G(v^2)d^3v = G(v^2) 4\pi v^2 dv \equiv F(v)dv

F(v) = 4 \pi \left(\frac{m}{2\pi kT}\right)^{3/2} v^2 e^{\frac{-mv^2}{2kT}}

qu'on appelle distribution de Maxwell-Boltzman.