Blundell Thermal Physics · Problem 26.6

Real gases

Physics — Statistical Mechanics · van-der-waals-heat-capacities

Problem

The total energy of one mole of a van der Waals gas can be written as

U = \frac{f}{2}RT - \frac{a}{V}, \tag{26.67}

where

f

is the number of degrees of freedom (see eqn 19.22). Show that

C_V = \frac{f}{2}R \tag{26.68}

and

C_p - C_V \approx R + \frac{2a}{TV}. \tag{26.69}