The second law of thermodynamics

Theexpressionofthelaw

In1824,theFrenchengineerSadieCarnotproposedtheCarnottheorem.TheGermanRudolphClausiusandtheBritishLordKelvinreviewedCarnot'stheoremaftertheestablishmentofthefirstlawofthermodynamics,realizingthatCarnot'stheoremmustbebasedonanewtheorem,thesecondlawofthermodynamics.TheyputforwardClausius'sformulationandKelvin'sformulationin1850and1851respectively.Thesetwoexpressionsareequivalentinconcept.

Perpetualmotionmachinesthatviolatethesecondlawofthermodynamicsarecalledperpetualmotionmachinesofthesecondtype.

Indicatedbysymbols,thatis,dS≥0.

Clausiusstated

Itisimpossibletotransferheatfromalow-temperatureobjecttoahigh-temperatureobjectwithoutcausingotherchanges.

TheBritishphysicistKelvin(formerlyknownasThomson)discoveredacertainkindofdisharmonywhenstudyingtheworkofCarnotandJoule:Accordingtothelawofconservationofenergy,heatandworkshouldbeequivalentYes,butaccordingtoCarnot'stheory,heatandworkarenotexactlythesame,becauseworkcanbecompletelyturnedintoheatwithoutanyconditions,andheat-generatingworkmustbeaccompaniedbyheat-to-colddissipation.Hesaidinapaperin1849:"Thetheoryofheatneedstobereformedseriously,andnewexperimentalfactsmustbefound."ThecontemporaryClausiusalsostudiedtheseissuescarefully,andhekeenlysawtheexistenceofdisharmony.WithintheCarnotTheory.HepointedoutthattheconclusioninCarnot'stheorythattheworkofheatgenerationmustbeaccompaniedbythetransferofheattocoldiscorrect,butthattheamountofheat(ie,thermalmass)doesnotchangeiswrong.Clausiusproposedinapaperpublishedin1850thatinthetheoryofheat,inadditiontothelawofconservationofenergy,anotherbasiclawmustbeadded:"Withoutcertainpowerconsumptionorotherchanges,itisimpossibletomakeheatchangefromalowtemperature.Transfertohightemperature.”Thislawwaslatercalledthesecondlawofthermodynamics.

Kelvinexpression

ItisimpossibletomakeacyclicactionHeatengine,Takeheatfromsingleheatsource,sothatitcanbecompletelyturnedintoworkwithoutcausingotherchanges.

Thisisfromtheperspectiveofenergyconsumption.TheKelvinexpressioncanalsobeexpressedas:thesecondtypeofperpetualmotionmachinecannotberealized.

Kelvin’sstatementmoredirectlypointedouttheimpossibilityofthesecondtypeofperpetualmotionmachine.Theso-calledsecondtypeofperpetualmotionmachinereferstosomepeople,forexample,tocreateamachinethatabsorbsheatfromseawaterandusestheheattodowork.Thisideadoesnotviolatethelawofconservationofenergy,becauseitconsumestheinternalenergyofseawater.Theseaissovast.Aslongasthetemperatureoftheentireseaisloweredalittle,theamountofheatreleasedisastronomical.Forhumans,theseaisaninexhaustibleandinexhaustiblesourceofenergy.Therefore,themachineinthiskindofimaginationisItiscalledthesecondtypeofperpetualmotionmachine.Andtodoworkbyabsorbingheatfromseawateristoabsorbheatfromasingleheatsourcetocompletelyturnitintousefulworkwithoutothereffects.Kelvin’sstatementpointsoutthatthisisimpossibletoachieve,thatis,thesecondtypeofperpetualmotionmachineisimpossibletoachieve..

Principleofincreaseinentropy

Theentropyofanisolatedsystemneverautomaticallydecreases,andtheentropydoesnotchangeinthereversibleprocess.InIncreaseinirreversibleprocess.

Theprincipleofincreaseinentropyisanotherexpressionofthesecondlawofthermodynamics.ItpointsoutthedirectionoftheirreversibleprocessmoregenerallythantheexpressionsofKelvinandClausius;atthesametime,itismoreprofoundItispointedoutthatthesecondlawofthermodynamicsisastatisticallawoftheirregularmovementofalargenumberofmolecules,soitisonlyapplicabletoasystemcomposedofalargenumberofmolecules,andnotapplicabletoasystemcomposedofasinglemoleculeorasmallnumberofmolecules.

