Numerical on adiabatic expansion

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SUMMARY

An ideal gas with a specific heat ratio (γ) of 1.5 undergoes adiabatic expansion, necessitating a volume increase of 16 times to achieve a reduction in the root mean square (rms) velocity of its molecules by half. The rms speed is defined by the equation √(3kT/m), indicating that halving the speed requires a quarter of the original absolute temperature. The relationship governing the adiabatic process is expressed as T.V^(γ-1) = constant, confirming the calculations presented in the discussion.

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  • Understanding of ideal gas laws
  • Familiarity with thermodynamic concepts, particularly adiabatic processes
  • Knowledge of the root mean square speed formula
  • Basic grasp of specific heat ratios (γ)
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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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