G = U + PV – TS

or

G = H – TS

The expression is named after American engineer Willard Gibbs.

Etymology

In the first 75-years of thermodynamics, different symbols were assigned to different functions. In 1897, referring to the 1882 words of Hermann Helmholtz, Max Planck states that the following formula:

G = U – F = TΦ

is the

“The function G [H–TS] is due to Gibbs, and is often referred to by modern writers as ‘free energy’. We shall callGthe ‘Gibbs free energy’.”

Hence, ever since, G as referred to Gibbs free energy.

Gibbs energy

In circa 1980, IUPAC made an attempt to “banish” the term ‘free’ from the name Gibbs free energy, replacing it with Gibbs energy, symbol G. [3] This effort, however, has had a marginal effect.

References

1. Planck, Max. (1897).

2. Guggenheim, Edward, A. (1933).

3. (a) Battino, Rubin. (2001). "Ch. 4: A Brief History of Thermodynamics Notation", in:

(b) Mills I, Cvitas T, Homann K, et al. (1988).