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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 Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and eve ...
and
volume Volume is a measure of regions in three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch) ...
of a confined gas. Boyle's law has been stated as:
The absolute pressure exerted by a given mass of an
ideal gas An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is ...
is inversely proportional to the volume it occupies if the
temperature Temperature is a physical quantity that quantitatively expresses the attribute of hotness or coldness. Temperature is measurement, measured with a thermometer. It reflects the average kinetic energy of the vibrating and colliding atoms making ...
and amount of gas remain unchanged within a
closed system A closed system is a natural physical system that does not allow transfer of matter in or out of the system, althoughin the contexts of physics, chemistry, engineering, etc.the transfer of energy (e.g. as work or heat) is allowed. Physics In cl ...
.Levine (1978) p. 12 gives the original definition.
Mathematically, Boyle's law can be stated as: or 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 Mass is an Intrinsic and extrinsic properties, intrinsic property of a physical body, body. It was traditionally believed to be related to the physical quantity, quantity of matter in a body, until the discovery of the atom and particle physi ...
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: P_1 V_1 = P_2 V_2. showing that as volume increases, the pressure of a gas decreases proportionally, and vice versa. Boyle's law is named after
Robert Boyle Robert Boyle (; 25 January 1627 – 31 December 1691) was an Anglo-Irish natural philosopher, chemist, physicist, Alchemy, alchemist and inventor. Boyle is largely regarded today as the first modern chemist, and therefore one of the foun ...
, who published the original law in 1662. An equivalent law is Mariotte’s law, named after French physicist
Edme Mariotte Edme Mariotte (; ; c. 162012 May 1684) was a French physicist and priest (abbé). He is particularly well known for formulating Boyle's law independently of Robert Boyle. Mariotte is also credited with designing the first Newton's cradle. Biog ...
.


History

The relationship between pressure and volume was first noted by Richard Towneley and Henry Power in the 17th century.
Robert Boyle Robert Boyle (; 25 January 1627 – 31 December 1691) was an Anglo-Irish natural philosopher, chemist, physicist, Alchemy, alchemist and inventor. Boyle is largely regarded today as the first modern chemist, and therefore one of the foun ...
confirmed their discovery through experiments and published the results. According to Robert Gunther and other authorities, it was Boyle's assistant,
Robert Hooke Robert Hooke (; 18 July 16353 March 1703) was an English polymath who was active as a physicist ("natural philosopher"), astronomer, geologist, meteorologist, and architect. He is credited as one of the first scientists to investigate living ...
, who built the experimental apparatus. Boyle's law is based on experiments with
air An atmosphere () is a layer of gases that envelop an astronomical object, held in place by the gravity of the object. A planet retains an atmosphere when the gravity is great and the temperature of the atmosphere is low. A stellar atmosph ...
, 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 An experiment is a procedure carried out to support or refute a hypothesis, or determine the efficacy or likelihood of something previously untried. Experiments provide insight into cause-and-effect by demonstrating what outcome occurs whe ...
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 A physicist is a scientist who specializes in the field of physics, which encompasses the interactions of matter and energy at all length and time scales in the physical universe. Physicists generally are interested in the root or ultimate cau ...
Edme Mariotte Edme Mariotte (; ; c. 162012 May 1684) was a French physicist and priest (abbé). He is particularly well known for formulating Boyle's law independently of Robert Boyle. Mariotte is also credited with designing the first Newton's cradle. Biog ...
(1620–1684) discovered the same law independently of Boyle in 1679, after Boyle had published it in 1662. Mariotte did, however, discover that air volume changes with temperature. 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 Elastic is a word often used to describe or identify certain types of elastomer, Elastic (notion), elastic used in garments or stretch fabric, stretchable fabrics. Elastic may also refer to: Alternative name * Rubber band, ring-shaped band of rub ...
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 dependance 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 Daniel Bernoulli ( ; ; – 27 March 1782) was a Swiss people, Swiss-France, French mathematician and physicist and was one of the many prominent mathematicians in the Bernoulli family from Basel. He is particularly remembered for his applicati ...
(1738) and more fully by
Rudolf Clausius Rudolf Julius Emanuel Clausius (; 2 January 1822 – 24 August 1888) was a German physicist and mathematician and is considered one of the central founding fathers of the science of thermodynamics. By his restatement of Sadi Carnot's principle ...
(1857),
Maxwell Maxwell may refer to: People * Maxwell (surname), including a list of people and fictional characters with the name ** James Clerk Maxwell, mathematician and physicist * Justice Maxwell (disambiguation) * Maxwell baronets, in the Baronetage of N ...
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.


