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. Triatomic gas: 6 degrees of freedom, C_v = 3 R.Q = μ C_v Δ T = 0.15 × 3 × 8.31 × 25 = 93.4875 J ≈ 93.5 J. Substituting values gives 93.5 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.