Practice question

**Mean free path variation** λ ∝1/n ∝1/P at constant T, λ ∝ T/P, temperature increase increases λ because n decreases at constant P, but also v increases, overall λ ∝ T/P, for gas at 2 atm λ=4×10⁻⁷ m, at 4 atm λ=2×10⁻⁷ m halves when pressure doubles, as n doubles. Triatomic gas: 3 translational + 3 rotational = 6 degrees of freedom.C_v = 3R, C_p = C_v + R = 4R.γ = (C_p)/(C_v) = (4R)/(3R) = (4)/(3) = 1.33. Substituting values gives 1.33, which matches expected kinetic theory result, confirming mean free path λ = 1/(√2 n π d²), ideal gas law P V =