A solid has a molar specific heat capacity of 24.9 J mol⁻¹ K⁻¹. What is the energy per degree of freedom per atom? (R =
**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. C = f × (R)/(2), 24.9 = f × (8.31)/(2), f = (24.9 × 2)/(8.31) ≈ 6.Energy per degree of freedom = (1)/(2) k_B T, per mole = (1)/(2) R T.For 1 degree of freedom, energy per mole = (8.31)/(2) = 4.155 J mol⁻¹ K⁻¹ . Substituting values gives 4.16 J mol⁻¹ K⁻¹, which matches expected kinetic theory result, confirming mean free path λ = 1/(√2
Ref: NCERT > Physics Book > Behaviour of Perfect Gas and Kinetic Theory > Degrees of Freedom and Molar Specific Heat