FIRST T-dS RELATION

Consider,

S = S(T, V)

1.112

1.113

or,

1.114

Now, for a reversiable process.

dQ = dU + pdV = TdS

1.115

and,

1.116

where C_v is the heat capacity at control volume ( kJ/K).

Hence,

1.117

Therefore, applying the third Maxwell relations,

1.118

Equation (1.118) is known as First T - dS relation.