I think your intuition of Order and Disorder is reverse. The situation described HallsofIvy is said to be ordered. The homogenous distribution of gas which will result is said to be disordered.
It won't stay half-half, because it's a much less probable state than the equidistributed one...
Hi !
You can actually derive the form of the potential energy going out from its definition.
Place a corpse of mass M in a polar coordinate system, for simplicity's sake, and look at the gravitationnal force F(r) acting on a mass m.
Then, W(r) = - \int \limits_{\infty}^{r}...