# Difference between revisions of "Maxwell speed distribution"

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− | 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 | + | The '''Maxwell velocity distribution''' <ref>J. C. Maxwell "", British Association for the Advancement of Science '''29''' Notices and Abstracts 9 (1859)</ref> |

+ | <ref>[http://dx.doi.org/10.1080/14786446008642818 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)]</ref> | ||

+ | <ref>[http://dx.doi.org/10.1080/14786446008642902 J. C. Maxwell "II. Illustrations of the dynamical theory of gases", Philosophical Magazine '''20''' pp. 21-37 (1860)]</ref> | ||

+ | <ref>[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)]</ref> 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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==Derivation== | ==Derivation== | ||

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

− | + | <references/> | |

− | + | ;Related reading | |

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

− | + | *[http://arxiv.org/abs/1105.4813 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== | ==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)]. | *[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 12:56, 27 May 2011

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).