# Maxwell speed distribution

The **Maxwell velocity distribution** ^{[1]}
^{[2]}
^{[3]}
^{[4]} provides probability that the speed of a molecule of mass *m* lies in the range *v* to *v+dv* is given by

where *T* is the temperature and is the Boltzmann constant.
The maximum of this distribution is located at

The mean speed is given by

and the root-mean-square speed by

## Derivation

## References

- ↑ J. C. Maxwell "", British Association for the Advancement of Science
**29**Notices and Abstracts 9 (1859) - ↑ J. C. Maxwell "V. Illustrations of the dynamical theory of gases.—Part I. On the motions and collisions of perfectly elastic spheres", Philosophical Magazine
**19**pp. 19-32 (1860) - ↑ J. C. Maxwell "II. Illustrations of the dynamical theory of gases", Philosophical Magazine
**20**pp. 21-37 (1860) - ↑ J. Clerk Maxwell "On the Dynamical Theory of Gases", Philosophical Transactions of the Royal Society of London
**157**pp. 49-88 (1867)

- Related reading

- J. S. Rowlinson "The Maxwell-Boltzmann distribution", Molecular Physics
**103**pp. 2821 - 2828 (2005) - Elyas Shivanian and Ricardo Lopez-Ruiz "A New Model for Ideal Gases. Decay to the Maxwellian Distribution", arXiv:1105.4813v1 24 May (2011)

## External resources

- Initial velocity distribution sample FORTRAN computer code from the book M. P. Allen and D. J. Tildesley "Computer Simulation of Liquids", Oxford University Press (1989).