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 ω\omega about a vertical axis passing through one of its ends. The tube contains carbon dioxide at a temperature TT =300 K=300 \mathrm{~K}. The length of the tube is l=100 cm.l=100 \mathrm{~cm} . Find the value ω\omega at which the ratio of molecular concentrations at the opposite ends of the tube is equal to η=2.0\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}