Solution
= Solution
The fundamental thermodynamic relation is
$$
dE=T\,dS-p\,dV+\mu\,dN.
$$
Because $E(S,V,N)$ is extensive, the <Euler theorem for homogeneous functions> gives
$$
E=TS-pV+\mu N.
$$
Substitution into the <Gibbs free energy> $G=E+pV-TS$ therefore yields
$$
\boxed{G=\mu(T,p)N}.
$$
For a one-component equilibrium phase, the intensive <chemical potential> depends on the intensive state variables $T$ and $p$.