[UPSC IFoS 2024] Thermodynamics (Q17, 15M)

Deduce the thermodynamic relation : \left(\frac{\partial S}{\partial V}\right)_T = \left(\frac{\partial P}{\partial T}\right)_V Using the expression establish Clausius-Clapeyron latent heat equation \frac{dP}{dT} = \frac{L}{T(V_2 - V_1)}