Maxwell speed distribution: Difference between revisions

Revision as of 16:48, 3 July 2007

The probability that the speed of a molecule 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)

where T is the temperature and $k_{B}$ is the Boltzmann constant. The maximum of this distribution is located at

v_{\rm {max}}={\sqrt {\frac {2k_{B}T}{m}}}

The mean speed is given by

{\overline {v}}={\frac {2}{\sqrt {\pi }}}v_{\rm {max}}

and the root-mean-square speed by

v_{\rm {rms}}={\sqrt {\frac {3}{2}}}v_{\rm {max}}

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