Thermodynamic work

Thermodynamic work is the energy a system transfers to its surroundings by moving its boundary against an opposing force. For a gas expanding against a piston, a small displacement at pressure P sweeps out a volume dV and does work P dV, so the total work over a change of volume is W = ∫P dV — geometrically, the area between the process curve and the volume axis on a pressure–volume diagram. For constant pressure this reduces to W = P ΔV.

Unlike mechanical work on a point mass, thermodynamic work is a path function: the same change of state reached by different routes does different amounts of work, because the area under each path differs. In the physics sign convention, work is positive when the system does it on the surroundings (expansion) and negative when the surroundings do it on the system (compression).

Work is one of the two ways — heat being the other — that a system's internal energy can change, as set out in the first law ΔU = Q − W. Over a closed cycle the net work equals the net heat absorbed and equals the area enclosed by the loop on a PV diagram, which is the useful output of every heat engine.

Made quantitative once Watt's engines forced engineers to reckon the 'duty' of an engine, and given its modern integral form by Clapeyron's 1834 pressure–volume diagram, which turned work into a measurable area.