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Transport Phenomena

Problem 2.232

An ideal gas goes through a polytropic process with exponent n.n . Find the mean free path λ\lambda and the number of collisions of each molecule per second vv as a function of (a) the volume VV; (b) the pressure pp; (c) the temperature TT.

Reveal Answer
2.232. (a) λ∝V,v∝V−(n+1)/2\lambda \propto V, \quad v \propto V^{-(n+1) / 2} (b) λ∝p−1/n,v∝p(n+1)/2n\lambda \propto p^{-1 / n}, \quad v \propto p^{(n+1) / 2 n} (c) λ∝T1/(1−n),v∝T(n+1)/2(n−1)\lambda \propto T^{1 /(1-n)}, v \propto T^{(n+1) / 2(n-1)}
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