The Helmholtz function is defined as: F = U - TS, where U is the internal energy, T the Kelvin temperature, and S the entropy of the system. F, U, and S are extensive quantities. In an infinitesimal process, dF = dU - TdS - SdT, and recognizing that dW = TdS - dU, this yields an expression for the path dependent reversible work in terms of the Helmholtz function: dW = - dF - SdT. Also, if the only work is pdV work the Helmholtz function may be written as: dF = - SdT - pdV. From this relationship: 
                                (dF/dT)_p = -S, and (dF/dV)_T = - p.
The Gibbs function is defined as: G = U - TS + pV = H - TS, H being the enthalpy of the system. In a general infinitesimal process, dG = dU - TdS - SdT + pdV + Vdp. Using the expression for reversible work from the combined first and second laws gives: dW = -dG - SdT +pdV +Vdp. If the process occurs at constant pressure and temperature this reduces to: dW = -dG +pdV. The work term includes both pdV work and any other work done on the system in the process. The Gibbs function change: dG = (dW - pdV), is therefore a measure of the reversible non-pdV work done on the system in the process. Also, since dG = -SdT + Vdp;    (dG/dT)_p = -S, and (dG/dp)_T = V