorsarecontainedintheexpressionofEDTR!84AdvantagesofEDTRmethodEDTRdirectlyconnectsgeometricalstructuresandboundaryconditionstoentransydissipation.Differenttypesofheatexchangersshareageneralformulaformostheatexchangers.EDTRisconvenientfortheoptimizationofheatexchanger(networks).85Relation:resistance~effectivenessSmallerresistance,largereffectivenessifheatcapacityflowratesaregiven.or86Example1:areadistribution

ofHXsHotstreamColdstreamHX1HX2Inlettemperatureandheatcapacityflowratearegivenisknown，thesumofareaofHXs:A1+A2=constObjective：thesumofheatexchangedislargestHowtodistributeA1/A?K87Resistance

=sumofentransydissipationinHX1andHX2dividedbythesumoftotalheatexchangeThetotalentropygenerationduetoheatexchangeTheoutlettemperaturecanbeobtainedbyenergybalanceequations88Example1:ResultMinresistance

~

MaxheatexchangeMinentropygeneration

~?Heatexchange89Example2:two-streamHXs(networks)90EntransydissipationEntransydissipationnumberEDTR91

EntropygenerationnumberRevisedentropygenerationnumberEntropygeneration92Example2:two-streamHXsCase1:heatcapacityflowratesandtheinlettemperaturesareprescribedCh=5W/K,Cc=8W/K,Tin-h=360K,andTin-c=300KWithincreasing

R,NRS,NG

Sg,NS,dis:notmonotonic93Example2:two-streamHXsCase2:

theprescribedparametersaretheinlettemperatures,theratioQ/ChandtheratioQ/CcinsteadoftheheatcapacityflowratesWithincreasing

R

Sg,dis

NRS,NG,NS~

constant94Example2:two-streamHXsCase3:

theheattransferrateisprescribed.AllsixconceptsaresuitableforoptimizingTHsdesignswithaprescribedheattransferrate(theentropygeneration,entropygenerationnumber,revisedentropygenerationnumber,entransydissipation,entransydissipationnumberandEDBthermalresistance).95Example3:One-dimensionalheattransferTheoptimizationobjectiveoftheheattransferprocessisthemaximumheattransferrate96Example3:one-dimensionalheattransferSmallerresistanceRlargerQ,Sg,

dis;

NRS,NG

:constant97CasesCasedescriptionCaseIHXswithprescribedstreaminlettemperaturesandheatcapacityflowCaseIIHXswithprescribedstreaminlettemperaturesandprescribedratiosoftheheattransferratetotheheatcapacityflowratesCaseIIIHXswithprescribedheattransferrateCaseIVOnedimensionalheattransferCaseVVolume-to-PointproblemConceptCaseICaseIICaseIIICaseIVCaseVOpt.objectiveSgnon-monotonicmonotonicmonotonicnon-monotonicmonotonicmin

(1/T)NSnon-monotonicconstantmonotonic------------NRSmonotonicconstantmonotonicconstantmonotonicmin

(1/T)

disnon-monotonicmonotonicmonotonicnon-monotonicmonotonicmin

(T)ormax(Q)NGmonotonicconstantmonotonicconstant--------Rmonotonicmonotonicmonotonicmonotonicmonotonicmin

(T)ormax(Q)98GlobalOptimizationofGasRefrigerationSystemsPart5

ApplicationtoathermodynamicsystemAglobaloptimizationofgasrefrigerationsystems99GasrefrigerationsystemThefluidflowsintotheHXlandheatsthegas:T4

