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P–V diagrams
Intermediate
Work equals the area under the curve.
carnotA PV diagram shows the thermodynamic path; the work done by the gas is the area under the curve; direction matters.
Expansion along a higher path does more work than along a lower one.
Work depends on the path, not just the endpoints.
In more detail
A PV diagram plots pressure against volume for a gas. The area enclosed by a cycle equals the net work done, which makes these diagrams a powerful tool for engines.
Real-world uses
- Engine designers use PV diagrams to compare cycles.
- Analysing refrigerators and heat pumps on PV diagrams.
- Engineers measure the work done by an engine from the area enclosed by its pressure-volume diagram.
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Frequently asked questions
What does the area mean?
The work done by the gas during the process, positive for expansion.
What does a clockwise cycle mean?
The cycle produces net work, as in a heat engine.
Why is the area under the curve the work?
Work is the integral of pressure with respect to volume, which is exactly the area under the P-V curve.
Related topics in Heat & Thermodynamics
Cyclic process · Heat capacities C_p and C_v · Ratio of specific heats · Second law of thermodynamics · Kelvin–Planck statement · Clausius statement