Suppose there are two gases in a recipient with a movable piston in the middle, separating the recipient into two halves. If both halves have different pressure, work can be extracted from the system by letting the pressure difference move the piston in one direction or the other.
But, if the two halves are connected to each other by a hole in the middle of the piston, such that they are in thermodynamical equilibrium with each other, no work can be extracted, by the Second Law of Thermodynamics.
Suppose, after some time, we close the hole. At this moment, it is likely that one side will have slightly more pressure than the other. We can then let the piston move and extract work from this (extremely small) pressure difference.
This process can then be repeated after both pressures return to equilibrium again, apparently extracting work from a gas in equilibrium. However, this goes against the Second Law of Thermodynamics, so what is wrong in this process?
