Gibbs-Duhem equation (source code)

= Gibbs-Duhem equation
{c}
{wiki=Gibbs–Duhem_equation}

The <Euler theorem for homogeneous functions> applied to an <extensive quantity>, together with $dE=T\,dS-p\,dV+\mu\,dN$ give
$$
E=TS-pV+\mu N,
\qquad
S\,dT-V\,dp+N\,d\mu=0.
$$