Gibbs Function, Gibbs Free Energy, G
Index
The Gibbs Function, G, is a thermodynamic parameter defined as: 
G = H - TS, where H is the enthalpy, T the Kelvin temperature, and S the entropy of the system. G is often called the Gibbs free energy.

In an arbitrary process, the change in the Gibbs function is given by: 
dG = dH - TdS - SdT. Expanding H to get: dH = dU + pdV + vdP, and recognizing that the First law states that 
dU + pdV = TdS, gives: 
                dG = VdP - SdT.
From this relationship two identifications can be made: 
    (dG/dP)T = V, and (dG/dT)P = -S

Josiah Willard Gibbs, USA, (1839-1903)