a summary of thermodynamic processes：热力学过程的总结

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1、ThermodynamicProcessesCalorimetryChangeofphase?TypeofheatEquationTemperatureCalculationChange?NospecificheatdQ=mCdT[1]YesYeslatentheatdQ=mLNo[1]Caution!Becarefulofmolarversusmassbasedspecificheatconstants.IdealGasLawPV=nRT,P=>pressureinPascals(N/m2)V=>volumei

2、nm3n=>numberofmoles(dimensionless)R=>gasconstantT=>temperatureinKelvin(notCelsius!)OtherKeyEquationsdU=dQ–dW(firstlawofthermodynamics)dQ=nCVDT(idealgas,specificheatatconstantvolume)dQ=nCPDT(idealgas,specificheatatconstantpressure)dU=nCVDT(idealgas,derivationa

3、ttached)CP–CV=R(statisticalmechanics)InternalEnergyofanIdealGasTheinternalenergydependsonlyontheendpoints.Pickaconstantvolumeandconstantpressurelinesegmentstoconnecttheendpoints.Usingthefirstlaw:DU=nCV(T’–T0)+nCP(Tf–T’)–0–Pf(Vf-V0)=nCV(Tf–T0),sincePfV0=nRT’Co

4、pyright,2004,JohnR.Newport,Ph.D.LawsofThermodynamicsforIdealGasesprocessmeaningwork(DW)heat(DQ)entropy(DS)isobaricconstantpressureP0(VF–V0)nCP(TF–T0)nCPln(TF/T0)isochoricconstantvolume0nCV(TF–T0)nCVln(TF/T0)isothermalconstanttemperature(nRT0)ln(VF/V0)[1](nR)l

5、n(VF/V0)adiabatic[2]noheatexchange(PFVF-P0V0)/(1-g)00[3][1]Fromthefirstlawofthermodynamics,dU=dQ–dW;dU=0foranisothermalprocess,sodQ=dW,orDQ=DW[2]Fromthefirstlawofthermodynamics,dU=dQ–dW;dQ=0foranadiabaticprocess,sodU=-dW=>nCVdT=-PdV;fromtheidealgaslaw,dT=d(PV

6、/nR),son(CV/nR)d(PV)=-PdVn(CV/nR)[PdV+VdP]=-PdV,VdP=-PdV[1+(CV/R)]/(CV/R);sinceR=CP-CV,gºCP/CVVdP=-gPdV,orP/P0=(V/V0)-g,orPVg=P0V0g.[3]dW=PdV,soDW=ò(P0V0g)V-gdV=(P0V0g)V1-g/(1-g),VÎ[V0,VF]DW=(P0V0g)V1-g/(1-g)=(PFVF-P0V0)/(1-g)Examplesfollow(1)asimpleexample(2

7、)Carnotcycle(3)Ottocycle(4)Dieselcycle(5)StirlingcycleCopyright,2004,JohnR.Newport,Ph.D.Example1:ASimpleExamplePV4P0P03V0V01243Heatcalculations:Workcalculations:DQ12=8(CP/R)P0V0DW12=8P0V0DQ23=-9(CV/R)P0V0DW23=DW41=0DQ34=-2(CP/R)P0V0DW34=-2P0V0DQ41=3(CV/R)P0V0

8、Entropycalculations:Sums:DS12=nCPln(3)DQ=DW=6P0V0DS23=-nCVln(4)DU=DQ-DW=0(expected,closedcycle)DS34=-nCPln(3)DS=0(reversibleprocess)DS41=nCVln(4)efficiency:QH=DQ12+DQ41=(8CP+3CV)P0V0/R(su