Maxwell speed distribution: Difference between revisions
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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).