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A pressure–volume diagram (or PV diagram, or volume–pressure loop) is used to describe corresponding changes in
volume Volume is a measure of regions in three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch) ...
and
pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and eve ...
in a system. It is commonly used in
thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed b ...
,
cardiovascular physiology Cardiovascular physiology is the study of the cardiovascular system, specifically addressing the physiology of the heart ("cardio") and blood vessels ("vascular"). These subjects are sometimes addressed separately, under the names cardiac physiolog ...
, and
respiratory physiology In physiology, respiration is the transport of oxygen from the outside environment to the cells within tissues, and the removal of carbon dioxide in the opposite direction to the environment by a respiratory system. The physiological definition ...
. PV diagrams, originally called indicator diagrams, were developed in the 18th century as tools for understanding the efficiency of
steam engine A steam engine is a heat engine that performs Work (physics), mechanical work using steam as its working fluid. The steam engine uses the force produced by steam pressure to push a piston back and forth inside a Cylinder (locomotive), cyl ...
s.


Description

A PV diagram plots the change in pressure ''P'' with respect to volume ''V'' for some
process A process is a series or set of activities that interact to produce a result; it may occur once-only or be recurrent or periodic. Things called a process include: Business and management * Business process, activities that produce a specific s ...
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 State most commonly refers to: * State (polity), a centralized political organization that regulates law and society within a territory **Sovereign state, a sovereign polity in international law, commonly referred to as a country **Nation state, a ...
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 Work may refer to: * Work (human activity), intentional activity people perform to support themselves, others, or the community ** Manual labour, physical work done by humans ** House work, housework, or homemaking ** Working animal, an ani ...
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. ().


History

The PV diagram, then called an indicator diagram, was developed in 1796 by
James Watt James Watt (; 30 January 1736 (19 January 1736 OS) – 25 August 1819) was a Scottish inventor, mechanical engineer, and chemist who improved on Thomas Newcomen's 1712 Newcomen steam engine with his Watt steam engine in 1776, which was f ...
and his employee John Southern. Volume was traced by a plate moving with the piston, while pressure was traced by a
pressure gauge Pressure measurement is the measurement of an applied force by a fluid (liquid or gas) on a surface. Pressure is typically measured in units of force per unit of surface area. Many techniques have been developed for the measurement of press ...
whose indicator moved at right angles to the piston. A
pencil A pencil () is a writing or drawing implement with a solid pigment core in a protective casing that reduces the risk of core breakage and keeps it from marking the user's hand. Pencils create marks by physical abrasion, leaving a trail of ...
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 Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and eve ...
of steam versus the volume of steam in a cylinder, throughout a
piston A piston is a component of reciprocating engines, reciprocating pumps, gas compressors, hydraulic cylinders and pneumatic cylinders, among other similar mechanisms. It is the moving component that is contained by a cylinder (engine), cylinder a ...
's cycle of motion in a steam engine. The diagram enables calculation of the
work Work may refer to: * Work (human activity), intentional activity people perform to support themselves, others, or the community ** Manual labour, physical work done by humans ** House work, housework, or homemaking ** Working animal, an ani ...
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 In thermodynamics, the specific volume of a substance (symbol: , nu) is the quotient of the substance's volume () to its mass (): :\nu = \frac It is a mass-specific intrinsic property of the substance. It is the reciprocal of density (rho) ...
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 Cardiovascular physiology is the study of the cardiovascular system, specifically addressing the physiology of the heart ("cardio") and blood vessels ("vascular"). These subjects are sometimes addressed separately, under the names cardiac physiolog ...
, the diagram is often applied to the left ventricle, and it can be mapped to specific events of the
cardiac cycle The cardiac cycle is the performance of the heart, human heart from the beginning of one heartbeat to the beginning of the next. It consists of two periods: one during which the heart muscle relaxes and refills with blood, called diastole, fo ...
. 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. File:PV loop example of left ventricle.svg, Example PV loop diagram of a mouse left ventricle File:Diagram of the human heart (cropped).svg, 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 In cardiovascular physiology, stroke volume (SV) is the volume of blood pumped from the ventricle (heart), ventricle per beat. Stroke volume is calculated using measurements of ventricle volumes from an Echocardiography, echocardiogram and subtra ...
* the line joining the top-left corner of several loops is the contractile or inotropic state.Systolic dysfunction
/ref> See external links for a much more precise representation.


See also

*
Indicator diagram An indicator diagram is a chart used to measure the thermal, or cylinder, performance of Reciprocating engine, reciprocating steam and Internal combustion engine, internal combustion engines and compressors. An indicator chart records the press ...
* Temperature–entropy diagram *
Wiggers diagram A Wiggers diagram, named after its developer, Carl Wiggers, is a unique diagram that has been used in teaching cardiac physiology for more than a century. In the Wiggers diagram, the X-axis is used to plot time subdivided into the cardiac phases ...
*
Stroke volume In cardiovascular physiology, stroke volume (SV) is the volume of blood pumped from the ventricle (heart), ventricle per beat. Stroke volume is calculated using measurements of ventricle volumes from an Echocardiography, echocardiogram and subtra ...
* Cyclic process * Pressure–volume loop experiments * Pressure–volume loop analysis in cardiology


References


Bibliography

* * * Pacey, A. J. & Fisher, S. J. (1967) "Daniel Bernoulli and the ''vis viva'' of compressed air", ''The British Journal for the History of Science'' 3 (4), p. 388–392, * British Transport Commission (1957) ''Handbook for Railway Steam Locomotive Enginemen'', London : B.T.C., p. 81, (facsimile copy publ. Ian Allan (1977), )


External links

*
Diagram at cvphysiology.com


* {{DEFAULTSORT:Pressure-volume diagram Thermodynamics Cardiovascular physiology Diagrams Energy conversion Piston engines Steam power