Past exam of the physics course of the year 4 of the natural sciences course of the University of Cambridge / 2015 / Paper 1 / Section B / B3 / a / Solution

The quasistatic pressure-volume work done on the body is $\delta W=-PdV$. If its volume remains constant throughout the process, every $dV$ vanishes, so the work is zero. Equal initial and final volumes alone would not suffice: an expansion and compression cycle can have nonzero work. Other work modes are excluded by this simple elastic-volume model.