thumb|upright=1.3|An animation showing the relationship between pressure and volume when mass and temperature are held constant

Boyle's law, also referred to as the Boyle–Mariotte law or Mariotte's law (especially in France), is an empirical gas law that describes the relationship between pressure and volume of a confined gas. Boyle's law has been stated as:

<blockquote>

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.

</blockquote>

Mathematically, Boyle's law can be stated as:

{|

|-

| style="padding: 0.2em 0.4em;" | <math>P \propto \frac{1}{V}</math>

| style="padding: 0.2em 0.4em;" | Pressure is inversely proportional to the volume

|}

or

{|

|-

| style="padding: 0.2em 0.4em;" |

| style="padding: 0.2em 0.4em;" | The product of pressure and volume is a constant number (here denoted as )

|}

where is the pressure of the gas, is the volume of the gas, and is a constant for a particular temperature and amount of gas.

Boyle's law states that when the temperature of a given mass of confined gas is constant, the product of its pressure and volume is also constant. When comparing the same substance under two different sets of conditions, the law can be expressed as:<math display="block">P_1 V_1 = P_2 V_2.</math>showing that as volume increases, the pressure of a gas decreases proportionally, and vice versa.

Boyle's law is named after Robert Boyle, who published the original law in 1662. An equivalent law is Mariotte’s law, named after French physicist Edme Mariotte.

History

thumb|Graph of Boyle's original data showing the [[Hyperbola#Hyperbola with equation y = A/x|hyperbolic curve of the relationship between pressure () and volume () of the form ]]

The relationship between pressure and volume was first noted by Richard Towneley and Henry Power in the 17th century. Robert 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. Boyle may have begun experimenting with gases due to an interest in air as an essential element of life; for example, he published works on the growth of plants without air. Boyle used a closed J-shaped tube and after pouring mercury from one side he forced the air on the other side to contract under the pressure of mercury. After repeating the experiment several times and using different amounts of mercury he found that under controlled conditions, the pressure of a gas is inversely proportional to the volume occupied by it.

The French physicist Edme Mariotte (1620–1684) discovered the same law independently of Boyle in 1679, after Boyle had published it in 1662. Thus this law is sometimes referred to as Mariotte's law or the Boyle–Mariotte law. Later, in 1687 in the , Newton showed mathematically that in 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, but this mathematical treatise does not involve any Mariott temperature dependence and is not the proper physical explanation for the observed relationship. Instead of a static theory, a kinetic theory is needed, which was developed over the next two centuries by Daniel Bernoulli (1738) and more fully by Rudolf Clausius (1857), Maxwell and Boltzmann.

This law was the first physical law to be expressed in the form of an equation describing the dependence of two variable quantities. The deviation is expressed as the compressibility factor.

Boyle (and Mariotte) derived the law solely by experiment. 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 1737–1738) derived Boyle's law by applying Newton's laws of motion at the molecular level. It remained ignored until around 1890, 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.

The debate between proponents of energetics and atomism led Boltzmann to write a book in 1898, which endured criticism until his suicide in 1906.

See also

Related phenomena:

  • Water thief
  • Industrial Revolution
  • Steam engine

Other gas laws:

Citations

de:Thermische Zustandsgleichung idealer Gase#Gesetz von Boyle-Mariotte