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).T = 327 + 273 = 600 K, V = 4 × 10⁻³ m³.P = (0.4 × 8.31 × 600)/(4 × 10⁻³) = 4.986 × 10⁵ Pa ≈ 5.0 atm (1 atm ≈ 10⁵ Pa). Substituting values gives 5.0 atm, which matches expected kinetic theory result, confirming mean free path