The molar specific heat at constant pressure for a polyatomic gas with 2 vibrational modes is: (R = 8.31 J mol⁻¹ K⁻¹)
**Mean free path variation** λ ∝1/n ∝1/P at constant T, λ ∝ T/P, temperature increase increases λ because n decreases at constant P, but also v increases, overall λ ∝ T/P, for gas at 2 atm λ=4×10⁻⁷ m, at 4 atm λ=2×10⁻⁷ m halves when pressure doubles, as n doubles. Polyatomic gas: 3 translational + 3 rotational + 2 vibrational modes.Total degrees of freedom = 3 + 3 + 2 × 2 = 10.C_v = 5R, C_p = C_v + R = 6R = 6 × 8.31 = 49.86 J mol⁻¹ K⁻¹ . Substituting values gives 49.86 J mol⁻¹ K⁻¹, which matches expected kinetic theory
Ref: NCERT > Physics Book > Behaviour of Perfect Gas and Kinetic Theory > Collision Frequency and Mean Free Path Variation