at constant P, λ = T
at constant T, λ = 1/P
at same constant P & T, λ = 1/d2
At constant pressure, the mean free path (λ) of a gas molecule is directly proportional to temperature (T). At constant temperature, λ is inversely proportional to pressure (P). If you compare two different gas molecules at the same temperature and pressure, λ is inversely proportional to the square of the diameter (d) of the gas molecules. Put these facts together to create a formula for the mean free path of a gas molecule with a proportionality constant (call it Rmfp , like the ideal-gas constant).
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