Average relative velocity in calculating mean free path

[dsdsuster]

Hello,

Does anyone know why we use the root mean square of the relative velocity in calculating the mean free path? As is done in this example:

http://galileo.phys.virginia.edu/classes/152.mf1i.spring02/MolecularCollisions.htm

Seems like it would make more sense to find the mean of the relative velocity.

 

[Simon Bridge]

Try it and see what happens when you use the mean-relative-velocity. ;)

 

[dsdsuster]

Thanks Simon,

I'm not really following. The mean-relative-velocity would be 0 since velocity is a vector. I think I meant to say mean-relative-speed. I would expect the mean-relative-speed to be less than the rms-relative-speed but that's about it.

Thanks

 

[Simon Bridge]

Ri-ight - so, look through your notes about mean free path, where it is applied (say: brownian motion) and use your idea of the mean-speed instead of the rms speed. (You'll have to adjust the derivation to account for the difference.) See what you get.

I could go and just describe in words why the rms speed is preferred etc etc ... but that's a lot of typing when I can just make you do the math. You asked the question: are you prepared to find the answer?