What is Helmholtz energy (A) defined as?

Helmholtz energy, often represented by the symbol A, is defined as the difference between the internal energy (U) of a system and the product of its temperature (T) and entropy (S). This relationship is mathematically expressed as A = U - TS.

The Helmholtz energy is a critical thermodynamic potential used to describe systems at constant volume and temperature. It provides insight into the amount of useful work that can be extracted from a closed system at constant temperature and volume. The term "TS" accounts for the energy that is not available for doing work due to the disorder associated with the entropy of the system. Thus, the Helmholtz energy combines considerations of both energy and entropy, highlighting the balance between internal energy and the tendency towards disorder.

This definition is key in thermodynamics as it helps predict the direction of spontaneous processes and is particularly relevant in applications involving physical and chemical equilibria at constant temperature and volume.