Q.Verify that the area under the p-V curve has dimensions of work.

A p-V diagram (also called a p-V curve or indicator diagram) is a graph of a system's pressure against its volume, on which every equilibrium state of the system corresponds to a single point, and every quasi-static process corresponds to a continuous curve (its 'path') connecting an initial point to a final point. Because the work done by a system during a volume change is $W = \int p\,dV$, the AREA under a p-V curve between two volumes directly represents the work done during that segment of the process — a curve sloping downward as volume increases (expansion) encloses positive work; a curve running the other way (compression) encloses negative work; and a perfectly vertical segment (constant volume) encloses no area, and hence no work, at all. …