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Kinetic theory of gases. Boltzmanns Law and Maxwell distribution

Problem 2.96

A gas consists of molecules of mass mm and is at a temperature TT. Making use of the Maxwell velocity distribution function, find the corresponding distribution of the molecules over the kinetic energies ε.\varepsilon . Determine the most probable value of the kinetic energy εn.\boldsymbol{\varepsilon}_ {n} . Does εn\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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