Statistical Mechanics · Problem 9.4

Statistical Mechanics of Interacting Systems: The Method of Quantized Fields — R. K. Pathria

Physics — Statistical Mechanics · coefficient-of-volume-expansion-bulk-modulus

Problem

The coefficient of volume expansion

\alpha

and the isothermal bulk modulus

B

of a gas are given by the empirical expressions

\alpha = \frac{1}{T}\left(1 + \frac{3a'}{vT^2}\right) \quad \text{and} \quad B = P\left(1 + \frac{a'}{vT^2}\right)^{-1}

where

a'

is a constant parameter. Show that these expressions are mutually compatible. Also derive the equation of state of this gas.