[UPSC CSE 2020] Thermodynamics (Q46, 15M)

Obtain the Clausius-Clapeyron equation. Using this equation, show that for the phase boundary of the liquid and vapour phases, p--T relation can be written as p=p_0e^{-L/kT}. Here it has been assumed that the latent heat L is independent of temperature, that vapour is treated as an ideal gas and that V_{\mathrm{vapour}}=V\gg V_{\mathrm{liquid}} and that p\to p_0 as T\to\infty.