How Long to Achieve Uniform Mixture in Helium Gas Experiment?

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SUMMARY

The discussion centers on estimating the time required to achieve a uniform mixture of helium isotopes in a spherical vessel. The experiment involves a 1-meter diameter vessel initially filled with 4He gas at one atmosphere, into which a small amount of 3He gas is introduced. Participants emphasize the importance of using the equation for the time dependence of the root mean square (RMS) travel distance in a one-dimensional random walk to calculate the mixing time. Suggestions for improving the mixing process include enhancing the introduction method of the 3He gas.

PREREQUISITES
  • Understanding of random walk theory
  • Familiarity with gas laws and behavior
  • Knowledge of isotopic mixtures
  • Basic principles of diffusion
NEXT STEPS
  • Study the equation for time dependence of root mean square distance in random walks
  • Research methods to enhance gas mixing techniques
  • Explore the properties of helium isotopes and their behavior in mixtures
  • Learn about diffusion coefficients and their impact on gas mixing
USEFUL FOR

This discussion is beneficial for physicists, chemists, and researchers involved in gas dynamics, particularly those studying isotopic mixtures and diffusion processes.

Jameskd
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Homework Statement
Estimating how long it would take to achieve a uniform mixture.
Relevant Equations
J = DA dC/dx, C=N/V
This is an experiment on a dilute isotopic mixture of helium gas. A spherical vessel of diameter 1 m is first filled with 4He gas to one atmosphere pressure. Then a small amount of 3He gas is introduced through a valve on one side of the vessel. Make a rough estimate of how long one must wait before a uniform mixture has formed (use the result for the time dependence of the root mean square travel distance in a random walk in 1D.) Suggest a better way to make a uniform mixture.

I am unsure how to begin this question, for starters I thought of a high concentration to a low concentration, so where the valve is to the rest of the sphere. But I'm just struggling to start. Any tips?

Thank you in advance.
 
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Start out by writing down for us the equation for the time dependence of the rms distance in random walk.
 

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