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

AI Thread Summary
A user seeks assistance with a physics problem involving the calculation of average energy for gas molecules passing through a small hole in a wall separating two gas reservoirs at different temperatures. The user has attempted a solution but feels uncertain about its completeness and is looking for feedback. They mention the conditions of equal number densities and a significant temperature difference, with one side being four times hotter than the other. The user has attached their solution as a PDF for review and expresses frustration over a lack of responses. The discussion highlights the importance of understanding molecular energy in relation to temperature differences in gas dynamics.
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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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