Practice question
Question
The rms speed of a gas is 400 m/s at 100 K. At what temperature will the rms speed be 800 m/s?
Explanation
**Partial pressure concept** for mixture of non-reacting gases, total pressure sum of partials, each gas behaves independently, kinetic theory still holds with effective n = Σ n_i, mean free path depends on total n and cross-sections, mixture properties weighted by mole tions. v_rms ∝ √(T), (v₂)/(v₁) = √((T₂)/(T₁)).(800)/(400) = √((T₂)/(100)), 2 = √((T₂)/(100)).Square both sides: 4 = (T₂)/(100), T₂ = 400 K. Substituting values gives 400 K, 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.
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