Numerical on adiabatic expansion

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naimagul
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An ideal gas with g =1.5 is expanded adiabatically. How many times has the gas to be expanded to reduce the rms velocity of molecules 2 times?
 

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rms speed = √(3kT/m), where k is the Boltzmann constant and m the mass of one molecule.
So to halve the speed you need 1/4 of the absolute temperature.
For adiabatic process, T.V[itex]^{γ-1}[/itex] = constant
With γ = 1.5 you'd need 16 times the volume.
 
Thanks for your help. It was great solving the problem.
 

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