《材料热力学》第5章General Procedure（2）.pptx

GeneralProcedure（2）第5章

INTRODUCTION

INTRODUCTION

INTRODUCTION

INTRODUCTION

INTRODUCTION

INTRODUCTION

INTRODUCTIONIfyourindependentvariablesofchoicehappentobeTandP,thenyoucanjustlookatthesixexpressionsintheSummaryofThermodynamicfunctionsfordZ(P,T)andwritedownthevariousrelationshipsthatresultbyapplyingcoeffcientandMaxwellrelationstotheexactdifferentials.Ifontheotherhand;however,youareinterestedinrelationshipsthatinvolvevariablesotherthantemperatureandpressurethenyouneedtodoabitmorework.Inthischapterwewilldevelopageneralmethodfordeterminingtherelationshipbetweenthermodynamicvariables.

OUTLINEGeneralProcedureExamplesUsingtheGeneralProcedureApplicationstoIdealGasesApplicationstoSolids

GeneralProcedureIdentifythevariablesofinterest.Ifyouhaveasystemwithonlytwodegreesoffreedomthenyouwillhavethreevariables,onedependentandtwoindependent.Writedownthedependentvariableasafunctionofthetwoindependentvariables.

2.WritethetotaldifferentialofZGeneralProcedure

GeneralProcedure3.ConvertthetotaldifferentialfromtheindependentvariablesofXandYtoPandT

GeneralProcedure4.Thefourthstepistocollectliketerms:5.ThefifthstepinvolveswritingSummaryofThermodynamicStateFunctionsintermsofTandP

GeneralProcedure6.TheSixthstepinvolvessolvingthesetwoequationsforMandN.SolvingasystemoftwolinearequationsbyusingtheJacobiansofthesystem.ForthetwolinearequationsinthetwounknownsMandNabovetheJacobiansare:

GeneralProcedureExamplesTorPasanIndependentVariableIndependentVariablesNotTorPTorPastheDependentVariable

TorPasanIndependentVariableWritetheentropyofasystemasafunctionofitstemperatureandvolume.S=S(T,V)Writetheentropyofasystemintermsofitspressureandvolume.S=S(P,V)FindtherelationshipneededtocomputethechangeinHelmholtzfreeen