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Kinetic theory of gases. Boltzmanns Law and Maxwell distribution

Problem 2.95

Making use of the Maxwell distribution function, find \(\langle 1 / v\rangle,\) the mean value of the reciprocal of the velocity of molecules in an ideal gas at a temperature \(T,\) if the mass of each molecule is equal to \(m .\) Compare the value obtained with the reciprocal of the mean velocity.

Reveal Answer
⟨1/v⟩=2m/πkT=4π⟨v⟩\langle 1 / v\rangle=\sqrt{2 m / \pi k T}=4 \pi\langle v\rangle
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