All Problems Kinetic theory of gases. Boltzmanns Law and Maxwell distribution
Problem 2.99
The velocity distribution of molecules in a beam coming out of a hole in a vessel is described by the function \(F(v)=A v^{3} \mathrm{e}^{-m v^{2} / 2 k T}\), where \(T\) is the temperature of the gas in the vessel. Find the most probable values of (a) the velocity of the molecules in the beam; compare the result obtained with the most probable velocity of the molecules in the vessel; (b) the kinetic energy of the molecules in the beam.
(a) \(v_{p r}=\sqrt{3 k T / m}\) (b) \(\varepsilon_{p r}=k T\)