Gibbs energy function
From SklogWiki
Definition:
\[\left.G\right.=A+pV\]
where p is the pressure, V is the volume, and A is the Helmholtz energy function, i.e.
\[\left.G\right.=U-TS+pV\]
Taking the total derivative
\[\left.dG\right.=dU-TdS-SdT+pdV+Vdp\]
From the Second law of thermodynamics one obtains
\[\left.dG\right.=TdS -pdV-TdS-SdT+pdV+Vdp\]
thus one arrives at
\[\left.dG\right.=-SdT+Vdp\]
For G(T,p) we have the following total differential
\[dG=\left(\frac{\partial G}{\partial T}\right)_p dT + \left(\frac{\partial G}{\partial p}\right)_T dp\]
