Solution
= Solution
Extensivity makes $\Phi(T,V,\mu)$ proportional to $V$. Comparing its differential
$d\Phi=-S\,dT-p\,dV-\langle N\rangle d\mu$
with Euler scaling gives
$$
\boxed{\Phi=-pV}.
$$
= Solution
Extensivity makes $\Phi(T,V,\mu)$ proportional to $V$. Comparing its differential
$d\Phi=-S\,dT-p\,dV-\langle N\rangle d\mu$
with Euler scaling gives
$$
\boxed{\Phi=-pV}.
$$