An ideal gas `(gamma = 1.5)` is expanded adiabatically. How many times has the gas to be expanded to reduce the roo-mean-square velocity of molecules becomes half ?

Options

A. 4 times
B. 16 times
C. 8 times
D. 2 times

Answer

B

Explanation

`v_(rms)=sqrt((3RT)/(M)) or v_(rms)prop sqrt(T)`
`v_(rms)` is to reduce two times i.e. Temperature of the gas will have to reduce four times or
`(T')/(T) = 1/4`
During adiabatic process, ltbgt `TV^(gamma-1) = T^(')V'^(gamma-1)`
or `(V')/(V) =((T)/(T'))^(1/(gamma-1))`
`=(4)^((1)/(1.5-1))= 4^(2)=16`
`:. V^(')=16V`.