Practice question

**Ideal gas equation** combines Boyle, Charles, Avogadro laws, P V = N k_B T, N number of molecules, k_B Boltzmann constant, for 1 mole N_A=6.022×10²³, R = N_A k_B, enabling calculation of volume from P,T,n. Diatomic gas: 5 degrees of freedom, C_v = (5)/(2) R.Q = μ C_v Δ T = 0.25 × (5)/(2) × 8.31 × 20 = 207.75 J ≈ 207.8 J. Substituting values gives 207.8 J, 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.