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?

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