What is the total internal energy of 0.3 moles of a triatomic gas at 300 K with no vibrational modes? (R = 8.31 J mol⁻¹
**Molar specific heat** from equipartition C_v = f/2 R, C_p = f/2 R + R, γ = C_p/C_v =1+2/f, for f=3 γ=1.67, f=5 γ=1.4, f=6 γ=1.33, explaining specific heat variation with molecular structure, degrees of freedom determine heat capacity. Triatomic gas: 6 degrees of freedom, U = 3 μ R T.U = 3 × 0.3 × 8.31 × 300 = 2243.7 J ≈ 2.24 kJ. Substituting values gives 2.24 kJ, 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.
Ref: NCERT > Physics Book > Behaviour of Perfect Gas and Kinetic Theory > Degrees of Freedom and Molar Specific Heat