Heat Capacities and Derivatives of Fugacity with Volume per Particle

[ehrenfest]

Homework Statement

This question refers to Pathria's Statistical Mechanics textbook.

In this problem, there is the equation:

$$\frac{C_P}{C_V} = \frac{\left(\partial z /\partial T \right)_P}{\left(\partial z /\partial T\right)_{\nu}}$$

where z is the fugacity and \nu is the volume per particle.

I am not really sure if they want me to prove this or if they are "giving it to me" or what but in any case I want to know why it is true. Do you obtain this just by manipulating partial derivatives with the chain rule somehow?

Homework Equations

The Attempt at a Solution

 

[ehrenfest]

anyone?

 

[ehrenfest]

anyone?