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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 UU to U+dUU+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.

Reveal Answer
(a) dN=(2πn0/a3/2)e−U/kTUdUd N=\left(2 \pi n_{0} / a^{3 / 2}\right) \mathrm{e}^{-U / k T} \sqrt{U} d U (b) Upr=1/2kTU_{p r}={ }^{1} /_{2} k T.
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