Otherexpressionsofthelaw

Inadditiontotheabove-mentionedexpressions,thesecondlawofthermodynamicshasotherexpressions.Forexample,Planck'sexpressionfortheJouleheatequivalentexperiment:

"Therecanbenomachinethatraisesaheavyobjectwhilecoolingaheatreservoiratthesametimeduringthecycle."

AndthemorerecentHatsopoulos-Keenanstatement:

“Forasystemwithagivenenergy,materialcomposition,andparameters,thereissuchastableequilibriumstate:Otherstatescanalwaysbereachedthroughareversibleprocess."

ItcanbearguedthattheseexpressionsareequivalenttoClausius’sandKelvin’s.

Thesecondlawofthermodynamicsstates:heatcanbetransferredspontaneouslyfromahotterbodytoacolderbody,butitcannotbetransferredspontaneouslyfromacolderbodytoahotterbody(ClausiusExpression);Itcanalsobeexpressedas:Theresultoffrictionbetweentwoobjectsturnsworkintoheat,butitisimpossibletoconvertthisfrictionalheatbackintoworkwithoutproducingothereffects.Forthermalprocessessuchasdiffusion,permeation,mixing,combustion,electricheating,andhysteresis,althoughtheinverseprocessstillconformstothefirstlawofthermodynamics,itcannothappenspontaneously.Thefirstlawofthermodynamicsdoesnotsolvetheproblemsofdirection,conditionsandlimitsintheprocessofenergyconversion,whichispreciselyregulatedbythesecondlawofthermodynamics.

Lawexplanation

Formation

①Thesecondlawofthermodynamicsisoneofthebasiclawsofthermodynamics,whichmeansthatheatisalwaysonlyItcanbetransferredfromahotplacetoacoldplace(initsnaturalstate).Itisanexperiencesummaryoftheirreversibilityofallphysicalandchemicalprocessesrelatedtothermalmotioninalimitedspaceandtime.

Themethodof①in(1)abovewasputforwardbytheGermanscientistClausiusin1850.Themethodof②wasputforwardbyKelvinin1851.Theseexpressionsareequivalent.

Inthelectureof①,itispointedoutthatundernaturalconditions,heatcanonlybetransferredfromhigh-temperatureobjectstolow-temperatureobjects,butnotfromlow-temperatureobjectstohigh-temperatureobjects.Thatistosay,undernaturalconditions,thisThetransformationprocessisirreversible.Toreversethedirectionofheattransfer,itcanonlybeachievedbyconsumingwork.

Inthelectureof②,itispointedoutthatanyformofenergyinnaturecaneasilybecomeheat,whileheatcannotbecompletelytransformedintootherformsofenergywithoutothereffects.Thisshowsthatthistransformationisalsoirreversibleundernaturalconditions.Thermalenginecontinuouslyconvertsheatintomechanicalwork,whichmustbeaccompaniedbyheatloss.Thesecondlawisdifferentfromthefirstlaw.Thefirstlawdeniesthepossibilityofcreatinganddestroyingenergy.Thesecondlawclarifiesthedirectionalityoftheprocessanddeniesthepossibilityofusingenergyinaspecialway..

②Peopleonceimaginedmakingamachinethatcantakeheatfromasingleheatsourceandturnitintousefulworkwithoutanyotherinfluence.Thisimaginaryheatengineiscalledthesecondtypeofperpetualmotionmachine.Itdoesnotviolatethefirstlawofthermodynamics,butitviolatesthesecondlawofthermodynamics.Someonehascalculatedthatthereare1billioncubickilometersofseawaterontheearth'ssurface,andseawaterisusedasasingleheatsource.Ifthetemperatureoftheseawaterisreducedbyonly0.25degreesandtheheatisreleased,itwillbeabletoturnintoonequadrilliondegreesofelectricityenoughfortheworld.Usedforathousandyears.However,aheatenginethatusestheoceanasasingleheatsourceviolatesthesecondstatementabove.Therefore,itisabsolutelyimpossibletocreateaheatenginewithathermalefficiencyof100%.

