Problem 2.100

An ideal gas consisting of molecules of mass $m$ with concentration $n$ has a temperature $T$ . Using the Maxwell distribution function, find the number of molecules reaching a unit area of a wall at the angles between $\theta$ and $\theta+d \theta$ to its normal per unit time.

d v=\int_{v=0}^{\infty} d n(d \Omega / 4 \pi) v \cos \theta=n(2 k T / \pi m)^{1 / 2} \sin \theta \cos \theta d \theta

Kinetic theory of gases. Boltzmanns Law and Maxwell distribution