On a pressure versus volume diagram for a gas, what quantity does the source say equals the work done on or by the system in going from one state to another?
AThe slope of the line connecting the two states
BThe distance between the two points along the curve
CThe highest pressure reached anywhere on the graph
DThe area under the curve between the two states
Answer & Solution
Correct answer: D. The area under the curve between the two states
1. On a pressure-volume diagram, work is calculated by summing P times small changes in volume along the path.
2. That sum is exactly what the area under the curve represents, which is why the source identifies the area under the curve as the work done.
3. The slope of a line and the length of a curve are geometric properties unrelated to this area-based rule, ruling out options A and B.
4. The single highest pressure point tells you nothing about how much volume changed, so it cannot represent the total work either, ruling out option C.
_Source: OpenStax College Physics (CC BY 4.0), Ch 15 "Thermodynamics", section 15.2 The First Law of Thermodynamics and Some Simple Processes_
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