All Problems

Kinetic theory of gases. Boltzmanns Law and Maxwell distribution

Problem 2.110

A horizontal tube with closed ends is rotated with a constant angular velocity \(\omega\) about a vertical axis passing through one of its ends. The tube contains carbon dioxide at a temperature \(T\) \(=300 \mathrm{~K}\). The length of the tube is \(l=100 \mathrm{~cm} .\) Find the value \(\omega\) at which the ratio of molecular concentrations at the opposite ends of the tube is equal to \(\eta=2.0\).

Reveal Answer
ω=(2RT/Ml2)lnη=280rad/s\omega=\sqrt{\left(2 R T / M l^{2}\right) \ln \eta}=280 \mathrm{rad} / \mathrm{s}