# Derivation of Pressure/Kinetic Therory problem involving hole in box

A box of volume $V_0$ has a small hole of area $A_0$. The box initially has one mole of an ideal gas at $t = 0$, which is at an initial temperature $T (t = 0)$. Find the rate of energy flow through the hole as a function of temperature and other parameters.

I'm still reading chapters on kinetic theory, and this problem requires a derivation of pressure, and some sort of 1/6 or 1/4 factor. I still have a lot of reading before I can write anything down, I was wondering if anybody knows what this problem is about and can help. This isn't for any credit, but it is from a old study guide. Thanks.

The problem is basically about the number of molecules exiting the box through the hole in a time $t$. Think of it this way: all molecules hitting any of the walls will be reflected back into the box. Do you know how to calculate the number of such molecules?

Now molecules that hit the hole are not reflected back, but leave the box. But the number of molecules hitting the hole is the same as the number of molecules hitting a spot of area $A_o$ on a regular hole.

And of course you can assume that the average temperature of the molecules hitting the hole is $T$, and that will allow you to calculate the energy of the molecules.

I'm going to leave the details for you. I'm sure most of them are worked out in your textbook.

• Hi, I actually don't have any specific textbook. This problem is from a practice candidacy exam. I see what you mean. If you have any texts in mind that handle this particularly well, please let me know. Thanks. – walczyk Aug 17 '13 at 1:15
• I'm still working on this problem, and I found this useful resource: ronispc.chem.mcgill.ca/ronis/chem223/hnd4.pdf Would the correct energy (per molecule) be E=1/2 m*v^2 where v is the average speed, or E=3/2kT? I remember that these are equivalent for a certain speed, I'm not sure if its average or rms. – walczyk Aug 18 '13 at 21:07