All Problems Kinetic theory of gases. Boltzmanns Law and Maxwell distribution
Problem 2.112
From the conditions of the foregoing problem find: (a) the number of molecules whose potential energy lies within the interval from \(U\) to \(U+d U\); (b) the most probable value of the potential energy of a molecule; compare this value with the potential energy of a molecule located at its most probable distance from the centre of the field.
(a) \(d N=\left(2 \pi n_{0} / a^{3 / 2}\right) \mathrm{e}^{-U / k T} \sqrt{U} d U\) (b) \(U_{p r}={ }^{1} /_{2} k T\).