Material equilibrium

Setting dP=0 in the Gibbs equation $dG=-SdT+VdP$ gives:

\begin{equation} \left(\frac{\partial G}{\partial T}\right)_P=-S \end{equation}

Putting dT=0 in the Gibbs equation gives:

\begin{equation} \left(\frac{\partial G}{\partial P}\right)_T=V \end{equation}