Gibbs energy function

Definition:

G = A + p V

G = U - T S + p V

Taking the total derivative

d G = d U - T d S - S d T + p d V + V d p

but from equation \ref{secondlaw} we obtain

d G = T d S - p d V - T d S - S d T + p d V + V d p

thus one arrives at

$d G = - S d T + V d p$

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

d G = {(\frac{\partial G}{\partial T})}_{p} d T + {(\frac{\partial G}{\partial p})}_{T} d p

Good for $NpT$

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