Thermodynamics Relations - Proof 7


U can be written as a function of the independent variables T and V as,

   à (7.1)

differentiating,

   à (7.2)

By the definition of CV,

From fundamental relation I,

dividing by dV and at consatnt T,

   à (7.3)

From the Maxwell relation 2 ,

Therefore,

   à (7.4)

substituting these in Equn.7.2,

   à (7.5)