Thermodynamics Relations - Proof 3


Entropy S can be considered as a function of the independent varaiables T and V.

i.e.,    à (3.1)

The differential change in the entropy associated with the simultaneous change in the independent variables can be written as,

   à (3.2)

From fundamental property relation I,

dividing by dT with constant volume restriction,

and, by the definition of CV,

Therefore,

From the Maxwell relation 2,

   à (3.3)

substituting these in Equn.3.2, we obtain,

   à (3.4)