Kinetic Theory of Gases: Effusion and Collisions

[xatu]

Question:

In the following link I'm concerned with only pages 1 and 2. I'm wondering if there is a typo or an error of some kind. I feel like there is some inconsistency to what the author refers to as \upsilon, \theta, and \phi. The only angle shown in the diagram is \upsilon, which is the angle the constructed parallelepiped makes with the surface normal.

For instance, the volume of the parallelepiped involves \upsilon and the # of molecules crossing through dA in time dt involves \theta, but then the flux again involves \upsilon. Shouldn't all of those quantities involve only \upsilon?

http://ocw.mit.edu/courses/chemistr...y-ii-spring-2008/lecture-notes/29_562ln08.pdf

Hopefully I am wrong. Thanks in advance for any help guys.

 

[haruspex]

The only angle shown in the diagram is \upsilon, which is the angle the constructed parallelepiped makes with the surface normal.

It's not \upsilon, it's a somewhat stylised \theta. Does that resolve it?

 

[xatu]

Wow, I feel horrendously stupid. Sorry for wasting your time, haruspex.

 

[xatu]

However, I did stumble across a legitimate error. The distribution, as well as the average flux, should contain e^{\frac{-mv^{2}}{2kT}}. What is shown is e^{\frac{-mv^{2}}{kT}} - missing the factor of 2 in the dominator of fractional exponent. However, the correct answer is shown for the result of the integral. Still should have that factor of 2 though.

 

[haruspex]

Wow, I feel horrendously stupid. Sorry for wasting your time, haruspex.

If it allows you to progress, my time was not wasted.