InterviewSolution
Saved Bookmarks
InterviewSolution
| 1. |
An ideal gas consisting of rigid diatimic molecules goes through an adiabatic process process. How do the mean free path `lamda` and the number of collisions of each molecule per second `v` depend in this process on (a) the volume`V` , (b) the pressure `p` , ( c) the temperature `T` ? |
|
Answer» (a) `lamda alpha(1)/(n) = gt (1)/(N//V) = (V)/(N)` Thus `lamda alpha V` and `v alpha (T^(1//2))/(V)` But in an adiabatic process `(gamma = (7)/(5) "here")` `TV^(gamma - 1) = "constant so" TV^(2//5) =` constant or `T^(1//2) alpha V^(-1//5)` Thus `v alpha V^(-6//5)` (b) `lamda alpha (T)/(p)` But `p((T)/(p))^gamma =` constant or `(T)/(p) alpha p^(-1//gamma)` or `T alpha p^(1-1//gamma)` Thus `lamda alpha p^(-1//gamma) = p^(-5//7)` `v = (lt v gt )/(lamda) alpha(p)/(sqrt(T)) alpha p^(1//2 + (1)/(2 gamma)) =p^((gamma + 1)/(2 gamma) = p^(6//7))` ( c) `lamda alpha V` But `TV^(2//5) =` constant or `V alpha T^(-5//2)` Thus `lamda alpha T^(-5//2)` `v alpha(T^(1//2))/(V) alpha T^3`. |
|