Editing Maxwell–Boltzmann distribution (section)

===Distribution for the speed===

The Maxwell–Boltzmann distribution for the speed follows immediately from the distribution of the velocity vector, above. Note that the speed is
<math display="block">v = \sqrt{v_x^2 + v_y^2 + v_z^2}</math>
and the [[volume element]] in [[spherical coordinates]]
<math display="block"> dv_x\, dv_y\, dv_z = v^2 \sin \theta\, dv\, d\theta\, d\phi = v^2 \, dv \, d\Omega</math>
where <math>\phi</math> and <math>\theta</math> are the [[Spherical coordinate system|spherical coordinate]] angles of the velocity vector. [[Spherical coordinate system#Integration and differentiation in spherical coordinates|Integration]] of the probability density function of the velocity over the solid angles <math>d\Omega</math> yields an additional factor of <math>4\pi</math>.
The speed distribution with substitution of the speed for the sum of the squares of the vector components:
{{Equation box 1 |indent=: |equation=<math>
f (v) =
\sqrt{\frac{2}{\pi}} \, \biggl[\frac{m}{k_\text{B}T}\biggr]^{3/2} v^2 \exp\left(-\frac{mv^2}{2k_\text{B}T}\right).
</math>}}