Maxwell speed distribution: Difference between revisions

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:<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>


where ''T'' is the [[temperature]] and <math>k_B</math> is the [[Boltzmann constant]].
The maximum of this distribution is located at  
The maximum of this distribution is located at  



Revision as of 14:58, 3 July 2007

The probability that 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

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)