Problem 2.36

A piston can freely move inside a horizontal cylinder closed from both ends. Initially, the piston separates the inside space of the cylinder into two equal parts each of volume \(V_{0}\), in which an ideal gas is contained under the same pressure \(p_{0}\) and at the same temperature. What work has to be performed in order to increase isothermally the volume of one part of gas \(\eta\) times compared to that of the other by slowly moving the piston?