Entropy from heat capacity
= Entropy from heat capacity
Along a reversible path at fixed volume, $dS=C_V(T)dT/T$. Hence entropy differences can be measured macroscopically from
$$
S(T_2)-S(T_1)=\int_{T_1}^{T_2}\frac{C_V(T)}T\,dT,
$$
with an additional $L/T_c$ across a first-order transition of <latent heat> $L$ at $T_c$.