Definition
Thermodynamic work
(T2.3.1) T2.3 · Work in Thermodynamic Processes →Statement
Work done by a gas as it expands or contracts, generalizing mechanical work to a pressure-volume boundary.
Symbols and units
| work done by the gas | J | |
| pressure | Pa | |
| volume element | m³ |
When it applies
A quasi-static (slow, near-equilibrium) process, so pressure is well defined throughout.
Don't use when
Assumes a quasi-static process where pressure is well-defined throughout — a rapid or irreversible expansion (e.g. into a vacuum) is not described by this integral.
Derivation
Force on a piston is pressure times area; multiplying by the piston's displacement and using dV = A\,dx converts this into an integral over volume:
Watch out for
On a P-V diagram, work equals the area under the curve — so two different paths between the same initial and final states generally involve different amounts of work, even though the change in internal energy is the same for both.