"Perform the following calculation in spherical coordinates. The Maxwell-Boltzman velocity distribution function has the form:
f(u)=(mβ/2Π)
3/2e
-mβu2/2 where β is a constant. Using the fact that ε = (mu
2)/2 = (3/2)k
BT = int(du
x)int(du
y)int(du
z)((mu
2)/2)f(u) and using also the definition u
2=u
x2+u
y2+u
z2 complete the integral and show that β=1/(k
BT)
I'll link to my instructor's lecture notes, which I didn't find especially helpful but would give you a sense of what path I'm trying to follow.
http://faculty.washington.edu/gdrobny/Lecture453_1-14_Intro.pdf I'm currently at page 5, figure 1.14.
I was thinking that the integral in figure 1.14 may be solvable using a generic form but haven't found one that I can fit the equation to.
Any help or insight would be greatly appreciated, as I've been trying to figure it out all weekend and made zero progress.