Past exam of the mathematics course of the University of Cambridge / 2022 / ii / Paper 4 / 35A / e / Solution

At coexistence, $G_{\mathrm{I}}(T_0,p,N)=G_{\mathrm{II}}(T_0,p,N)$. Stability saysThus $G_{\mathrm{I}}-G_{\mathrm{II}}$ crosses zero with negative slope as $T$ increases through $T_0$. On the two smooth phase branches,ThereforeThe transition from phase II to phase I consequently absorbs positive latent heat $T_0(S_{\mathrm{I}}-S_{\mathrm{II}})$.