What is an indicator diagram? Show that the work done by a gas during expansion is equal to the area under its indicator diagram.

1. 1 · Define. An indicator diagram is a P-V graph showing how the pressure of a system changes with its volume during a process.
2. 2 · Draw the graph. A curve from A (P₁, V₁) to B (P₂, V₂), the area under it shaded, and one thin strip of width ΔV and height P.
3. 3 · Work for a small step. The force PA on the piston moves it Δx, so ΔW = PAΔx = PΔV.
4. 4 · Link to the area. PΔV is the area of the thin strip under the curve.
5. 5 · Total work. Adding all the strips from V₁ to V₂, the total work = area under the curve.
6. 6 · Real life. Engineers read indicator diagrams of car and diesel engines to find the work done in each cycle.
7. 7 · Close in one line. Work done is the area under the P-V curve, so it depends on the path.

Scoring tip: Shade the area and write 'work done = area' on the graph itself. The labelled graph carries a mark.