# Helmholtz free energy

In thermodynamics, Helmholtz free energy is the isothermal (constant temperature) isochoric (constant volume) thermodynamic potential of a closed system (constant species), defined by:

F ≡ E – TS

where E represents the energy of the system and S its entropy. [1] In short, the Helmholtz free energy is the measure of an isothermal-isochoric closed system’s ability to do work. [2] In the absence of any external field, the Helmholtz free energy may be defined as:

$H = U - TS \,$

Synonyms for the Helmholtz free energy include: free energy, Helmholtz function, among others. The Helmholtz free energy is commonly used in experiments such as in explosives research (where explosive reactions by their nature induce pressure changes). A related potential, used commonly in biology, is the Gibbs free energy where volume changes occur, but where temperature and pressure remain constant.

History
The Helmholtz free energy was introduced independently in 1875 by American engineer Willard Gibbs and in 1882 by German physician-physicist Hermann Helmholtz. [1]

References
1. Perrot, Pierre. (1998). A to Z of Thermodynamics, Oxford: Oxford University Press.
2. Daintith, John. (2005). Oxford Dictionary of Science. Oxford: Oxford University Press.