PV diagram
A plot of pressure against volume on which every state of a gas is a point, every quasi-static process a curve, and every cycle a closed loop whose area is the work.
Definition
A pressure–volume diagram plots a gas's pressure on the vertical axis against its volume on the horizontal. Each equilibrium state of the gas is a single point; each quasi-static process is a curve linking states; and each cyclic process is a closed loop. The diagram's great virtue is that it makes work visible: the area under a process curve is the work done, ∫P dV, and the area enclosed by a cycle is the net work per loop.
The four canonical processes have distinctive shapes. An isobaric process is a horizontal line, an isochoric process a vertical line, an isothermal process a hyperbola PV = const, and an adiabatic process a steeper hyperbola PVᵞ = const. Reading an engine off the plane becomes a matter of geometry: a clockwise loop is an engine delivering work, a counter-clockwise loop a refrigerator consuming it.
Introduced by Émile Clapeyron in 1834 to render Sadi Carnot's verbal reasoning in graphical form, the PV diagram turned thermodynamics into something engineers could draw and calculate with. It remains the standard language for analysing engines, refrigerators, and the cycles of working gases.
History
Devised by Benoît Clapeyron in 1834, who recast Carnot's 1824 prose into pressure–volume curves; the indicator diagram James Watt had earlier used to monitor steam engines was an empirical ancestor of the same idea.