Derive the following relations (∂T/∂v)u

Question

Derive the following relations

\(\left(\cfrac{∂T}{∂v}\right)_u\) = \(\cfrac{T\left(\cfrac{∂p}{∂T}\right)_v-p}{c_v}\)

Answer 1

\(\left(\cfrac{∂T}{∂v}\right)_u\) can be expressed as follows :

Dividing eqn. (i) by eqn. (ii), we get

... Maxwell relation Substituting these value in eqn. (iii), we get

\(\left(\cfrac{∂T}{∂v}\right)_u\) = \(\cfrac{T\left(\cfrac{∂p}{∂T}\right)_v-p}{c_v}\)