Practice question

**Specific heat relation** C_p - C_v = R for ideal gas per mole, Mayer's relation, due to work done at constant pressure, degrees of freedom include translational, rotational, vibrational, each quadratic term contributes ½ R to C_v. Charles’ law: (V₁)/(T₁) = (V₂)/(T₂).V₁ = 8 litres, T₁ = 400 K, T₂ = 200 K.V₂ = V₁ × (T₂)/(T₁) = 8 × (200)/(400) = 4 litres. Substituting values gives 4 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.