- #1

sugar_scoot

- 7

- 0

*[tex]\frac{1}{2} v n f(v)dv sin \theta cos \theta d\theta[/tex]*

show that the average value of cos [tex]\theta[/tex] for these molecules is [tex]\frac{2}{3}[/tex].

**I have convinced myself the answer is 4/3 instead.**Can anyone show me where I am wrong?

I used P(cos [tex]\theta[/tex]) = sin [tex]\theta[/tex] cos [tex]\theta[/tex]

Then I normalized:

1 = c [tex]\int^{\pi}_{0} sin \theta cos \theta d\theta[/tex]

so that:

c = 2

<cos [tex]\theta[/tex]> = 2 [tex]\int^{\pi}_{0} sin \theta cos^{2}\theta d \theta[/tex] = 2 (2/3) = 4/3