# Work content

In thermodynamic analysis of chemical reactions, the term free energy denotes either of two related concepts of importance expressing the total amount of energy which is used up or released during a chemical reaction. Both attempt to capture that part of the total energy of a system which is available for "useful work" and is hence not stored in "useless random thermal motion". As a system undergoes changes, its free energy will decrease.

When a system of molecules undergoes change, whether chemical reaction or changes in physical states such as phase changes, there are two tendencies driving the changes:

If ${\displaystyle U}$ represents the internal energy, ${\displaystyle T}$ the temperature, and ${\displaystyle S}$ the entropy, these two tendencies can be combined by stating that the expression

${\displaystyle A=U-TS}$, the Helmholtz free energy function (named after Hermann von Helmholtz)

tends to decrease. Strictly, this is only true in situations where the volume is constant, as in sealed containers. The change in Helmholtz free energy is equal to the maximum work accompanying the process of the system occurring at constant volume

${\displaystyle \delta W=dA}$

At constant temperature

${\displaystyle \delta W=dA=dU-T\,dS}$

If the pressure is constant, as in open containers, the enthalpy ${\displaystyle H=U+PV}$ (where ${\displaystyle P}$ represents the pressure and ${\displaystyle V}$ represents the volume) replaces the energy, and thus the quantity that must be minimized is

${\displaystyle G=H-TS=U+PV-TS}$, the Gibbs free energy function (named after Willard Gibbs)