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A ideal gas (gamma=1.5) is expanded adia...

A ideal gas `(gamma=1.5)` is expanded adiabatically. How many times has the gas to be expanded to reduce the root mean square velocity of molecules `2.0` times

A

4 times

B

16 times

C

8 times

D

2 times

Text Solution

Verified by Experts

The correct Answer is:
B
`v_(rms)= sqrt((3RT)/(M)) or v_(rms)`
`prop sqrt(T)`
`v_(rms)` is to reduce two times, i.e. the temperature of the gas will have to reduce four times or
`(T.)/(T)=(1)/(4)`
During the adiabatic process,
`TV^(gamma-1)=T.V^(gamma-1)`
or `(V.)/(V)=((T)/(T))^((1)/(gamma-1))`
`=(4)^((1)/(1.5-1))=4^(2)=16`
`:. V.=16 V`
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