Which of the following graphs between pressure ' p ' versus volume ' V ' represents the maximum work done?

Solution

Chemistry ma’am · 3 steps

Work on a p–V graph is an area: under the curve for one path, inside the loop for a full cycle.

1. Read work as area. For a single path, the magnitude of work is the area under the curve down to the V-axis. For a closed cycle, the net work is only the area enclosed by the loop, because the compression takes back part of what the expansion did.
2. Area in graph (a). The curve joins (22.4 L, 2.0 bar) to (44.8 L, 1.0 bar). The product pV is 44.8 L bar at both ends, so this is a reversible isothermal expansion.

   |w| = p₁V₁ln V₂/V₁ = 2.0 × 22.4 × ln 2 ≈ 31 L bar

   Graph	What it shows	Work (magnitude)
   (a)	isothermal expansion, 22.4 L to 44.8 L	area under curve ≈ 31 L bar
   (b)	vertical line, volume fixed at 22.4 L	Δ V = 0, so 0
   (c)	same expansion, then compression at 1 bar, then pressure rise at constant volume	loop area = 31 - 22.4 ≈ 8.7 L bar
   (d)	cycle between two curves joining the same points	thin lens-shaped loop, well below 31 L bar

3. So. The single expansion in (a) sweeps the largest area, about 31 L bar (roughly 3.1 kJ). The answer is (a).

The idea to keep. On a p–V graph, never judge work by how big the figure looks. A vertical line gives zero work. A cycle gives only the enclosed area. One expansion gives the full area under its curve.

Answer from the NTA final answer key. Solution by PrepWiser.