If the velocities in such a beam followed the Maxwell-Boltzmann distribution the average velocity would be given by: = a π ve−av2 v=0 ∞ ∫ dv where a = m / 2kT . What would be the average velocity in m/s of a beam of O2 molecules at 100 K?

Question

If the velocities in such a beam followed
the Maxwell-Boltzmann distribution the average velocity would be given by:
< v >=
a
π
ve−av2
v=0
∞
∫ dv where a = m / 2kT . What would be the average velocity in
m/s of a beam of O2 molecules at 100 K?

nottim · Answer

$$<v>=\sqrt{\frac{ m/2KT }{ \pi }}\int\limits_{v=o}^{\infty}ve ^{-av ^{2}}dv$$

nottim · Answer

Getting kicked out my my working space soon. Will be back in an hour.

nottim · Answer

Hiyo

empty · Answer

So basically you want to find <v> by evaluating the stuff on the right. So there are two major things to do:

1) plug in all the values for m, k, and T.
2) solve the integral/look it up in a chart.

I suggest plugging in everything once you're sure you have the integral solved.

nottim · Answer

This is a little embarassing, but I can't, for the life of me, remember how calculus works.

aaronq · Answer

If you don't want to revisit calculus (which i think you should), you can use wolfram alpha or other software. Look here, https://www.wolframalpha.com/input/?i=0+to+inf+integral+xe%5E(ax%5E2)+dx

aaronq · Answer

I omitted the stuff under the squared root sign since it's only a constant, btw.