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. Degrees of freedom = 3 + 2 = 5.C_v = (5)/(2) R, C_p = C_v + R = (5)/(2) R + R = (7)/(2) R.γ = (C_p)/(C_v) = (7)/(2) R(5)/(2) R = (7)/(5) = 1.4. Substituting values gives 1.4, 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.