Practice question

**Molecular diameter from mean free path** uses λ =1/(√2 n π d²), solving d = √(1/(√2 n π λ)). At higher pressure n ∝ P, λ ∝1/P, so doubling P halves λ, illustrating pressure dependence of collision distance. C_p = C_v + R = 12.7 + 8.31 = 21.01 J mol⁻¹ K⁻¹.γ = (C_p)/(C_v) = (21.01)/(12.7) ≈ 1.65. Substituting values gives 1.65, which matches expected kinetic theory result, confirming mean free path λ = 1/(√2 n π d²), ideal gas law P V = n R T and v_rms = √(3 R T/M) relations.