In symbols, G is mathematical shorthand for Gibbs free energy, defined by the function:

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 latent energy (gebundene energy) of the system. [1] A number of other formulations came about in the mean time. In 1933, however, English chemical thermodynamicist Edward Guggenheim set the following definition in stone: [2]

“The function G [H–TS] is due to Gibbs, and is often referred to by modern writers as ‘free energy’. We shall call G the ‘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). Treatise on Thermodynamics (G, pg. 113). Longmans, Green and Co.
2. Guggenheim, Edward, A. (1933). Modern Thermodynamics by the Methods of Willard Gibbs (pg. 11). London: Methuen & Co.
3. (a) Battino, Rubin. (2001). "Ch. 4: A Brief History of Thermodynamics Notation", in: Drug-Receptor Thermodynamics: Introduction and Application by Robert Raffa. Wiley.
(b) Mills I, Cvitas T, Homann K, et al. (1988). Quantities, Units and Symbols in Physical Chemistry, IUPAC, Blackwell Scientific Publications. Oxford.

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