Lecture-1-Computerized-thermodynamics

CTChapter1CTChapter1BasicThermodynamics©MatsHillertandMalinSellebyDeptMaterialsScienceandEngineeringKTHRoyalInstituteofTechnologyDistributedbyTHERMO-CALCSOFTWAREStockholm–nottheabsolutevalueIfthesystemreceivesanamountofheatdQandifanamountofworkdWisperformedonthesystem,thentheinternalenergyhasincreasedbydQ+dWi.e.dU=dQ+dWdU=dQ+dWWeconsideronlypressure-volumework,i.e.dW=-PdVPdVdQdU-=2©MatsHillertandMalinSellebyDeptMaterialsScienceandEngineeringKTHRoyalInstituteofTechnology1.1FirstlawofthermodynamicsdU=dQ-PdVUnderconstantvolume(i.e.dV=0):dQ=dUUnderconstantpressure(rewrite):i.e.dQ=dHVdPPVddUVdPVdPPdVdUdQ-+=-++=)(PdVdUdQ+=dHVdPPVUddQ=-+=)(i.e.dQ=dHwherewehaveintroducedenthalpy,H=U+PVInthermodynamicswecannotdistinguishbetweenheatandwork-theyarejustdifferentwaystotransferenergy3©MatsHillertandMalinSellebyDeptMaterialsScienceandEngineeringKTHRoyalInstituteofTechnology1.2SecondlawofthermodynamicsIntroducesthequantityentropy,S.ItrequiresthataprocessorreactionoccurringspontaneouslyinsideaprocessorreactionoccurringspontaneouslyinsideasystemmustincreaseSofthesystemifthereisnoheatexchangewiththesurroundings.foraspontaneousinternalprocessAheatexchangeitselfwillchangetheentropyby0SdipTdQ/AheatexchangeitselfwillchangetheentropybyTotalchangeofS:TdQSdTdQdSip+=4TdQ/©MatsHillertandMalinSellebyDeptMaterialsScienceandEngineeringKTHRoyalInstituteofTechnologyΔQ1.2SecondlawofthermodynamicsHeatonlygoesspontaneouslyfromhightolowtemperatureTbTaEntropyproduced!abbaababtotTTTTTTQTQTQS-Δ=Δ+Δ-=Δwhere0)(5©MatsHillertandMalinSellebyDeptMaterialsScienceandEngineeringKTHRoyalInstituteofTechnologyPdVdQdU-=1stlaw1.3Combinedlaw2ndlawrewrittenCombinedlawRewriteIntroduceSdTVdPSTPVUdTdSPdVdUSTdip+--+=-+=-)(TSPVUG-+=STdPdVdUTdSip++=STddQTdSip+=sincedipSalwayspositiveSdTVdPSTdSdTVdPdGip---=RewriteAtconstantPandT:0-=STddGipor0=-STddGip6©MatsHillertandMalinSellebyDeptMaterialsScienceandEngineeringKTHRoyalInstituteofTechnologyEquilibriumcondition0)/(,ξGTP=∂∂1.4Drivingforceanddissipation),,(,ξTPGGTP=Theslope,therateofdecreaseofGmayberegardedasthedrivingforce,D.ξξdSTdGDipPT/)/(,=∂∂-=ξeq0ξGξeq0ξG(ξistheextentoftheinternalprocess)ipPT,IdentifyDwithTdipS/dξi.e.TdipS=Ddξinpreviouseqs.ξDdSdTVdPdG--=ξ0ξξ0ξFIG.1.1.7©MatsHillertandMalinSellebyDeptMaterialsScienceandEngineeringKTHRoyalInstituteofTechnologyWhatisaninternalprocess?Internalprocess1.4DrivingforceanddissipationEverythingthathappensspontaneouslyinsideasystemasthesystemapproachesequilibrium,i.e.processesthatarenot”directlycontrollable”.Example:solidificationofasupercooledliquid.8©MatsHillertandMalinSellebyDeptMaterialsScienceandEngineeringKTHRoyalInstituteofTechnology1.4DrivingforceanddissipationImagineforinstanceisothermalsolidificationofapuresupercooledliquidmetal.TheonlythingthatInternalprocess–Example1puresupercooledliquidmetal.Theonlythingthatchangesduringtheprocessistheamountsofsolidandliquidmetal.Letξdenotethenumberofmolesofsolidmetal,n(solid).Externalvariable=canbedirectlycontrolledduringanexperimentInternalvariable=propertyofthesystemthatadjustsasequilibriumisapproachedandcannotbedirectlycontrolledfromtheoutside9©MatsHillertandMalinSellebyDeptMaterialsScienceandEngineeringKTHRoyalInstituteofTechnologyThecombinedlaw:DuringthesolidificationPandTareconstantξDdSdTVdPdG--=1.4DrivingforceanddissipationInternalprocess–Example1DuringthesolidificationPandTareconstantandwegetD=-dG/dξ=-ΔG/Δξ=-ΔG/ΔNsolTheprocess:liquid
solidΔG=Gsol-Gliqandthedrivingforce:andthedrivingforce:D=(Gliq-Gsol)/ΔNsol=Gmliq-Gmsol10©MatsHillertandMalinSellebyDeptMaterialsScienceandEngineeringKTHRoyalInstituteofTechnology1.4DrivingforceanddissipationInternalprocess–Example1HereanexamplewhereGmforsolidandliquidNihavebeencalculated.Solidification:liq
fcc-101-100-99-98-97Gm(kJ)FCCLIQUIDfccliqGGD-=i.e.positivebelowTmandnegativeaboveThelinescrossatthemeltingtemperature.-103-102-101170017251750TfccmliqmGGD-=11©MatsHillertandMalinSellebyDeptMaterialsScienceandEngineeringKTHRoyalInstituteofTechnology1.4DrivingforceanddissipationInternalprocess–Example1-1000100200300D=Gm(liq)-Gm(fcc)HeresamecalculationbutwithDonthey-axis.-300-200-100D=G170017251750T12©MatsHillertandMalinSellebyDeptMaterialsScienceandEngineeringKTHRoyalInstituteofTechnology1.4DrivingforceanddissipationT,V1andV2arefixed.SupposeweblowinnmolesofcomponentA,whatareInternalprocess–Example2SupposeweblowinnAmolesofcomponentA,whatarethentheequilibriumcontentofnA’andnA’’?AnA’nA’’ExternalvariablesareT,V1,V2andnAandtheinternalvariablesarenA’andnA’’.V1V213©MatsHillertandMalinSellebyDeptMaterialsScienceandEngineeringKTHRoyalInstituteofTechnologyTheinternalvariablenA’andnA’’arenotindependent:n=n’+n’’1.4DrivingforceanddissipationInternalprocess–Example2nA=nA’+nA’’Weintroduce:ξ=nA’andgetnA’’=nA-ξAtequilibrium:P’=P’’Thegaslaw,PV=nRT,givesP’=ξRT/V=P’’=(n-ξ)RT/VP’=ξRT/V1=P’’=(nA-ξ)RT/V2ξ/V1=(nA-ξ)/V2
ξ=nA/(1+V2/V1)V1V214©MatsHillertandMalinSellebyDeptMaterialsS