The work done during a pressure-volume process can be determined by integrating the pressure-volume curve.

In such processes, work is performed when the volume changes against a constant external pressure. This work can be visualized as the area under the pressure-volume curve, which can be computed using calculus through integration.

The equation for the work done, denoted as $W$, in a pressure-volume process is given by:

In this equation, $P$ represents the external pressure and $dV$ signifies the change in volume. This formula can be applied to calculate the work for any pressure-volume process, provided that the pressure and volume are known at each stage.

It’s crucial to understand that the sign of the work done is contingent upon the direction of the process. During an expansion, the system does work on the surroundings, resulting in positive work. Conversely, during compression, work is performed on the system, leading to negative work.

In summary, the work done in a pressure-volume process can be calculated by integrating the pressure-volume curve using the equation $W = \int P \, dV$. The sign of the work is determined by the process’s direction: it is positive for expansion and negative for compression.