# Difference between revisions of "Maxwell speed distribution"

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

:<math>P(v)dv = 4 \pi v^2 dv \left( \frac{m}{2 \pi k_B T} \right)^{3/2} \exp (-mv^2/2k_B T) </math> | :<math>P(v)dv = 4 \pi v^2 dv \left( \frac{m}{2 \pi k_B T} \right)^{3/2} \exp (-mv^2/2k_B T) </math> | ||

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#[http://dx.doi.org/10.1098/rstl.1867.0004 J. Clerk Maxwell "On the Dynamical Theory of Gases", Philosophical Transactions of the Royal Society of London '''157''' pp. 49-88 (1867)] | #[http://dx.doi.org/10.1098/rstl.1867.0004 J. Clerk Maxwell "On the Dynamical Theory of Gases", Philosophical Transactions of the Royal Society of London '''157''' pp. 49-88 (1867)] | ||

#[http://dx.doi.org/10.1080/002068970500044749 J. S. Rowlinson "The Maxwell-Boltzmann distribution", Molecular Physics '''103''' pp. 2821 - 2828 (2005)] | #[http://dx.doi.org/10.1080/002068970500044749 J. S. Rowlinson "The Maxwell-Boltzmann distribution", Molecular Physics '''103''' pp. 2821 - 2828 (2005)] | ||

+ | ==External resources== | ||

+ | *[ftp://ftp.dl.ac.uk/ccp5/ALLEN_TILDESLEY/F.24 Initial velocity distribution] sample FORTRAN computer code from the book [http://www.oup.com/uk/catalogue/?ci=9780198556459 M. P. Allen and D. J. Tildesley "Computer Simulation of Liquids", Oxford University Press (1989)]. | ||

[[category: statistical mechanics]] | [[category: statistical mechanics]] |

## Revision as of 18:41, 8 February 2009

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).