# Maxwell speed distribution

The **Maxwell velocity distribution** 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 "", Philosophical Magazine
**19**pp. 19 (1860) - J. C. Maxwell "", Philosophical Magazine
**20**pp. 21 (1860) - J. Clerk Maxwell "On the Dynamical Theory of Gases", Philosophical Transactions of the Royal Society of London
**157**pp. 49-88 (1867) - J. S. Rowlinson "The Maxwell-Boltzmann distribution", Molecular Physics
**103**pp. 2821 - 2828 (2005)

## 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).