Using the Maxwell distribution function, determine the pressure exterted by gas on a wall, if the gas temperature is `T` and the concentration of molecules is `n`.

Explanation

Let, `dn(v_x) = n ((m)/(2 pi k T))^(1//2) e^(-mv_x^2//2 kT) dv_x`
be the number of molecules per unit volume with `x` component of velocity in the range `v_x` to `v_x + dv_x`
Then `p = int_0^oo 2mv_x.v_x dn(v_x)`
=`int_0^oo 2 mv_x^2 n((m)/(2 pi kT))^(1//2) e^(-mv_x^2//2 kT) dv_x`
=`2mn (1)/(sqrt(pi)) (2kT)/(m) int_0^oo u^2 e^(-u^2) du`
=`(4)/(sqrt(pi)) nkT. int_0^oo x ^(-x) (dx)/(2 sqrt(x)) = nkT`.