Reading a PV Diagram

A PV diagram tracks a gas's state as pressure and volume change. The key fact: work done by the gas equals the area under the curve on a PV plot, and that area depends on the exact path taken, not just the start and end points. Two processes can start and end at identical pressure and volume, but if one bulges out to higher volumes along the way, it sweeps more area and does more work. That is why path matters even when a gas returns to its starting point after a full cycle.

Each type of process traces a distinct shape. Isobaric (constant pressure) is a flat horizontal line, so work is just a rectangle: p times delta V. Isochoric (constant volume) is a vertical line with zero area underneath, so it does no work at all. Isothermal (constant temperature) follows a curve where p times V stays fixed, so as V doubles, p is cut in half, giving a smooth downward-bending hyperbola. Adiabatic (no heat exchange) looks similar but drops more steeply, because the gas cools as it expands with no heat coming in to support the pressure.

Closed cycles connect this to energy bookkeeping for engines and refrigerators. Walking clockwise around a loop, the expansion parts of the path sit at higher pressure than the compression parts, so the gas does more work expanding than is done on it compressing. Net work is positive and flows out, which is how an engine behaves. Running the identical loop counterclockwise flips which parts are high pressure, making net work negative, so the surroundings must do work on the gas instead. That reversal is exactly how a refrigerator or heat pump operates.