Difference between revisions of "Maxwell speed distribution"

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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>
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The maximum of this distribution is located at
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:<math>v_{\rm max} = \sqrt{\frac{2k_BT}{m}}</math>
 
==References==
 
==References==
 
# J. C. Maxwell "", British Association for the Advancement of Science '''29''' Notices and Abstracts 9 (1859)
 
# J. C. Maxwell "", British Association for the Advancement of Science '''29''' Notices and Abstracts 9 (1859)

Revision as of 12:51, 3 July 2007

The probability that speed of a moleculae of mass m lies in the range v to v+dv is given by

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)

The maximum of this distribution is located at

v_{\rm max} = \sqrt{\frac{2k_BT}{m}}

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)