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Kinetic theory of gases. Boltzmanns Law and Maxwell distribution

Problem 2.100

An ideal gas consisting of molecules of mass \(m\) with concentration \(n\) has a temperature \(T\). Using the Maxwell distribution function, find the number of molecules reaching a unit area of a wall at the angles between \(\theta\) and \(\theta+d \theta\) to its normal per unit time.

Reveal Answer
dv=∫v=0∞dn(dΩ/4π)vcos⁡θ=n(2kT/πm)1/2sin⁡θcos⁡θdθd v=\int_{v=0}^{\infty} d n(d \Omega / 4 \pi) v \cos \theta=n(2 k T / \pi m)^{1 / 2} \sin \theta \cos \theta d \theta
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