Which thermodynamic potential is usually denoted by G?

The thermodynamic potential usually denoted by G is Gibbs free energy, also called Gibbs energy.

For a simple system, Gibbs free energy is defined as G = H − TS, or equivalently G = U + pV − TS. Here H is enthalpy, T is absolute temperature, S is entropy, U is internal energy, p is pressure, and V is volume. Its natural variables are temperature, pressure, and composition.

Gibbs free energy is especially useful for processes at constant temperature and pressure. Under those conditions, a decrease in G indicates a spontaneous direction when no additional non-pressure–volume work is imposed. Chemical equilibrium corresponds to a minimum in Gibbs free energy, subject to the system’s constraints.

A frequent mix-up is Helmholtz free energy, denoted A or F, not G. Helmholtz energy is the useful potential for constant temperature and volume. Enthalpy is H, while internal energy is U. Josiah Willard Gibbs developed the concept in the 1870s; modern IUPAC usage often prefers “Gibbs energy” to “Gibbs free energy.”