Editing Boyle's law (section)

== Definition ==
[[File:Boyle's Law Demonstrations.webm|thumb|Boyle's law demonstrations]]

The law itself can be stated as follows:

{{quotation|For a fixed mass of an [[ideal gas]] kept at a fixed temperature, pressure and volume are inversely proportional.<ref name="levine_1"/>}}
Boyle's law is a [[Gas laws|gas law]], stating that the pressure and volume of a gas have an inverse relationship. If volume increases, then pressure decreases and vice versa, when the temperature is held constant.

Therefore, when the volume is halved, the pressure is doubled; and if the volume is doubled, the pressure is halved.

=== Relation with kinetic theory and ideal gases ===
As the pressure on a gas increases, the volume of the gas decreases because the gas particles are forced closer together. 

Most gases behave like [[ideal gas]]es at moderate pressures and temperatures. The technology of the 17th century could not produce very high pressures or very 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.<ref name="levine_2">Levine, Ira. N. (1978), p. 11 notes that deviations occur with high pressures and temperatures.</ref>  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 [[atom]]s and [[molecule]]s 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 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.<ref name="levine_3">Levine, Ira. N. (1978), p. 400 – Historical background of Boyle's law relation to Kinetic Theory</ref>

The debate between proponents of [[Thermodynamics|energetics]] and [[atomism]] led Boltzmann to write a book in 1898, which endured criticism until his suicide in 1906.<ref name="levine_3" /> [[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]].<ref name="levine_3" />

===Equation===
{{Ideal gas law relationships.svg}}
The mathematical equation for Boyle's law is:

<math display="block"> PV = k </math>

where {{mvar|P}} denotes the [[pressure]] of the system, {{mvar|V}} denotes the [[volume]] of the gas, {{mvar|k}} is a constant value representative of the temperature of the system and [[Amount of substance|amount]] of gas.

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 {{mvar|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 {{mvar|V}}, but will have a [[limit (mathematics)|limit]] when [[differential calculus|differentiating]] such values over a given time. Forcing the volume {{mvar|V}} of the fixed quantity of gas to increase, keeping the gas at the initially measured temperature, the pressure {{mvar|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 initial and final volumes and pressures of the fixed amount of gas, where the initial and final temperatures are the same (heating or cooling will be required to meet this condition), are related by the equation:

<math display="block">P_1 V_1 = P_2 V_2. </math>

Here {{math|''P''<sub>1</sub>}} and {{math|''V''<sub>1</sub>}} represent the original pressure and volume, respectively, and {{math|''P''<sub>2</sub>}} and {{math|''V''<sub>2</sub>}} represent the second pressure and volume.

Boyle's law, [[Charles's law]], and [[Gay-Lussac's law#Pressure-temperature law|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]].