# Helmholtz Free Energy

## $\LARGE F=-kT{\ln}Z$

### The Terms

$F$ - Helmholtz free energy [Units: Joules, J]

$k$ - Boltzmann constant. [Value: 1.381 x 10-23 J K-1]

$T$ - Absolute temperature. [Units: Kelvins, K]

$Z$ - Partition function

### What it means

In statistical mechanics and thermodynamics the Helmholtz free energy is a theremodynamic potential which measures the "useful" work obtainable from a closed thermodynamic system at constant temperature, volume and particle number. For such a system in equilibrium the Helmholtz free energy is minimised.

### Further information at Warwick

Helmholtz free energy is covered in the second year module "PX265 Thermal Physics II" and the third year module "PX366 Statistical Physics".