# Difference between revisions of "Maxwell speed distribution"

The Maxwell velocity distribution [1] [2] [3] [4] provides 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

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

The mean speed is given by

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

and the root-mean-square speed by

$\sqrt{\overline{v^2}} = \sqrt \frac{3}{2} v_{\rm max}$