Callen H.B - Thermodynamics And An Introduction To Thermostatistics · Problem 7.4-7

STABILITY OF THERMODYNAMIC SYSTEMS

Physics — Statistical Mechanics · specific-heat-volume-derivative

Problem

Show that

\left(\partial c_v/\partial v\right)_T = T\left(\partial^2 P/\partial T^2\right)_v

and evaluate this quantity for a system obeying the van der Waals equation of state.