An ideal gas consisting of rigid diatomic molecules goes through an adiabatic process. If λ is the mean free path, then its dependance on pressure (P), Volume (V), temperature (T)

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λ = 2 ​ π d 2 N V ​ ⇒ λ ∝ V and λ ∝ d − 2 . For an adiabatic process p V γ = constant with γ = 7/5 : T V 2/5 = C ⇒ V ∝ T − 5/2 , so λ ∝ T − 5/2 ; also V ∝ P − 5/7 , so λ ∝ P − 5/7 , not P − 5/2 .

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