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. v_rms = √((3k_B T)/(m)), so v_rms ∝ (1)/(√(m)).Ratio: v_rms,H₂v_rms,O₂ = √(m_O₂)m_H₂ = √((32)/(2)) = √(16) = 4.v_rms,H₂ = 4 × 500 = 2000 m/s . Substituting values gives 2000 m/s, 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.