p-V diagrams represent the work done by or on a gas

Work done and gas expansion

• When a gas expands, it does work on its surroundings by exerting pressure on the walls of its container.
• For a gas inside a piston, the force exerted by the gas pushes the piston outwards. Work is done by the gas as the piston moves a distance $s$, expanding the volume by $\Delta V = A \times s$.
• If an external force compresses the gas, work is done on the gas.

The area under a p-V diagram

• p-V diagramsPressure-volume diagrams used to represent changes in the state of a gas during thermodynamic processes. In the context of engines, these are called indicator diagrams. (pressure-volume diagrams) represent changes in the state of a gas in thermodynamic processes.
• The key part is this: the area under a p-V curve tells us the work done.

Expansion (positive work)

• When a gas expands at constant pressure, the volume increases ($+\Delta V$), so the work done is positive ($+W$).
• Work is done by the gas on the surroundings.
• On the p-V diagram, the process moves to the right and the shaded area beneath the curve equals the work done.

Compression (negative work)

• When a gas is compressed at constant pressure, the volume decreases ($-\Delta V$), so the work done is negative ($-W$).
• Work is done on the gas by the surroundings.
• On the p-V diagram, the process moves to the left.

Non-constant pressure changes

• When both volume and pressure change simultaneously, the work done is still the area under the curve on the p-V diagram.
• For irregular curves, you can estimate the area by counting squares or splitting into geometric shapes (rectangles and triangles).
• In the context of engines, p-V diagrams are referred to as indicator diagramsA p-V diagram specifically for an engine cycle. The enclosed area of the loop represents the net work done per cycle..