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.