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.

Copyright 2022 American Meteorological Society (AMS). For permission to reuse any portion of this work, please contact Any use of material in this work that is determined to be “fair use” under Section 107 of the U.S. Copyright Act (17 U.S. Code § 107) or that satisfies the conditions specified in Section 108 of the U.S.Copyright Act (17 USC § 108) does not require AMS’s permission. Republication, systematic reproduction, posting in electronic form, such as on a website or in a searchable database, or other uses of this material, except as exempted by the above statement, require written permission or a license from AMS. Additional details are provided in the AMS Copyright Policy statement.