Derive the following relations :(∂T/∂p)s

Question

Derive the following relations :

(i) \(\left(\cfrac{\partial T}{\partial p}\right)_s\) = \(\cfrac{Tv\beta}{c_p}\)

(ii) \(\left(\cfrac{\partial T}{\partial v}\right)_s\) = - \(\cfrac{T\beta}{c_vK}\) 

where β = Co-efficient of cubical expansion, and 

K = Isothermal compressibility.

Answer 1

(i) Using the Maxwell relation we have

(ii) Using the Maxwell relation