Final answer:
The work done by the gas in one cycle represented by a rectangular path on a pV diagram is equal to twice the product of the pressure change and the volume change, which is 2 p0V0.
Step-by-step explanation:
The work done by a gas during a thermodynamic cycle is equal to the area enclosed by the cycle on the pV diagram. If we assume that the cycle provided in the question looks like a rectangle with sides corresponding to a pressure change of p0 and a volume change of V0, then the area, and thus the work done by the gas over one cycle, would be simply the length times the width of the rectangle, which would be p0 times V0. In this case, considering the cycle is rectangular and the process returns to its original state after completion of the cycle, the work done by the gas would be the area of two such 'steps' made by the gas, resulting in 2 p0V0.