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Kinetic theory of gases. Boltzmanns Law and Maxwell distribution

Problem 2.96

A gas consists of molecules of mass \(m\) and is at a temperature \(T\). Making use of the Maxwell velocity distribution function, find the corresponding distribution of the molecules over the kinetic energies \(\varepsilon .\) Determine the most probable value of the kinetic energy \(\boldsymbol{\varepsilon}_ {n} .\) Does \(\varepsilon_ {n}\) correspond to the most probable velocity?

Reveal Answer
dN/N=2π(πkT)−3/2θ−ε/kTεdε;εpr=1/2kT; no. d N / N=2 \pi(\pi k T)^{-3 / 2} \theta^{-\varepsilon / k T} \sqrt{\varepsilon} d \varepsilon ; \varepsilon_{p r}=1 / 2 k T ; \text { no. }
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