Practice question

**Temperature dependence of RMS speed** v_rms ∝ √T, doubling T increases v_rms by √2≈1.414, e.g., at 300 K v_rms for O₂ ≈483 m/s, at 600 K ≈683 m/s, illustrating kinetic theory relation between temperature and molecular motion, average kinetic energy ½ m v_rms² =3/2 k_B T. PV = μ R T, P = (μ R T)/(V).Total moles = 1 + 2 = 3, V = 30 × 10⁻³ m³.P = (3 × 8.31 × 500)/(30 × 10⁻³) = 4.155 × 10⁵ Pa ≈ 4.16 atm. Substituting values gives 4.16 atm, which matches expected kinetic theory result, confirming mean free path λ = 1/(√2 n π