All Problems Transport Phenomena
Problem 2.232
An ideal gas goes through a polytropic process with exponent \(n .\) Find the mean free path \(\lambda\) and the number of collisions of each molecule per second \(v\) as a function of (a) the volume \(V\); (b) the pressure \(p\); (c) the temperature \(T\).
2.232. (a) \(\lambda \propto V, \quad v \propto V^{-(n+1) / 2}\) (b) \(\lambda \propto p^{-1 / n}, \quad v \propto p^{(n+1) / 2 n}\) (c) \(\lambda \propto T^{1 /(1-n)}, v \propto T^{(n+1) / 2(n-1)}\)