# Difference between revisions of "Maxwell speed distribution"

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and the root-mean-square speed by | and the root-mean-square speed by | ||

− | :<math> | + | :<math>\sqrt{\overline{v^2}} = \sqrt \frac{3}{2} v_{\rm max}</math> |

==Derivation== | ==Derivation== | ||

==References== | ==References== |

## Revision as of 13:32, 2 August 2007

The 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)