# Difference between revisions of "Maxwell speed distribution"

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:<math>v_{\rm max} = \sqrt{\frac{2k_BT}{m}}</math> | :<math>v_{\rm max} = \sqrt{\frac{2k_BT}{m}}</math> | ||

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+ | The mean speed is given by | ||

+ | |||

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

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

+ | |||

+ | :<math>v_{\rm rms} = \sqrt \frac{3}{2} v_{\rm max}</math> | ||

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

# J. C. Maxwell "", British Association for the Advancement of Science '''29''' Notices and Abstracts 9 (1859) | # J. C. Maxwell "", British Association for the Advancement of Science '''29''' Notices and Abstracts 9 (1859) |

## Revision as of 14:20, 3 July 2007

The probability that speed of a molecule of mass *m* lies in the range *v* to *v+dv* is given by

The maximum of this distribution is located at

The mean speed is given by

and the root-mean-square speed by

## 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)