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Gibbs energy function

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


Taking the total derivative


From the Second law of thermodynamics one obtains

\left.dG\right.=TdS -pdV-TdS-SdT+pdV+Vdp

thus one arrives at


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