10.2 Relation Between the Thermodynamic Functions

In Eq. 10.15, F is a function of v and T; hence,

 

image

 

By Eq. 10.15,

 

dF = –pdvSdT

 

Hence,

 

image

 

Again, H is a function of S and p. Hence,

 

image

 

By Eq. 10.16,

 

dH = TdS + vdp

 

Hence,

 

image

 

G is a function of T and p. Hence,

 

 

By Eq. 10.17, dG = –SdT+ vdp

 

Hence,

 

 

Now,

 

F = UTS

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