A container holds 0.5 moles of an ideal gas at 2 atm pressure and 27°C. What is the volume of the gas? (R = 8.31 J mol⁻¹
**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. Ideal gas equation: PV = μ R T.T = 27 + 273 = 300 K, P = 2 × 1.01 × 10⁵ Pa = 2.02 × 10⁵ Pa, μ = 0.5 mol.V = (μ R T)/(P) = (0.5 × 8.31 × 300)/(2.02 × 10⁵) = 6.17 × 10⁻³ m³ = 6.17 litres . Substituting values gives 6.2 litres, which
Ref: NCERT > Physics Book > Behaviour of Perfect Gas and Kinetic Theory > RMS Speed and Temperature Dependence