→

T1.Theheatedgasentersthecompressor:p1→p2,T1→

T2.ThegasiscooledintheHXh:T2

→T3.Thecooledgasenterstheexpander:p2

→p1,T3

→T4.C：compressorE：expanderHXh：hot-endheatexchangerHXl:cold-endheatexchanger100OptimizationofagasrefrigerationcycleDesignRequirementsTemperaturesatthehotandcoldends:Th,TlPerformanceofcompressorandexpander.Coolingcapacityofthecycle:QlMassflowrateoftheworkingmedia:ma,mh,mlDesignParametersThermalconductanceofheatHXs:(KA)h,(KA)l101OptimizationobjectivesMinimizethecost,e.g.theheattransferarea,ofexchanger,

whenthenetpowerconsumptionisgiven:Minimizethe

netpowerconsumption,whenthecostofexchangerisgiven:102thelackofamathematicalrelationbetweengivenquantitiesanddesignparameters;individualparameteranalysiswiththeotherparametersfixedinoptimization,i.e.,“try-anderror”method.Systemoptimization?Establishthemathematicalrelationbetweenthedesignrequirementsanddesignparameters.Thekeypointoftheoptimizationproblem:103TheoreticalanalysisCompressionincompressorExpansioninexpanderHeattransferinHXlHeattransferinHXh104T-qdiagramforheatexchangers

Theshadowarea

istheentransydissipationrateinaHX.105TheentransydissipationrateinHXsisalsothefunctionofthethermalconductanceofHX,(KA),andtheheatcapacityratesofhotandcoldfluids,Ch=mhcp,h

andCc

=mccp,cCombiningtwoequations:ApplythisrelationtothehotandcoldendHXs106ApplytotheHXatthehotendChThenCaisheatcapacityflowrateofgas107ApplytotheHXatthecoldend108ThermodynamicanalysisnC

:polytrophicindexCompresionprocessExpansionprocessTherelationsbetweentemperaturesareestablished109HeattransferanalysisThermodynamicanalysis110Combiningbothheattransferandthermodynamicrelations,wetheoreticallyestablishthemathematicalrelationbetweenallthedesignparametersandtherequirements.Thisrelationmakesthetheoreticalglobaloptimizationfortherefrigerationsystemspossible!111OptimizationmodelBasedontherelationabove,theoptimizationproblemisconvertedintoaconditionalextremumproblem:whereT1

andT2arefunctionsaboutdesignparameters112ConstructaLagrange

function:OptimizationEquations:Tofindoptimalparameters113OptimizationresultsGivenquantities:Th=303K,Tl=273K,Ch

=400W/K,Cl=250W/K,Ql=1000W,Wnet=500W,FC=50WParametersCaW/K(KA)hW/K(KA)lW/K∑(KA)W/KResults913.528.028.656.6Optimizationresults:114TheΣ(KA)reachesitsminimumwhendesignparametersequaltotheoptimizedvalues.(KA)h115Theoptimalthermalconductanceversusthenetpowerconsumptions116Thebasicideaintheaboveapplication?Applyentransydissipationrelationtosetuprelationbetweenparameters,andconstraint,sothatwecanmakeatheoreticalderivationtofindtheoptimalparameters.117Part6

Anattempt:entransyanalysisofthermodynamiccycle--entransyloss

118Work

WEnergybalance119Heat

QEntransybalance120

TheprocessentransyHeatentransy：entransychangedueheatexchangeWorkentransy：entransychangeduetoinput/outputworkBothcanaffectinternalenergyandthusentransyEntransystateHeatentransyprocessWorkentransyprocessTermnatureTheCarnotcycleACarnotengineworksbetweenheatreservoirswithtemperaturesTH,TL.ItreceiveheatQH–CfromTH,releaseheatQL–CtoTL,andoutputW.121EntransyflowfromTH:

EntransyflowintoTL:PartoftheentransyflowfromTHisdeliveredintoTL,andtherestisusedinoutputtingwork:122GWC,theworkentransy,isthelargestconversionalentransybecauseWCislargest(Carnotcyle).TheCarnotcycleTheCarnotcycleforidealgasFourprocesses1-2:isothermalexpansion,receivingheat2-3:adiabaticexpansion3-4:isothermalcompression,releasingheat4-1:adiabaticcompression123TheCarnotcycleforidealgas1-2:isothermalexpansion,receivingheat124Integratefrom1to2TheCarnotcycleforidealgas2-3:adiabaticexpansion125Integratefrom2to3TheCarnotcycleforidealgas3-4:isothermalcompression