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. v_rms ∝ √(T), (v₂)/(v₁) = √((T₂)/(T₁)).(v₂)/(516) = √((600)/(300)) = √(2) ≈ 1.414.v₂ = 516 × 1.414 ≈ 729 m/s . Substituting values gives 729 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.