In a pressure-volume graph, the magnitude of work done is represented by the area under the curve bounded by the volume axis.
Let's analyze the area under the curve for each graph:
Graph represents an expansion from to . The area is the integral , which covers a significant region under the curve.
Graph represents a cyclic process. The net work done is the area enclosed by the loop. This area is much smaller than the total area under the expansion curve in graph .
Graph represents an isochoric process (constant volume ). Since , the work done .
Graph also represents a cyclic process. Similar to graph , the net work done is the area enclosed by the loop, which is smaller than the area under the expansion curve in graph .
Comparing all cases, the expansion process in graph covers the maximum area under the curve, thus representing the maximum work done.