Irreversible sand problem

From class today we were calculating the work done when the sand is raised irreversibly by the piston. Here is perhaps a clearer way to look at that problem.

Before the piston is raised, it has some potential energy U1. After the piston is raised, it has a new potential energy U2, given in this case by U1 - mgz, where m is the mass of the piston, g is the gravitational potential, and z is how high it was raised. The difference in energy (U2-U1) is equal to whatever work energy the gas put into the piston, W (the gas does work on the system).

W = (U2 - U1)
= -mgz

But since Pext = mg/A:

W = -Pext * A * z
= -Pext * Delta V