Maxwell-Boltzmann Distribution

#Physics
Describes the proportion of gases at certain speeds

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

• Math version

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

$\displaystyle \displaystyle f(v)~d^{3}v={\biggl [}{\frac {m}{2\pi kT}}{\biggr ]}^{\frac {3}{2}},\exp \left(-{\frac {mv^{2}}{2kT}}\right)~d^{3}v$

• Physics version with velocity $\displaystyle v$
  Desmos