= Solution
At coexistence, $G_{\rm I}(T_0,p,N)=G_{\rm II}(T_0,p,N)$. Stability says
$$
G_{\rm I}<G_{\rm II}\quad(T>T_0),
\qquad
G_{\rm II}<G_{\rm I}\quad(T<T_0).
$$
Thus $G_{\rm I}-G_{\rm II}$ crosses zero with negative slope as $T$ increases through $T_0$. On the two smooth phase branches,
$$
\left(\frac{\partial}{\partial T}
(G_{\rm I}-G_{\rm II})\right)_{p,N}
=-S_{\rm I}+S_{\rm II}<0.
$$
Therefore
$$
\boxed{S_{\rm I}-S_{\rm II}>0}.
$$
The transition from phase II to phase I consequently absorbs positive latent heat $T_0(S_{\rm I}-S_{\rm II})$.
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