Thermodynamics Relations - Proof 14


From the relationships between specific heat and entropy,

         à (14.1)

By Cyclic Rule of partial differentiation,

   à (14.2)

Similarly,

   à (14.3)

By the Maxwell relations 4 & 1,

   i.e.,   

and

   i.e,   

Therefore, Equn.14.2 & 14.3 reduces to,

   à (14.4)    à (14.5)

Substituting from Equn.14.4 and 14.5 in Equn.14.1,

   à (14.6)

i.e.,

   à (14.7)    à (14.8)

By Cyclic Rule,

   à (14.9)

Substituting from Equn.14.9 in Equn.14.8,

   à (14.10)