Free Expansion - Paradox?

If the piston is massless then it can move without any force. Your situation does not make sens physically though.

Work:

$$W=Fd$$

$F$ is force done to do displacement $d$.

Think of it intuitively like this:

If you push something very hard (large force), but it doesn't move at all - like pushing on a building - you don't do any work of any use. If you push something very far, but it didn't require much force - like pushing a balloon - then you also really didn't do much work (it wasn't much of an effort).

If the piston is a balloon that you hold in place in front of the opening to the gas chamber, then when you let go, the gas pushes this very light balloon out of the way. That doesn't require much force from the gas, so not much work is done.

Remember that to make something move, you must apply a force $F=ma$. If this mass $m$ is very, very small, then the force needed is also very, very small.

A massless piston is a idealization - to move zero mass requires zero work.

Let the piston have a bit of mass, and just think it through. The piston will accelerate and this involves energy moving from the gas to the piston. The piston then hits the end of the rigid chamber and comes to a stop giving up its kinetic energy. Where does that energy go? It goes to raising the temperature of gas and piston. But the gas has, at this stage, cooled a little. So the temperature of the gas first falls a bit while the piston accelerates, and then rises back up as the piston gives up its energy. Eventually the system settles down to an equilibrium in which no energy has left the chamber (if we assume this piston is internal, so did no work on any external body).

In the case of an ideal gas, in this final equilibrium, the final temperature is the same as the initial temperature.

The point is that the gas does no work on anything outside the chamber, and nothing inside the chamber acquired any energy (in the end) from the gas if we assume the heat capacity of the piston is negligible.