How many times a diatomic gas should be expanded adiabatically so as to reduce the root mean square velocity to half. :

Answer

32

Explanation

`(u_("rms")T_(2))/(u_("rms")T_(2)) = sqrt(T_(1)/T_(2))`
`(2 xx u)/u = sqrt(T_(1)/T_(2))`
`T_(1)/T_(2)=4`
`T_(2) = T_(1)/4`
From `TV^(gamma-1)` = constant, for adiabatic expansion
`T_(1)V_(1)^(gamma-1) = T_(2)V_(2)^(gamma-1)`
`[V_(1)/V_(2)]^(gamma-1) = T_(2)/T_(1) = 1/4`
`[V_(1)/V_(2)]^(1.4-1) =1/4 rArr V_(2)/V_(1) = 32`