Solving an Energy Problem: Calculating Average Molecule Energy Through a Hole

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SUMMARY

The discussion centers on calculating the average energy of gas molecules passing through a small hole in a wall separating two gas reservoirs with different temperatures. The gas densities are equal, with one side at temperature T1=4T2. The key takeaway is that the average energy of the molecules must account for the temperature difference and the bidirectional flow through the hole. The user seeks feedback on their solution approach, which is shared as a PDF attachment.

PREREQUISITES
  • Understanding of kinetic theory of gases
  • Familiarity with the concept of mean free path
  • Basic knowledge of thermodynamics, specifically temperature and energy relationships
  • Ability to interpret and manipulate equations related to gas behavior
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  • Study the kinetic theory of gases to understand molecular motion and energy distribution
  • Learn about the mean free path and its implications in gas behavior
  • Explore thermodynamic principles related to temperature and energy transfer
  • Review LaTeX formatting for presenting scientific solutions clearly
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Students and professionals in physics, particularly those focused on thermodynamics and kinetic theory, as well as anyone involved in gas dynamics and energy calculations.

asmpic
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Hello everyone.

I was hoping someone could help me out with the following problem. I tried working it out, but I don't know if I did it correctly or if I missed an important point. It just seems too "short". it would be much appreciated if someone could go through my solution quickly and give me some feedback.

Thanks so much!

1. Consider a very large gas reservoir divided by a thin wall with a tiny (much smaller than the mean free path) hole in the middle. Both sides are filled with the same single-species gas. The number densities are identical in the two parts of the reservoir, n1=n2, but the temperature in one partition is four times larger than in the other, T1=4T2. What is the average energy of all the molecules passing through the hole? Note: remember to account for both directions

The Attempt at a Solution


I have attached my solution as a pdf since I couldn't figure out how to use latex on this site yet.
 

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no one can help? did I perhaps post in the wrong section?
 

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