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Deep Singh
Asked: 2022-11-10T05:22:49+05:30 In:

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`.

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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  1. 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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