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
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The '''Maxwell velocity distribution''' <ref>J. C. Maxwell "", British Association for the Advancement of Science '''29''' Notices and Abstracts 9 (1859)</ref>
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<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>
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<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>
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<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==
# J. C. Maxwell "", British Association for the Advancement of Science '''29''' Notices and Abstracts 9 (1859)
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<references/>
# J. C. Maxwell "", Philosophical Magazine '''19''' pp. 19 (1860)
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;Related reading
# J. C. Maxwell "", Philosophical Magazine '''20''' pp. 21 (1860)
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*[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/10.1098/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)]
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*[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)]
#[http://dx.doi.org/10.1080/002068970500044749 J. S. Rowlinson "The Maxwell-Boltzmann distribution", Molecular Physics '''103''' pp. 2821 - 2828 (2005)]
 
 
==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