华东理工大学：物理化学（中英文） 5. The Second Law: the machinery

O 5.1 Properties of the internal energy ) The Maxwell relations dz=gdx t hdy du=/aU U ds+ dU=Tds-pdvy aS S OU T, haU aS S OT aS Oy Ox )y 版权所有:华东理工大学物理化学教研

版权所有：华东理工大学物理化学教研室 11 1). The Maxwell relations dz = gdx + hdy V V U S S U U V S d d  d         +        = dU =TdS − pdV p V U T h S U g V S  = −         = =        = , S S V p V T          = −        x y x h y g         =           5.1 Properties of the internal energy

O 5.1 Properties of the internal energy 1). The Maxwell relations dz=gdx hdy dU=tds-pdv OT g=(oz/ax aS S h=(oz/ay dH=TdS+ vdp oT=av e ar S J (m)- dA=→pdV-SdT(a aS Maxwell relations dG= vd p-sdT aS OT 版权所有:华东理工大学物理化学教研

版权所有：华东理工大学物理化学教研室 12 1). The Maxwell relations dU =TdS − pdV S S V p V T          = −        S S p V p T         =           V V T S T p          =        dH=TdS + V dp dA= -p dV -SdT dG= Vd p -SdT p T p S T V            = −        Maxwell relations x y x h y g         =           ( ) ( )x y h z y g z x =   =   dz = gdx + hdy 5.1 Properties of the internal energy

O 5.1 Properties of the internal energy dU=Tds- pdy T aU a T aS S aS dh=Tds+ vd aT H\=T, aH aS da= -p dv-sdt(op aS dA dA p,\1 S T dG= vd p-sdT G dA T p OT 版权所有:华东理工大学物理化学教研

版权所有：华东理工大学物理化学教研室 13 dU =TdS − pdV S S V p V T          = −        S S p V p T         =           V V T S T p          =        dH=TdS + V dp dA= -p dV -SdT dG= Vd p -SdT p T p S T V            = −        p V U T S U V S  = −         =        , V p H T S H p S =            =        , S T A p V A T V  = −         = −        , S T A V p G T p  = −        =           , 5.1 Properties of the internal energy

O 5.1 Properties of the internal energy 2). The variation of internal energy with volume OU The internal pressure is defined as TT T Since duaU OU ds+ If divide both sides of equation by dy with the constraint of constant t OU OU OU p T p 版权所有:华东理工大学物理化学教研

版权所有：华东理工大学物理化学教研室 14 2). The variation of internal energy with volume T T V U         The internal pressure is defined as π = Since V V U S S U U V S d d  d         +        = If divide both sides of equation by dV with the constraint of constant T T V T V S U V S S U V U          +                 =        5.1 Properties of the internal energy

O 5.1 Properties of the internal energy 2). The variation of internal energy with volume U U aS OU a0 aU as,av S aS OT p aT Therefore T OT/p 版权所有:华东理工大学物理化学教研

版权所有：华东理工大学物理化学教研室 15 2). The variation of internal energy with volume T V T V S U V S S U V U          +                 =        p V U T S U V S  = −         =        , p V S T T  −        = V V T S T p          =        p T p T V  −        = Therefore: p T p T V T  −        π = 5.1 Properties of the internal energy