Van der Waals gas — UPSC Physics Optional CSE 2005 Paper I

(d) Consider the expression C_P - C_V = - T \left( \frac{\partial V}{\partial T} \right)_P^2 \left( \frac{\partial P}{\partial V} \right)_T and give reasoning regarding the values of T when C_P = C_V for water. Also, evaluate C_P - C_V for a vander Waals gas to elaborate that its value is larger for any real gas as compared to an ideal gas.