Statistical Mechanics · Problem 1.16

Elements of Ensemble Theory — R. K. Pathria

Physics — Statistical Mechanics · thermodynamic-identities-pressure-chemical-potential

Problem

Establish thermodynamically the formulae

V\left(\frac{\partial P}{\partial T}\right)_\mu = S \quad \text{and} \quad V\left(\frac{\partial P}{\partial \mu}\right)_T = N.

Express the pressure

P

of an ideal classical gas in terms of the variables

\mu

and

T

, and verify the above formulae.