Thermodynamics Relations - Proof 10


From the realtionships between specific heat and entropy, as given in Equn.3.3 and Equn.4.4,

   à (10.1)    à (10.2)

Therefore,

   à (10.3)

Considering S as a function of T & V, as

differentiating,

   à (10.4)

Dividing Equn.10.4 by dT at constant P,

i.e.,

   à (10.5)

By Maxwell relation 2,

Therefore,

   à (10.6)

Cyclic relation rule: (for the function in the variables x, y & z)

   à (10.7)

We can write similar relation for the function in the variables P, T & V as

   à (10.8)

i.e.,

   à (10.9)

and

   à (10.10)

Therefore,

   à (10.11)

Substituting for from Equn.10.11 in Equn.10.6,

   à (10.12)

Substituting from Equn.10.12, in Equn.10.3,

   à (10.13)