Pressure volume diagram

A pressure volume diagram (or PV diagram, or volume-pressure loop) is used to describe corresponding changes in volume and pressure in a system. They are commonly used in thermodynamics, cardiovascular physiology, and respiratory physiology.

PV diagrams, originally called indicator diagrams, were developed in the 18th century as tools for understanding the efficiency of steam engines.

A PV diagram plots the change in pressure P with respect to volume V for some process or processes. Typically in thermodynamics, the set of processes forms a cycle, so that upon completion of the cycle there has been no net change in state of the system; i.e. the device returns to the starting pressure and volume.

The figure shows the features of a typical PV diagram. A series of numbered states (1 through 4) are noted. The path between each state consists of some process (A through D) which alters the pressure or volume of the system (or both).

A key feature of the diagram is that the amount of energy expended or received by the system as work can be estimated as the area under the curve on the chart. For a cyclic diagram, the net work is that enclosed by the curve. In the example given in the figure, the processes 1-2-3 produce a work output, but processes from 3-4-1 require a smaller energy input to return to the starting position / state; thus the net work is the difference between the two.

Note that this figure is highly idealized, and a diagram showing the processes in a real device would tend to depict a more complex shape of the PV curve. (See section Applications, below).

The PV diagram, then called an indicator diagram, was developed by James Watt and his employee John Southern (1758–1815) to improve the efficiency of engines. In 1796, Southern developed the simple, but critical, technique to generate the diagram by fixing a board so as to move with the piston, thereby tracing the "volume" axis, while a pencil, attached to a pressure gauge, moved at right angles to the piston, tracing "pressure".

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