Question

How does the mean free path `lamda` and the number of collisions of each molecule per unit time `v` depend on the absolute temperature of an ideal gas undergoing
(a) an isochoric process ,
(b) an isobaric process ?

Answer 1

(a) `lamda = (1)/(sqrt(2) pi d^2 n)`
`d` is a constant and `n` is a constant for an isochoric process so `lamda` is constant for an isochoric process.
`v = (lt v gt)/(lamda) = (sqrt(8 RT)/(M pi))/(lamda) alpha sqrt(T)`
(b) `lamda = (1)/(sqrt(2) pi d^2)(kT)/(p) alpha T` for an isobaric process.
`v = (lt v gt)/(lamda) alpha (sqrt(T))/(T) = (1)/(sqrt(T))` for an isobaric process.