Definition

The law itself can be stated as follows: Boyle's law is a 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 An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions. The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is ...
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 Real gases are non-ideal gases whose molecules occupy space and have interactions; consequently, they do not adhere to the ideal gas law. To understand the behaviour of real gases, the following must be taken into account: * compressibility effec ...
theory.Levine, Ira. N. (1978), p. 11 notes that deviations occur with high pressures and temperatures. The deviation is expressed as the
compressibility factor In thermodynamics, the compressibility factor (Z), also known as the compression factor or the gas deviation factor, describes the deviation of a real gas from ideal gas behaviour. It is simply defined as the ratio of the molar volume of a gas ...
. Boyle (and Mariotte) derived the law solely by experiment. The law can also be derived theoretically based on the presumed existence of
atom Atoms are the basic particles of the chemical elements. An atom consists of a atomic nucleus, nucleus of protons and generally neutrons, surrounded by an electromagnetically bound swarm of electrons. The chemical elements are distinguished fr ...
s and
molecule A molecule is a group of two or more atoms that are held together by Force, attractive forces known as chemical bonds; depending on context, the term may or may not include ions that satisfy this criterion. In quantum physics, organic chemi ...
s and assumptions about motion and perfectly elastic collisions (see
kinetic theory of gases The kinetic theory of gases is a simple classical model of the thermodynamic behavior of gases. Its introduction allowed many principal concepts of thermodynamics to be established. It treats a gas as composed of numerous particles, too small ...
). 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 Daniel Bernoulli ( ; ; – 27 March 1782) was a Swiss people, Swiss-France, French mathematician and physicist and was one of the many prominent mathematicians in the Bernoulli family from Basel. He is particularly remembered for his applicati ...
(in 1737–1738) derived Boyle's law by applying
Newton's laws of motion Newton's laws of motion are three physical laws that describe the relationship between the motion of an object and the forces acting on it. These laws, which provide the basis for Newtonian mechanics, can be paraphrased as follows: # A body re ...
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 Rudolf Julius Emanuel Clausius (; 2 January 1822 – 24 August 1888) was a German physicist and mathematician and is considered one of the central founding fathers of the science of thermodynamics. By his restatement of Sadi Carnot's principle ...
and in particular
Ludwig Boltzmann Ludwig Eduard Boltzmann ( ; ; 20 February 1844 – 5 September 1906) was an Austrian mathematician and Theoretical physics, theoretical physicist. His greatest achievements were the development of statistical mechanics and the statistical ex ...
firmly established the
kinetic theory of gases The kinetic theory of gases is a simple classical model of the thermodynamic behavior of gases. Its introduction allowed many principal concepts of thermodynamics to be established. It treats a gas as composed of numerous particles, too small ...
and brought attention to both the theories of Bernoulli and Waterston.Levine, Ira. N. (1978), p. 400 – Historical background of Boyle's law relation to Kinetic Theory The debate between proponents of energetics and
atomism Atomism () is a natural philosophy proposing that the physical universe is composed of fundamental indivisible components known as atoms. References to the concept of atomism and its Atom, atoms appeared in both Ancient Greek philosophy, ancien ...
led Boltzmann to write a book in 1898, which endured criticism until his suicide in 1906.
Albert Einstein Albert Einstein (14 March 187918 April 1955) was a German-born theoretical physicist who is best known for developing the theory of relativity. Einstein also made important contributions to quantum mechanics. His mass–energy equivalence f ...
in 1905 showed how kinetic theory applies to the
Brownian motion Brownian motion is the random motion of particles suspended in a medium (a liquid or a gas). The traditional mathematical formulation of Brownian motion is that of the Wiener process, which is often called Brownian motion, even in mathematical ...
of a fluid-suspended particle, which was confirmed in 1908 by Jean Perrin.


