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 V0, in which an ideal gas is contained under the same pressure p0 and at the same temperature. What work has to be performed in order to increase isothermally the volume of one part of gas η times compared to that of the other by slowly moving the piston ?
Let volume of chambers changes by ∆V. According to the problem, the final volume of left chamber is η times final volume of right chamber.
As piston is moved slowly therefore, change in kinetic energy is zero. By work-energy theorem, we can write
