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Questions  

An ideal gas (γ = 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

detailed solution

Correct option is B

vrms = 3RTM or vrms ∝Tvrms, is to reduce two times, i.e., temperature of the gas will have to reduce four times orT'T = 14 During adiabatic process,TVγ-1 = T'V'γ-1or   V'V = (TT')γγ-1       = (4)11.5-1 = 42 = 16∴  V' = 16 V

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