Gibbs energy function

Definition:

$G=A+pV$

where p is the pressure, V is the volume, and A is the Helmholtz energy function, i.e.

$G=U-TS+pV$

Taking the total derivative

$dG=dU-TdS-SdT+pdV+Vdp$

From the Second law of thermodynamics one obtains

$dG=TdS-pdV-TdS-SdT+pdV+Vdp$

thus one arrives at

$dG=-SdT+Vdp$

For G(T,p) we have the following total differential

$dG={(\frac{\partial G}{\partial T})}_{p}dT+{(\frac{\partial G}{\partial p})}_{T}dp$