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

In summary, a large gas reservoir is divided by a thin wall with a tiny hole in the middle. Both sides have the same gas with identical number densities, but one partition has a temperature four times larger than the other. The problem asks for the average energy of all molecules passing through the hole, accounting for both directions.
  • #1
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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bump

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

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

What is the purpose of solving an energy problem?

The purpose of solving an energy problem is to understand and quantify the amount of energy required to overcome a specific barrier or obstacle. This can be useful in various fields, such as chemistry, physics, and engineering, to predict and optimize energy usage in different systems.

What is meant by "calculating average molecule energy through a hole"?

In this context, "calculating average molecule energy through a hole" refers to determining the average amount of energy that molecules possess as they pass through a small opening or hole. This energy is typically measured in joules and can be used to understand the behavior of particles in a system.

Why is it important to calculate average molecule energy through a hole?

Calculating average molecule energy through a hole is important because it allows us to study the behavior of particles in a system and determine the amount of energy required to overcome a specific barrier. This information can then be used to optimize energy usage and improve system efficiency.

What factors can affect the average molecule energy through a hole?

The average molecule energy through a hole can be affected by various factors, such as the size and shape of the hole, the temperature and pressure of the system, and the type of molecules passing through the hole. Other factors, such as the presence of external forces or interactions between particles, can also play a role.

How is average molecule energy through a hole calculated?

Average molecule energy through a hole can be calculated using the Boltzmann distribution, which takes into account the number of molecules, the size of the hole, and the temperature of the system. This equation can then be used to determine the average energy of the molecules passing through the hole.

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