Maxwell speed distribution: Difference between revisions

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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

  1. J. C. Maxwell "", British Association for the Advancement of Science 29 Notices and Abstracts 9 (1859)
  2. J. C. Maxwell "", Philosophical Magazine 19 pp. 19 (1860)
  3. J. C. Maxwell "", Philosophical Magazine 20 pp. 21 (1860)
  4. J. Clerk Maxwell "On the Dynamical Theory of Gases", Philosophical Transactions of the Royal Society of London 157 pp. 49-88 (1867)
  5. J. S. Rowlinson "The Maxwell-Boltzmann distribution", Molecular Physics 103 pp. 2821 - 2828 (2005)

External resources