How will the rate of collisions of rigid diatomic molecules against the vessel's wall change, if the gas is expanded adiabatically `eta` times ?

Explanation

No. of collisions `= (1)/(4) n lt v gt = v`
Now, `=1kT = kT_0 eta^(2//i) = 0.72 xx 10^-20 J`
(When the gas is expanded `eta` times, `n` decreases by a factor `eta`). Also
`T' (eta V)^(2//i) = TV^(2//i)` or `T' = eta^(2//i) T` so, `(v')/(v) = (1)/(eta) eta^(-1//i) = eta ^((-i - 1)/(i))`
i.e., collisions decrease by a factor `eta ^((i + 1)/(i)), i = 5` here.