Maxwell-Boltzmann Distribution

Describes the proportion of gases at certain speeds

$f\left(x\right)=\sqrt{\frac{2}{\pi }}\frac{x^2}{a^3}{e}^{-\frac{x^2}{2a^2}}$

• Math version

$f(E)=\frac{1}{e^{\beta \epsilon }}$

$f(v)d^{3}v=[\frac{m}{2\pi kT}{]}^{\frac{3}{2}}\exp \left(-\frac{m{v}^2}{2kT}\right)d^{3}v$

• Physics version with velocity $v$
  Desmos