③Fromthepointofviewofthetheoryofmolecularkinetics,workistheregularmotionofalargenumberofmolecules,whilethermalmotionistheirregularmotionofalargenumberofmolecules.Obviously,theprobabilityofirregularsportsbecomingregularsportsisextremelysmall,whiletheprobabilityofregularsportsbecomingirregularsportsishigh.Inanisolatedsystemthatisnotaffectedbytheoutsideworld,itsinternalspontaneousprocessalwaysprogressesfromastatewithasmallprobabilitytoastatewithahighprobability.Itcanbeseenfromthisthatitisimpossibleforheattobecomesuccessfulspontaneously.

④Thesecondlawofthermodynamicscanonlybeappliedtosystemscomposedofalargenumberofmoleculesandmacroscopicprocesseswithinalimitedrange.Itisnotsuitableforasmallnumberofmicroscopicsystems,norcanitbeextendedtoaninfiniteuniverse.

⑤Accordingtothezerothlawofthermodynamics,thestatefunction—temperatureisdetermined;

accordingtothefirstlawofthermodynamics,thestatefunction—internalenergyandenthalpyaredetermined;

Accordingtothesecondlawofthermodynamics,anewstatefunction-entropycanalsobedetermined.Entropycanbeusedtogiveaquantitativeexpressiontothesecondlaw.

Process

Thesecondlawstatesthatnoprocessinnaturecanbeautomaticallyrestored.Tomakethesystemreturnfromthefinalstatetotheinitialstate,itisnecessarytorelyonexternalinfluences.Itcanbeseenthatthereisasignificantdifferencebetweentheinitialstateandthefinalstateoftheirreversibleprocesscarriedoutbyathermodynamicsystem.Thisdifferencedeterminesthedirectionoftheprocess.Peopleusethestatefunctionentropytodescribethisdifference,whichcanbefurtherprovedtheoretically:

ReversibleadiabaticprocessS_f=S_i,irreversibleadiabaticprocessS_f>S_i,whereS_fandS_iarethefinalandinitialentropyofthesystemrespectively.

Inotherwords,inanisolatedsystem,theentropyofthesystemalwaysremainsunchangedforthereversibleprocess;fortheirreversibleprocess,theentropyofthesystemalwaysincreases.Thislawiscalledtheprincipleofentropyincrease.Thisisalsoanotherexpressionofthesecondlawofthermodynamics.Theincreaseinentropymeansthatthesystemevolvesfromastatewithasmallprobabilitytoastatewithahighprobability,thatis,fromamoreregularandorderlystatetoamoreirregularanddisorderedstate.Entropyreflectsthestatisticalpropertiesofthesystem.

Conditions

Thesecondlawalsoguaranteesthefollowingconditionsinafinitemacrosystem:

1.Thesystemislinear;

2.Thesystemisallisotropic.

Therearealsosomeinferences:suchasthermalradiation:theradiationintensityofanypositionandanywavelengthinaconstanttemperatureblackbodycavityisthesame,andwhenanobjectofanyopticalpropertyisadded,theradiationatanypositionandanywavelengthinthecavityTheintensityisthesame.

Questioningthelaw

Maxwell'stheory

Maxwell'stheoryisanidealmodelofJamesMaxwell'shypotheticalexistence.MaxwellenvisionedacontainerdividedintotwopartsAandBcontainingthesamegasatthesametemperature.Maxwell'stheoryisthatbyguardingthe"hiddendoor"betweenthetwoparts,youcanobservethespeedofmolecularmotion,andmakethemoleculeswiththefastermolecularmotionflowtoacertainpart,whiletheslowermoleculesflowtotheotherpart.Afterasufficientlylongperiodoftime,theaveragevelocityofthetwopartsofthemolecularmotion,thatis,thetemperature(refertothemicroscopicinterpretationoftemperatureinstatisticalmechanics),hasadifferenceandbecomeslargerandlarger.Aftercalculation,itcanbeobtainedthatthisprocessisaprocessofentropyreduction,andtheexistenceofMaxwell'sdemonmakesthisprocessaspontaneousprocess,whichisobviouslycontrarytothesecondlawofthermodynamics.

OneofitsmostfamousresponseswasmadebyLeoSzilardin1929.SzilardpointedoutthatifMaxwell'stheoryreallyexists,thenitsprocessofobservingmolecularspeedandobtaininginformationwillinevitablyproduceadditionalenergyconsumptionandgenerateentropy.

