Determine the ratio of the sonic velocity `v` in a gas to the root mean square velocity of molecules of this gas, if the molecules are
(a) momatomic ,
(b) rigid diatomic.

Explanation

`v_(sound) = sqrt((gamma p)/(rho)) = sqrt((gamma RT)/(M))`, and `v_(rms) = sqrt((3 kT)/(m)) = sqrt((3 RT)/(M))`
so, `(v_(sound))/(v_(rms)) = sqrt((gamma)/(3)) = sqrt((i + 2)/(3 i))`
(a) For monoatomic gases`i = 3`
`(v_(sound))/(v_(rms)) = sqrt((5)/(9)) = 0.75`
(b) For rigid diatomic molecules `i = 5`
`(v_(sound))/(v_(rms)) = sqrt((7)/(15)) = 0.68`.