Practice question

**Mean free path** λ = 1/(√2 n π d²) is average distance molecule travels between collisions, n number density (m⁻³), d molecular diameter (m), π≈3.14. Inversely proportional to n and d², larger n or d reduces λ. Rearranged d² = 1/(√2 n π λ), so d = √(1/(√2 n π λ)), enabling diameter estimation from measured λ and n. Diatomic gas: 5 degrees of freedom, C_v = (5)/(2) R.Q = μ C_v Δ T = 0.2 × (5)/(2) × 8.31 × 10 = 83.1 J. Substituting values gives 83.1 J, which matches expected kinetic theory result, confirming mean free path λ = 1/(√2 n π