Blundell Thermal Physics · Problem 16.3

Thermodynamic potentials

Physics — Statistical Mechanics · internal-energy-volume-derivative

Problem

Use the first law of thermodynamics to show that

\left(\frac{\partial U}{\partial V}\right)_T = \frac{C_p - C_V}{V\beta_p} - p, \tag{16.86}

where

\beta_p

is the coefficient of volume expansivity and the other symbols have their usual meanings.