The absolute pressure exerted by a given mass of an ideal gas is inversely proportional to the volume it occupies if the temperature and amount of gas remain unchanged within a closed system.
displaystyle Ppropto frac 1 V
P V = k
where P is the pressure of the gas, V is the volume of the gas, and k is a constant. The equation states that the product of pressure and volume is a constant for a given mass of confined gas as long as the temperature is constant. For comparing the same substance under two different sets of conditions, the law can be usefully expressed as
displaystyle P_ 1 V_ 1 =P_ 2 V_ 2 .
The equation shows that, as volume increases, the pressure of the gas decreases in proportion. Similarly, as volume decreases, the pressure of the gas increases. The law was named after chemist and physicist Robert Boyle, who published the original law in 1662.
1 History 2 Definition
2.1 Relation with kinetic theory and ideal gases 2.2 Equation
3 Human breathing system 4 See also 5 Citations 6 Sources 7 External links
History Main article: History of thermodynamics
A graph of Boyle's original data
This relationship between pressure and volume was first noted by
The law itself can be stated as follows:
For a fixed amount of an ideal gas kept at a fixed temperature, pressure and volume are inversely proportional.
P V = k
P denotes the pressure of the system. V denotes the volume of the gas. k is a constant value representative of the temperature and volume of the system.
So long as temperature remains constant the same amount of energy
given to the system persists throughout its operation and therefore,
theoretically, the value of k will remain constant. However, due to
the derivation of pressure as perpendicular applied force and the
probabilistic likelihood of collisions with other particles through
collision theory, the application of force to a surface may not be
infinitely constant for such values of v, but will have a limit when
differentiating such values over a given time. Forcing the volume V of
the fixed quantity of gas to increase, keeping the gas at the
initially measured temperature, the pressure p must decrease
proportionally. Conversely, reducing the volume of the gas increases
displaystyle P_ 1 V_ 1 =P_ 2 V_ 2 .,
Here P1 and V1 represent the original pressure and volume,
respectively, and P2 and V2 represent the second pressure and volume.
Boyle's law, Charles's law, and
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Other gas laws in chemistry:
Dalton's law Charles's law
^ Draper, John William (1861). A Textbook on chemistry. p. 46. ^ Levine, Ira. N (1978). "Physical Chemistry" University of Brooklyn: McGraw-Hill ^ a b Levine, Ira. N. (1978), p. 12 gives the original definition. ^ In 1662, he published a second edition of the 1660 book New Experiments Physico-Mechanical, Touching the Spring of the Air, and its Effects with an addendum Whereunto is Added a Defence of the Authors Explication of the Experiments, Against the Obiections of Franciscus Linus and Thomas Hobbes; see J Appl Physiol 98: 31–39, 2005. (Jap.physiology.org Online.) ^ See:
Henry Power, Experimental Philosophy, in Three Books … (London,
England: Printed by T. Roycroft for John Martin and James Allestry,
1663), pp. 126-130. Available on-line at: Early English Books Online.
On page 130, Power presents (not very clearly) the relation between
the pressure and the volume of a given quantity of air: "That the
measure of the Mercurial Standard, and Mercurial Complement, are
measured onely by their perpendicular heights, over the Surface of the
restagnant Quicksilver in the Vessel: But Ayr, the Ayr's Dilatation,
and Ayr Dilated, by the Spaces they fill. So that here is now four
Proportionals, and by any three given, you may strike out the fourth,
by Conversion, Transposition, and Division of them. So that by these
Analogies you may prognosticate the effects, which follow in all
Mercurial Experiments, and predemonstrate them, by calculation, before
the senses give an Experimental [eviction] thereof." In other words,
if one knows the volume V1 ("Ayr") of a given quantity of air at the
pressure p1 ("Mercurial standard", i.e., atmospheric pressure at a low
altitude), then one can predict the volume V2 ("Ayr dilated") of the
same quantity of air at the pressure p2 ("Mercurial complement", i.e.,
atmospheric pressure at a higher altitude) by means of a proportion
(because p1 V1 = p2 V2).
Charles Webster (1965) "The discovery of Boyle's law, and the concept
of the elasticity of air in seventeenth century," Archive for the
History of Exact Sciences, 2 (6) : 441-502 ; see especially
Charles Webster (1963) "
^ Gerald James Holton (2001). Physics, the Human Adventure: From Copernicus to Einstein and Beyond. Rutgers University Press. pp. 270–. ISBN 978-0-8135-2908-0. ^ R. Boyle, A Defence of the Doctrine Touching the Spring and Weight of the Air, … (London, England: Thomas Robinson, 1662). Available on-line at: Spain's La Biblioteca Virtual de Patrimonio Bibliográfico. Boyle presents his law in "Chap. V. Two new experiments touching the measure of the force of the spring of air compress'd and dilated.", pp. 57-68. On p. 59, Boyle concludes that " … the same air being brought to a degree of density about twice as that it had before, obtains a spring twice as strong as formerly." That is, doubling the density of a quantity of air doubles its pressure. Since air's density is proportional to its pressure, then for a fixed quantity of air, the product of its pressure and its volume is constant. On page 60, he presents his data on the compression of air: "A Table of the Condensation of the Air." The legend (p. 60) accompanying the table states: "E. What the pressure should be according to the Hypothesis, that supposes the pressures and expansions to be in reciprocal relation." On p. 64, Boyle presents his data on the expansion of air: "A Table of the Rarefaction of the Air." ^ The Boyle Papers BP 9, fol. 75v-76r at BBK.ac.uk Archived 2009-11-22 at the Wayback Machine. ^ The Boyle Papers, BP 10, fol. 138v-139r at BBK.ac.uk Archived 2009-11-22 at the Wayback Machine. ^ Britannica Educational Publishing 2012, p. 94. ^ See:
Mariotte, Essais de Physique, ou mémoires pour servir à la science des choses naturelles, … (Paris, France: E. Michallet, 1679); "Second essai. De la nature de l'air". (Mariotte, Edmé), Oeuvres de Mr. Mariotte, de l'Académie royale des sciences; … , vol. 1 (Leiden, Netherlands: P. Vander Aa, 1717); see especially pp. 151-153. Mariotte's essay "De la nature de l'air" was reviewed by the French Royal Academy of Sciences in 1679. See: (Anon.) (1733) "Sur la nature de l'air," Histoire de l'Académie Royale des Sciences, 1 : 270-278. Mariotte's essay "De la nature de l'air" was also reviewed in the Journal des Sçavans (later: Journal des Savants) on 20 November 1679. See: (Anon.) (20 November 1679) "Essais de physique, … ," Journal des Sçavans, pp. 265-269.
^ a b Britannica Educational Publishing 2012, p. 95.
^ Ley, Willy (June 1966). "The Re-Designed Solar System". For Your
Information. Galaxy Science Fiction. pp. 94–106.
^ Principia, Sec.V,prop. XXI, Theorem XVI
^ Levine, Ira. N. (1978), p11 notes that deviations occur with high
pressures and temperatures.
^ a b c Levine, Ira. N. (1978), p400 – Historical background of
Britannica Educational Publishing (1 December 2012). Scientists and Inventors of the Renaissance. Britannica Educational Publishing. ISBN 978-1-61530-884-2.
Boyle’s law calculator
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