Maxwell-boltzmann distribution

From Glossary of Meteorology

Maxwell–Boltzmann distribution

(Or Maxwell–Boltzmann law, Maxwell–Boltzmann distribution of kinetic energies or speeds.) The distribution law for kinetic energies (or, equivalently, speeds) of molecules of an ideal gas in equilibrium at absolute temperature T:
where k is Boltzmann's constant.

The integral of this function between any two energies is the fraction of the total number of molecules with energies in this range. Note the similarity between this function and the Planck's radiation law. The former is the distribution law for the energies of an ideal gas of molecules, whereas the latter is the distribution law for the energies of a gas of photons.