equipartition of energy

equipartition of energy, law of statistical mechanics stating that in a system in thermal equilibrium, on the average, an equal amount of energy will be associated with each degree of freedom. (A particle moving through space has three degrees of freedom because three coordinates are needed to describe its position.) Based on the work of physicists James Clerk Maxwell of Scotland and Ludwig Boltzmann of Germany, this law states specifically that a system of particles in equilibrium at absolute temperature T will have an average energy of 1/2kT associated with each degree of freedom, in which k is the Boltzmann constant. In addition, any degree of freedom contributing potential energy will have another 1/2kT associated with it. For a system of s degrees of freedom, of which t have associated potential energies, the total average energy of the system is 1/2(s + t)kT.

For example, an atom of a gas has three degrees of freedom (the three spatial, or position, coordinates of the atom) and will, therefore, have an average total energy of 3/2kT. For an atom in a solid, vibratory motion involves potential energy as well as kinetic energy, and both modes will contribute a term 1/2kT, resulting in an average total energy of 3kT.