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Kinetic theory of gases. Boltzmanns Law and Maxwell distribution

Problem 2.91

Using the Maxwell distribution function, calculate the mean velocity projection \(\left\langle v_{x}\right\rangle\) and the mean value of the modulus of this projection \(\left\langle\left|v_{x}\right|\right\rangle\) if the mass of each molecule is equal to \(m\) and the gas temperature is \(T\).

Reveal Answer
⟨vx⟩=0,⟨∣vx∣⟩=2kT/πm\left\langle v_{x}\right\rangle=0,\left\langle\left|v_{x}\right|\right\rangle=\sqrt{2 k T / \pi m}
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