A gas effuses into a vacuum though a small hole of area [tex]A[/tex]. Show that if the particles effused into an evacuated sphere and the particles condensed where they collided that there would be a uniform coating. (7.6 of Blundell and Blundell)
Angular probability distribution. The probability a particle is travelling between [tex]\theta[/tex] and [tex]\theta+d\theta[/tex] to the normal of the small hole.
cos\theta sin\theta d\theta
Surface area of a ring defined on the surface of a sphere with radius of unity where the angles go from [tex]\theta[/tex] to [tex]\theta+d\theta[/tex]
2\pi sin\theta d\theta
The Attempt at a Solution
Surely it would just be amount of particles over area which is proportional to [tex]cos\theta[/tex]. This is clearly not uniform