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

[asmpic]

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.

 

[asmpic]

bump

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

 

[gfd43tg]

Can't help you with your problem, but here is the latex guide

https://www.physicsforums.com/showpost.php?p=3977517&postcount=3