Practice question

**Collision frequency** Z = √2 n π d² v_avg, n number density, d molecular diameter, v_avg average speed, proportional to n and v_avg, mean free path λ = v_avg/Z =1/(√2 n π d²), inversely proportional to n, so λ ∝1/P at constant T because n ∝ P, collision frequency increases with pressure, λ decreases. Diatomic gas: 5 degrees of freedom (3 translational + 2 rotational).U = (5)/(2) μ R T = (5)/(2) × 0.5 × 8.31 × 200 = 2077.5 J ≈ 2.08 kJ. Substituting values gives 2.08 kJ, which matches expected kinetic theory result, confirming mean free path λ = 1/(√2 n π d²),