Practice question

**Gas laws** Boyle, Charles, Gay-Lussac are special cases of ideal gas equation, for constant pressure volume-temperature relation V ∝ T, for constant temperature pressure-volume inverse, for constant volume pressure-temperature direct, enabling calculation of new volume from temperature ratio. Let mass = m. N = (m)/(M) × N_A.For He (M = 4): N_He = (m)/(4) × N_A.For O₂ (M = 32): N_O₂ = (m)/(32) × N_A.Ratio N_HeN_O₂ = (m)/(4)(m)/(32) = (32)/(4) = 8:1. Substituting values gives 8:1, 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.