Roschmidt’sparadox

Roschmidt’sparadox,alsoknownasthereversibilityparadox,pointsoutthatiftheIfthemicroscopicparticlesareinverted,thenthesystemwillproducetheresultofentropyreduction,whichisobviouslycontrarytotheprincipleofentropyincrease.

Inresponsetothisparadox,Boltzmannproposedthattheprocessofentropyincreaseisindeednotamonotonicprocess,butforamacroscopicsystem,theprobabilityofentropyincreaseismuchgreaterthanthatofentropydecrease;Whenthethermalequilibriumisreached,theentropywillalsofluctuatearounditsmaximumvalue,andthegreaterthefluctuation,thesmallertheprobabilityofoccurrence.SomeoftheexistingexperimentalresultsarebasicallyconsistentwithBoltzmann'snarrative.

Thesecondlawofthermodynamicsisalawbasedontheobservationandsummaryofexperimentalresults.Althoughnoexperimentalphenomenoncontrarytothesecondlawhasbeendiscoveredinthepast100years,ithasnotbeenpossibletorigorouslyprovethecorrectnessofthesecondlawtheoretically.Since1993,DenisJ.Evansandotherscholarshavequestionedthesecondlawofthermodynamicstheoretically,andpublishedsometheoriesabout"fluctuationsofentropy"fromtheperspectiveofstatisticalthermodynamics,suchasthemoreimportantFTtheory.ThenG.M.Wangetal.publishedinPhysicalReviewLettersin2002entitled"ExperimentalProofthatSmallSystemsContrarytotheSecondLawofThermodynamicsinaShortTime".Fromtheperspectiveofexperimentalobservations,itisprovedthatundercertainconditions,thespontaneousentropyreductionreactionoftheisolatedsystemispossible.

GibbsParadox

Mainentry:GibbsParadox

Boltzmannrelationgivesanon-extensiveentropydisplaymethod.Thisleadstoaconclusionthatisclearlycontrarytothesecondlawofthermodynamics,theGibbsparadox,whichallowstheentropyofaclosedsystemtodecrease.Intheusualexplanations,theindistinguishabilityofparticlesinquantummechanicsisusedtoexplainthatthenatureoftheparticlesinthesystemdoesnotaffecttheentropyofthesystemtoavoidthisparadox.However,moreandmorepapersadoptthisview:thechangeinentropyinterpretationcanjustignoretheimpactofthechangeinthearrangementofthemoleculesthemselves.TheexistingSackur-Tetrodeequationexplainstheentropyoftheidealgasextension.

HeatDeathTheory

Mainarticle:HeatDeathTheory

HeatDeathTheoryisatheorythatextendsthesecondlawofthermodynamicstotheentireuniverse.Theenergyoftheuniverseremainsunchanged,andtheentropyoftheuniversewilltendtoitsmaximumvalue.Withthisprocess,theuniverse’sabilitytofurtherchangebecomessmallerandsmaller.Allmechanical,physical,chemical,andbiological,etc.Themovementisgraduallytransformedintothermalmovement,andfinallyreachesastateofthermalequilibriumwithequaltemperatureseverywhere.Atthistime,allchangeswillnotoccur,andtheuniverseisinadeadlyeternalstate.Thetheoryofcosmicheatdeathisonlyapossibleconjecture.

Ifthefirstandsecondlawsofthermodynamicsareappliedtotheuniverse,thistypicalisolatedsystemwillcometothefollowingconclusions:1.Theenergyoftheuniverseisconserved,and2.Theentropyoftheuniversewillnotdecrease.Thenitwillbeobtainedthattheentropyoftheuniversewilleventuallyreachamaximumvalue,thatis,theuniversewilleventuallyreachthermalequilibrium,whichiscalledheatdeath.

Inthenineteenthcentury,thereweretwomoreinfluentialrefutationstotheheatdeaththeory.TherefutationmadeinDialecticsofNature(1876).Thecurrentunderstandingoftheuniverse(1.Theuniverseisexpanding;2.Theuniverse,asaself-gravitationalsystem,isanunstablesystemwithnegativeheatcapacity)pointsoutthattheuniverseisanunstablethermodynamicsystem,notasenvisagedbythestaticuniversemodelIthasanequilibriumstate,soitsentropydoesnothaveamaximum,thatis,heatdeathdoesnotexist.