PV diagram
A PV diagram is a graph that plots a system's pressure P on the vertical axis against its volume V on the horizontal axis. Each point on the graph is one complete state of the gas — a particular pressure and volume — and a line traced across the diagram shows the whole journey a gas takes as it is squeezed, heated, or allowed to expand. It turns an invisible sequence of gas states into a picture you can read at a glance.
The great power of the PV diagram is that the area underneath a path equals the work done. As a gas expands from left to right, the area beneath its curve is the pressure-volume work W it does on the surroundings; as it is compressed from right to left, the area is the work done on the gas. If the gas goes around a closed loop and returns to its starting state, the enclosed area of the loop is the NET work done in one cycle — the very quantity a heat engine delivers.
Different processes trace different shapes: an isobaric (constant-pressure) step is horizontal, an isochoric (constant-volume) step is vertical, an isotherm curves gently as PV = constant, and an adiabat is a steeper curve. Reading these shapes is the working language of engine design. One caution: the PV diagram displays P and V directly, but temperature and internal energy are read off indirectly, using the gas law and which curve you happen to be on.
Draw a rectangle on a PV diagram: expand a gas at high constant pressure (top edge, left to right), drop the pressure, compress it at low pressure (bottom edge, right to left), then raise the pressure back. The area enclosed by the rectangle is the net work the gas does per cycle.
Area under a path is work; area enclosed by a loop is net work per cycle.
The work read off a PV diagram depends on the path, not just the endpoints — two routes between the same two states enclose different areas and give different work, which is why work is not a state function.