Heat Capacities and Derivatives of Fugacity with Volume per Particle

AI Thread Summary
The discussion centers on a problem from Pathria's Statistical Mechanics textbook regarding the relationship between heat capacities and the derivatives of fugacity with respect to temperature and volume per particle. The equation presented relates the ratio of heat capacities, C_P and C_V, to the partial derivatives of fugacity, z, with respect to temperature at constant pressure and volume per particle. Participants express uncertainty about whether the equation needs to be proven or is provided as a given. There is a request for clarification on how to derive this relationship, specifically whether it can be achieved through manipulation of partial derivatives using the chain rule. The conversation highlights the need for a deeper understanding of the underlying principles of statistical mechanics.
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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

 
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