Practice question

**Equipartition theorem** energy ½ k_B T per degree of freedom per molecule, f degrees give U = f/2 k_B T per molecule, f/2 R T per mole, internal energy function of T only for ideal gas, no intermolecular potential. For diatomic gas (rigid rotator): U = (5)/(2) μ R T.U = (5)/(2) × 1 × 8.31 × 300 = 6232.5 J ≈ 6.23 kJ . Substituting values gives 6.23 kJ, 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.