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 monatomic gas, C_v = (3)/(2) R.Q = μ C_v Δ T = 0.5 × (3)/(2) × 8.31 × 25 = 155.8125 J ≈ 155.8 J. Substituting values gives 155.8 J, 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.