Gibbs energy function

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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