Equation

The mathematical equation for Boyle's law is: PV = k where denotes the
pressure Pressure (symbol: ''p'' or ''P'') is the force applied perpendicular to the surface of an object per unit area over which that force is distributed. Gauge pressure (also spelled ''gage'' pressure)The preferred spelling varies by country and eve ...
of the system, denotes the
volume Volume is a measure of regions in three-dimensional space. It is often quantified numerically using SI derived units (such as the cubic metre and litre) or by various imperial or US customary units (such as the gallon, quart, cubic inch) ...
of the gas, is a constant value representative of the temperature of the system and amount of gas. So long as
temperature Temperature is a physical quantity that quantitatively expresses the attribute of hotness or coldness. Temperature is measurement, measured with a thermometer. It reflects the average kinetic energy of the vibrating and colliding atoms making ...
remains constant the same amount of energy given to the system persists throughout its operation and therefore, theoretically, the value of 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 Collision theory is a principle of chemistry used to predict the rates of chemical reactions. It states that when suitable particles of the Reagent, reactant hit each other with the correct orientation, only a certain amount of collisions result ...
, the application of force to a surface may not be infinitely constant for such values of , but will have a limit when differentiating such values over a given time. Forcing the volume of the fixed quantity of gas to increase, keeping the gas at the initially measured temperature, the pressure 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: P_1 V_1 = P_2 V_2. Here and represent the original pressure and volume, respectively, and and represent the second pressure and volume. Boyle's law,
Charles's law Charles's law (also known as the law of volumes) is an experimental gas law that describes how gases tend to expand when heated. A modern statement of Charles's law is: When the pressure on a sample of a dry gas is held constant, the Kelvin ...
, and
Gay-Lussac's law Gay-Lussac's law usually refers to Joseph-Louis Gay-Lussac's law of combining volumes of gases, discovered in 1808 and published in 1809. However, it sometimes refers to the proportionality of the volume of a gas to its Thermodynamic temperature ...
form the
combined gas law The ideal gas law, also called the general gas equation, is the equation of state of a hypothetical ideal gas. It is a good approximation of the behavior of many gases under many conditions, although it has several limitations. It was first sta ...
. The three gas laws in combination with
Avogadro's law Avogadro's law (sometimes referred to as Avogadro's hypothesis or Avogadro's principle) or Avogadro-Ampère's hypothesis is an experimental gas law relating the volume of a gas to the amount of substance of gas present. The law is a specific cas ...
can be generalized by the
ideal gas law The ideal gas law, also called the general gas equation, is the equation of state of a hypothetical ideal gas. It is a good approximation of the behavior of many gases under many conditions, although it has several limitations. It was first stat ...
.


Human breathing system

Boyle's law is often used as part of an explanation on how the
breathing Breathing (spiration or ventilation) is the rhythmical process of moving air into ( inhalation) and out of ( exhalation) the lungs to facilitate gas exchange with the internal environment, mostly to flush out carbon dioxide and bring in oxy ...
system works in the human body. This commonly involves explaining how the lung volume may be increased or decreased and thereby cause a relatively lower or higher air pressure within them (in keeping with Boyle's law). This forms a pressure difference between the air inside the lungs and the environmental air pressure, which in turn precipitates either inhalation or exhalation as air moves from high to low pressure.Gerald J. Tortora, Bryan Dickinson, 'Pulmonary Ventilation' in ''Principles of Anatomy and Physiology'' 11th edition, Hoboken: John Wiley & Sons, Inc., 2006, pp. 863–867


See also

Related phenomena: * Water thief *
Industrial Revolution The Industrial Revolution, sometimes divided into the First Industrial Revolution and Second Industrial Revolution, was a transitional period of the global economy toward more widespread, efficient and stable manufacturing processes, succee ...
*
Steam engine A steam engine is a heat engine that performs Work (physics), mechanical work using steam as its working fluid. The steam engine uses the force produced by steam pressure to push a piston back and forth inside a Cylinder (locomotive), cyl ...
Other
gas laws The laws describing the behaviour of gases under fixed pressure, volume, amount of gas, and absolute temperature conditions are called gas laws. The basic gas laws were discovered by the end of the 18th century when scientists found out that re ...
: * * *


Citations


External links

* {{DEFAULTSORT:Boyle's Law 1660s introductions 1662 beginnings 1662 in science Robert Boyle Gas laws Pressure Volume Scientific laws de:Thermische Zustandsgleichung idealer Gase#Gesetz von Boyle-Mariotte