This thermodynamic quantity states that the decrease in value during a process is equal to the useful work done by the system. It is denoted by G and the mathematical equation is:

G = H – TS

Where,

H = heat content

T = absolute temperature

S = entropy of the system

For isothermal process we have

G1 = H1 – TS1 for the initial state

G2 = H2 – TS2 for final stage

Therefore,

G2 – G1 = (H2 – H1) – T(S2 – S1)

Now,

ΔG = G2 – G1 is the change in Gibbs free energy

ΔH = H2 – H1 is the change in enthalpy of the system

ΔS = S2 – S1 Is the change in entropy of the system

Thus the above equation becomes:

ΔG = ΔH – TΔS is known as Gibbs-Helmoholtz equation.