# Effusing gas onto the interior of an evacuated sphere

## Homework Statement

A gas effuses into a vacuum though a small hole of area $$A$$. 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)

## Homework Equations

Angular probability distribution. The probability a particle is travelling between $$\theta$$ and $$\theta+d\theta$$ 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 $$\theta$$ to $$\theta+d\theta$$

$$2\pi sin\theta d\theta$$

## The Attempt at a Solution

Surely it would just be amount of particles over area which is proportional to $$cos\theta$$. This is clearly not uniform