InterviewSolution
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InterviewSolution
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An ideal gas goes through a polytropic process with exponent `n`. Find the mean free path `lamda` 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`. |
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Answer» In the polytropic process of index `n` `pV^n =` constant, `TV^(n -1) =` constant and `p^(1 - n) T^n =` constant (a) `lamda alpha V` `v alpha (T^(1//2))/(V) = V^((1 - n)/(2)) V^-1 = V^((-n + 1)/(2))` (b) `lamda alpha (T)/(p), T^n alpha p^(n -1)` or `T alpha p^(1 - (1)/(n)` so `lamda alpha p^(-1//n)` `v = (lt v gt)/(lamda) alpha (p)/(sqrt(T)) alpha p^(1 -(1)/(2) + (1)/(2n)) = p^((n + 1)/( 2n))` ( c) `lamda alpha (T)/(p), p alpha T^((n)/(n - 1))` `lamda alpha T^(1 -(n)/(n 1)) = T^(-(1)/(n -1)) = T^((1)/(1 - n))` `v alpha (p)/(sqrt(T)) alpha T^((n)/(n -1) -(1)/(2)) =T^((n + 1)/(2(n -1)))`. |
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