Solution
= Solution
From $E=\rho V$, $P=\rho/3$, and $dE=T,dS-P,dV$,
$$
T,dS=V,d\rho+\frac43\rho,dV.
$$
Using $\rho=4\sigma T^4/c$ gives
$$
dS=\frac{16\sigma}{3c}\left(T^3dV+3T^2VdT\right)
=d\left(\frac{16\sigma}{3c}VT^3\right).
$$
Therefore
$$
S=\frac{16\sigma}{3c}VT^3,
\qquad s=\frac SV=\frac{16\sigma}{3c}T^3,
$$
up to an irrelevant additive <entropy> constant.