Free Expansion in Szilard Engine? A crucial step in the definition of Szilard Engine is computing the work done by the single molecule in moving the piston from the middle to one end (left or right, depending on the location of the molecule). The textbook treatment calculates the work as resulting from a reversible isothermal expansion. I don't understand this step.
The second half of the engine (not containing the molecule) is vacuum, so shouldn't the expansion be a free expansion? I'm thinking on the similar lines as this answer, but the gas in one half of the engine contains just one molecule. If the expansion is indeed free, then the molecule doesn't lose any energy in pushing the piston, and no heat flows into the engine from the heat bath, and there is no decrease in entropy anywhere.
What am I missing here?
 A: It confused me too when I first I first saw it.
The thing is, if you want to extract any work, as you noted, pushing against the vacuum alone won't be very useful (you won't extract anything), so you have to add a "system" that would permit you to extract work from the molecule (otherwise it wouldn't be called an engine in the first place!). And this is not really clearly emphasized in a lot of papers.
Here is a good illustration (taken here)

The important part here the the mass attached to the pulley and linked to the piston. This way, the single molecule has to work against the gravity and since we supposed that the transformation is reversible, we say that $p_{molecule}=p_{pulley + gravity}$. And indeed, to go from $V/2$ to $V$, you have to extract energy from the particle (since the mass has moved upward in the gravitational field and thus gained energy).
In most of the figures we can find online, the engine "lacks" anything that can permit the single molecule do to work but this is essential!
