From the Maxwell distribution function frind `lt lt v_x^2 gt gt`, the mean value of the squared `v_x` projection of the molecular velocity in a gas at a temperature `T`. The mass of each molecule is equal to `m`.

Explanation

`lt v_x^2 gt = int_0^oo v_x^2 e - (mv_x^2)/(2 kt) dv_x//int_0^oo e - (mv_x^2)/(2 kt) dv_x`
`=(2 kT)/(m) int_0^oo xe^-x (dx)/(2 sqrt(x))//int_0 ^oo e^-x (dx)/(2 sqrt(x))`
=`(2 kT)/(m) Gamma((3)/(2))// Gamma ((1)/(2)) = (kT)/(m)`.