A gas consisting to rigid diatomic molecules is expanded adiabatically. How many times has the gas to be expanded to reduce the root mean square velocity of the molecules `eta = 1.50` times ?

Explanation

Here `I = 5, C_V = (5)/(2) R, gamma = (7)/(5)` given
`v'_(rms) = sqrt((3 R T)/(M)) = (1)/(eta) v_(rms) = (1)/(eta) sqrt((3 R T)/(M))` or `T = (1)/(eta^2) T`
Now in an adiabatic process
`TV^(gamma - 1) = TV^(2 //i) = constant` or `VT^(i//2) = constant`
`V'((1)/(eta^2) T)^(i//2) = V T^(i//2)` or `V' eta^-i = V` or `V' = eta^i V`
The gas must be expanded `eta^i` times, i.e., `7.6` times.