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Boyle's law
From Wikipedia, the free encyclopedia
Boyle's law (sometimes referred to as the Boyle-Mariotte
law) is one of many gas laws and a special case of the ideal
gas law. Boyle's law describes the inversely proportional
relationship between the absolute pressure and volume of a
gas, if the temperature is kept constant within a closed
system.[1][2] The law was named after chemist and physicist
Robert Boyle, who published the original law in 1662.[3] The
law itself can be stated as follows:
For a fixed amount of an ideal gas kept at a fixed
temperature, P [pressure] and V [volume] are
inversely proportional (while one doubles, the other
halves).
—[2]
An animation showing the
relationship between pressure and
volume when amount and
temperature are held constant.
Contents
■ 1 History
■ 2 Definition
■ 2.1 Relation to kinetic theory and
ideal gases
■ 2.2 Equation
■ 2.3 Examples
■ 3 See also
■ 4 References
History
Main article: History of thermodynamics
This relationship between pressure and volume was first
noted by two amateur scientists, Richard Towneley and
Henry Power. Boyle confirmed their discovery through
experiments and published the results. According to Robert
Gunther and other authorities, it was Boyle's assistant,
Robert Hooke, who built the experimental apparatus. Boyle's
law is based on experiments with air, which he considered to
be a fluid of particles at rest in between small invisible
springs. At that time, air was still seen as one of the four
elements, but Boyle disagreed. Boyle's interest was probably
to understand air as an essential element of life;[4] he
published e.g. the growth of plants without air.[5] The French
physicist Edme Mariotte (1620–1684) discovered the same
law independently of Boyle in 1676, but Boyle had already
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A graph of Boyle's original data
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published it in 1662. Thus this law may, improperly, be referred to as Mariotte's or the BoyleMariotte law. Later, in 1687 in the Philosophiæ Naturalis Principia Mathematica, Newton showed
mathematically that if an elastic fluid consisting of particles at rest, between which are repulsive
forces inversely proportional to their distance, the density would be directly proportional to the
pressure,[6] but this mathematical treatise is not the physical explanation for the observed
relationship. Instead of a static theory a kinetic theory is needed, which was provided two centuries
later by Maxwell and Boltzmann.
Definition
Relation to kinetic theory and ideal gases
Boyle’s law states that at constant temperature for a fixed mass, the absolute pressure and the
volume of a gas are inversely proportional. The law can also be stated in a slightly different manner,
that the product of absolute pressure and volume is always constant.
Most gases behave like ideal gases at moderate pressures and temperatures. The technology of the
17th century could not produce high pressures or low temperatures. Hence, the law was not likely to
have deviations at the time of publication. As improvements in technology permitted higher
pressures and lower temperatures, deviations from the ideal gas behavior became noticeable, and
the relationship between pressure and volume can only be accurately described employing real gas
theory.[7] The deviation is expressed as the compressibility factor.
Robert Boyle (and Edme Mariotte) derived the law solely on experimental grounds. The law can
also be derived theoretically based on the presumed existence of atoms and molecules and
assumptions about motion and perfectly elastic collisions (see kinetic theory of gases). These
assumptions were met with enormous resistance in the positivist scientific community at the time
however, as they were seen as purely theoretical constructs for which there was not the slightest
observational evidence.
Daniel Bernoulli in 1738 derived Boyle's law using Newton's laws of motion with application on a
molecular level. It remained ignored until around 1845, when John Waterston published a paper
building the main precepts of kinetic theory; this was rejected by the Royal Society of England.
Later works of James Prescott Joule, Rudolf Clausius and in particular Ludwig Boltzmann firmly
established the kinetic theory of gases and brought attention to both the theories of Bernoulli and
Waterston.[8]
The debate between proponents of Energetics and Atomism led Boltzmann to write a book in 1898,
which endured criticism up to his suicide in 1906.[8] Albert Einstein in 1905 showed how kinetic
theory applies to the Brownian motion of a fluid-suspended particle, which was confirmed in 1908
by Jean Perrin.[8]
Equation
The mathematical equation for Boyle's law is:
where:
p denotes the pressure of the system.
V denotes the volume of the gas.
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k is a constant value representative of the pressure 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 k, 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 the pressure.
Boyle's law is used to predict the result of introducing a change, in volume and pressure only, to the
initial state of a fixed quantity of gas. The before and after volumes and pressures of the fixed
amount of gas, where the before and after temperatures are the same (heating or cooling will be
required to meet this condition), are related by the equation:
Boyle's law, Charles's law, and Gay-Lussac's law form the combined gas law. The three gas laws in
combination with Avogadro's law can be generalized by the ideal gas law.
Examples
1.
2.
3.
4.
5.
Change of pressure in a syringe
The popping of a balloon
Increase in size of bubbles as they rise to the surface
Death of deep sea creatures due to change in pressure
Popping of ears at high altitude
See also
■
■
■
■
Avogadro's law
Charles's law
Combined gas law
Gay-Lussac's law
References
1. ^ Levine, Ira. N (1978). "Physical Chemistry" University of Brooklyn: McGraw-Hill
2. ^ a b Levine, Ira. N. (1978), p12 gives the original definition.
3. ^ J Appl Physiol 98: 31-39, 2005. Free download at Jap.physiology.org
(http://jap.physiology.org/cgi/content/full/98/1/31)
4. ^ The Boyle Papers BP 9, fol. 75v-76r at BBK.ac.uk
(http://www.bbk.ac.uk/boyle/boyle_papers/bp09_docs/bp9_075v-076r.htm)
5. ^ The Boyle Papers, BP 10, fol. 138v-139r at BBK.ac.uk
(http://www.bbk.ac.uk/boyle/boyle_papers/bp10_docs/bp10_138v-139r.htm)
6. ^ Principia, Sec.V,prop. XXI, Theorem XVI
7. ^ Levine, Ira. N. (1978), p11 notes that deviations occur with high pressures and temperatures.
8. ^ a b c Levine, Ira. N. (1978), p400 -- Historical background of Boyle's law relation to Kinetic Theory
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