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. Charles’ law: (V₁)/(T₁) = (V₂)/(T₂).V₁ = 12 litres, T₁ = 300 K, T₂ = 450 K.V₂ = V₁ × (T₂)/(T₁) = 12 × (450)/(300) = 18 litres. Substituting values gives 18 litres, 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.