# Pressure–volume diagram

Thermodynamics :
The classical Carnot heat engine :
Branches
Classical
Statistical
Chemical
Quantum thermodynamics
Equilibrium / Non-equilibrium :
Laws
Zeroth
First
Second
Third :
Systems
Closed system
Open system
Isolated system
State
Equation of state
Ideal gas
Real gas
State of matter
Phase (matter)
Equilibrium
Control volume
Instruments
Processes
Isobaric
Isochoric
Isothermal
Adiabatic
Isentropic
Isenthalpic
Quasistatic
Polytropic
Free expansion
Reversibility
Irreversibility
Endoreversibility
Cycles
Heat engines
Heat pumps
Thermal efficiency :
System propertiesNote: Conjugate variables in italics
Property diagrams
Intensive and extensive properties
Process functions
Work
Heat
Functions of state
Temperature / Entropy (introduction)
Pressure / Volume
Chemical potential / Particle number
Vapor quality
Reduced properties :
Material properties
Property databases
Specific heat capacity 
$c=$
$T$$\partial S$$N$$\partial T$
Compressibility 
$\beta =-$
$1$$\partial V$$V$$\partial p$
Thermal expansion 
$\alpha =$
$1$$\partial V$$V$$\partial T$ :
Equations
Carnot's theorem
Clausius theorem
Fundamental relation
Ideal gas law
Maxwell relations
Onsager reciprocal relations
Bridgman's equations
Table of thermodynamic equations :
Potentials
Free energy
Free entropy
Internal energy $U(S,V)$Enthalpy $H(S,p)=U+pV$Helmholtz free energy $A(T,V)=U-TS$Gibbs free energy $G(T,p)=H-TS$ :
HistoryCulture
History
General
Entropy
Gas laws
"Perpetual motion" machines
Philosophy
Entropy and time
Entropy and life
Brownian ratchet
Maxwell's demon
Heat death paradox
Loschmidt's paradox
Synergetics
Theories
Caloric theory
Vis viva ("living force")
Mechanical equivalent of heat
Motive power
Key publications
An Inquiry Concerning the Source ... Friction
On the Equilibrium of Heterogeneous Substances
Reflections on the Motive Power of Fire
Timelines
Thermodynamics
Heat engines
ArtEducation
Maxwell's thermodynamic surface
Entropy as energy dispersal :
Scientists
Bernoulli
Boltzmann
Bridgman
Carathéodory
Carnot
Clapeyron
Clausius
de Donder
Duhem
Gibbs
von Helmholtz
Joule
Kelvin
Lewis
Massieu
Maxwell
von Mayer
Nernst
Onsager
Planck
Rankine
Smeaton
Stahl
Tait
Thompson
van der Waals
Waterston :
Other
Nucleation
Self-assembly
Self-organization
Order and disorder :
Category :
vte :
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.

## Description

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 an idealized PV diagram. It shows a series of numbered states (1 through 4). 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 measured because the net work is represented by the area enclosed by the four lines. 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; so the net work is the difference between the two. This figure is highly idealized, in so far as all the lines are straight and the corners are right angles. A diagram showing the changes in pressure and volume in a real device will show a more complex shape enclosing the work cycle. (§ Applications).

## History

The PV diagram, then called an indicator diagram, was developed in 1796 by James Watt and his employee John Southern. Volume was traced by a plate moving with the piston, while pressure was traced by a pressure gauge whose indicator moved at right angles to the piston. A pencil was used to draw the diagram. Watt used the diagram to make radical improvements to steam engine performance.

## Applications
### Thermodynamics

Specifically, the diagram records the pressure of steam versus the volume of steam in a cylinder, throughout a piston's cycle of motion in a steam engine. The diagram enables calculation of the work performed and thus can provide a measure of the power produced by the engine.
To exactly calculate the work done by the system it is necessary to calculate the integral of the pressure with respect to volume. One can often quickly calculate this using the PV diagram as it is simply the area enclosed by the cycle.
Note that in some cases specific volume will be plotted on the x-axis instead of volume, in which case the area under the curve represents work per unit mass of the working fluid (i.e. J/kg).

### Medicine

In cardiovascular physiology, the diagram is often applied to the left ventricle, and it can be mapped to specific events of the cardiac cycle. PV loop studies are widely used in basic research and preclinical testing, to characterize the intact heart's performance under various situations (effect of drugs, disease, characterization of mouse strains)
The sequence of events occurring in every heart cycle is as follows. The left figure shows a PV loop from a real experiment; letters refer to points.
* Example PV loop diagram of a mouse left ventricle
* Human heart
* A is the end-diastolic point; this is the point where contraction begins. Pressure starts to increase, becomes rapidly higher than the atrial pressure, and the mitral valve closes. Since pressure is also lower than the aortic pressure, the aortic valve is closed as well.
* Segment AB is the contraction phase. Since both the mitral and aortic valves are closed, volume is constant. For this reason, this phase is called isovolumic contraction.
* At point B, pressure becomes higher than the aortic pressure and the aortic valve opens, initiating ejection.
* BC is the ejection phase, volume decreases. At the end of this phase, pressure lowers again and falls below aortic pressure. The aortic valve closes.
* Point C is the end-systolic point.
* Segment CD is the isovolumic relaxation. During this phase, pressure continues to fall. The mitral valve and aortic valve are both closed again so volume is constant.
* At point D pressure falls below the atrial pressure and the mitral valve opens, initiating ventricular filling.
* DA is the diastolic filling period. Blood flows from the left atrium to the left ventricle. Atrial contraction completes ventricular filling.
As it can be seen, the PV loop forms a roughly rectangular shape and each loop is formed in an anti-clockwise direction.
Very useful information can be derived by examination and analysis of individual loops or series of loops, for example:
* the horizontal distance between the top-left corner and the bottom-right corner of each loop is the stroke volume
* the line joining the top-left corner of several loops is the contractile or inotropic state.
See external links for a much more precise representation.