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.
1 Description 2 History 3 Applications
3.1 Thermodynamics 3.2 Medicine
4 See also 5 References 6 Bibliography 7 External links
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 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). History
Watt's indicator diagram
Richard's indicator instrument of 1875
The PV diagram, then called an indicator diagram, was developed by
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 Main article: Pressure-volume loop analysis in cardiology 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
A is the end-diastolic point; this is the point where contraction
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. See also
Temperature–entropy diagram Wiggers diagram Stroke volume Cyclic process PV loop experiments Pressure-volume loop analysis in cardiology
^ Physiology: 3/3ch5/s3ch5_16 - Essentials of Human Physiology ^ Bruce J. Hunt (2010) Pursuing Power and Light, page 13, The Johns Hopkins University Press ISBN 0-8018-9359-3 ^ (Anonymous), "Account of a steam-engine indicator," Quarterly Journal of Science, vol. 13, page 95 (1822). ^ Clapeyron, E. (1834) "Mémoire sur la puissance motrice de la chaleur" (Memoir on the motive power of heat), Journal de l'École Royale Polytechnique, vol. 14, no. 23, pages 153–190, 160–162. ^ Nicholas Procter Burgh. The Indicator Diagram Practically Considered. E. & F. N. Spon, 1869. p. 1 ^ Walter, John (2008). "The Engine Indicator" (PDF). pp. xxv–xxvi. Archived from the original (PDF) on 2012-03-10. ^ Richard L. Hills and A. J. Pacey (January 1972) "The measurement of power in early steam-driven textile mills," Technology and Culture, vol. 13, no. 1, pages 25–43. ^ Diagram at uc.edu ^ Systolic dysfunction
Cardwell, D. S. L. (1971). From Watt to Clausius: The Rise of
Wikimedia Commons has media related to Pressure-volume diagrams.
Walter, John. "The Engine Indicator. A collectors' guide to mechanical and optical/mechanical designs, 1800 to date". Canadian Museum of Making. Diagram at hofstra.edu Diagram at cvphysiology.com Interactive demonstration at davidson.edu Lohff B (1999). "Otto Frank". Sudhoffs Arch. 83 (2): 131–51. PMID 10705804.
v t e
Physiology of the cardiovascular system
Cardiac cycle Cardiac output
End-diastolic volume End-systolic volume
Cardiac function curve
Venous return curve
Fractional shortening = (End-diastolic dimension End-systolic dimension) / End-diastolic dimension Aortic valve area calculation Ejection fraction Cardiac index
Conduction system Cardiac electrophysiology Action potential
cardiac atrial ventricular
Effective refractory period Pacemaker potential Electrocardiography
P wave PR interval QRS complex QT interval ST segment T wave U wave
Hexaxial reference system
Central venous Right
Vascular system/ Hemodynamics
Compliance Vascular resistance Pulse Perfusion
Mean arterial pressure
Jugular venous pressure
Regulation of BP
Baroreflex Kinin–kallikrein system Renin–angiotensin system Vasoconstrictors Vasodilators Autoregulation
Myogenic mechanism Tubuloglomerular feedback Cerebral autoregulation
Aortic body Caroti