TheInfoList

Gas is one of the four fundamental states of matter (the others being
solid Solid is one of the four fundamental states of matter (the others being liquid A liquid is a nearly incompressible fluid In physics, a fluid is a substance that continually Deformation (mechanics), deforms (flows) under an applied ...

,
liquid A liquid is a nearly incompressible In fluid mechanics or more generally continuum mechanics, incompressible flow (isochoric process, isochoric flow) refers to a fluid flow, flow in which the material density is constant within a fluid parc ...

, and
plasma Plasma or plasm may refer to: Science * Plasma (physics), one of the four fundamental states of matter * Plasma (mineral) or heliotrope, a mineral aggregate * Quark–gluon plasma, a state of matter in quantum chromodynamics Biology * Blood plasma ...
). A pure gas may be made up of individual
atoms An atom is the smallest unit of ordinary matter that forms a chemical element Image:Simple Periodic Table Chart-blocks.svg, 400px, Periodic table, The periodic table of the chemical elements In chemistry, an element is a pure substance c ...

(e.g. a
noble gas The noble gases (historically also the inert gases; sometimes referred to as aerogens) make up a class of chemical elements with similar properties; under Standard conditions for temperature and pressure, standard conditions, they are all odorle ...
like
neon Neon is a chemical element Image:Periodic table (32-col, enwiki), black and white.png, upright=1.0, 500px, The chemical elements ordered by periodic table, link=Periodic table In chemistry, an element is a pure Chemical substance, substanc ...

),
elemental An elemental is a mythic being that is described in occult and alchemical works from around the time of the European Renaissance The Renaissance ( , ) , from , with the same meanings. was a period in European history marking the transiti ...
molecules made from one type of atom (e.g.
oxygen Oxygen is the chemical element with the chemical symbol, symbol O and atomic number 8. It is a member of the chalcogen Group (periodic table), group in the periodic table, a highly Chemical reaction, reactive nonmetal, and an oxidizing a ...

), or
compound Compound may refer to: Architecture and built environments * Compound (enclosure), a cluster of buildings having a shared purpose, usually inside a fence or wall ** Compound (fortification), a version of the above fortified with defensive structu ...
molecules made from a variety of atoms (e.g.
carbon dioxide Carbon dioxide (chemical formula ) is a colorless gas with a density about 53% higher than that of dry air. Carbon dioxide molecules consist of a carbon atom covalent bond, covalently double bonded to two oxygen atoms. It occurs naturally in At ...

). A gas
mixture In chemistry Chemistry is the science, scientific study of the properties and behavior of matter. It is a natural science that covers the Chemical element, elements that make up matter to the chemical compound, compounds composed of atoms, ...

, such as
air File:Atmosphere gas proportions.svg, Composition of Earth's atmosphere by volume, excluding water vapor. Lower pie represents trace gases that together compose about 0.043391% of the atmosphere (0.04402961% at April 2019 concentration ). Number ...

, contains a variety of pure gases. What distinguishes a gas from liquids and solids is the vast separation of the individual gas
particles In the Outline of physical science, physical sciences, a particle (or corpuscule in older texts) is a small wikt:local, localized physical body, object to which can be ascribed several physical property, physical or chemical , chemical properties ...

. This separation usually makes a colorless gas invisible to the human observer. The gaseous state of matter occurs between the liquid and plasma states, the latter of which provides the upper temperature boundary for gases. Bounding the lower end of the temperature scale lie degenerative quantum gases which are gaining increasing attention. High-density atomic gases super-cooled to very low temperatures are classified by their statistical behavior as either
Bose gas An ideal Bose gas is a quantum-mechanical phase of matter, analogous to a classical ideal gas. It is composed of bosons, which have an integer value of spin, and obey Bose–Einstein statistics. The statistical mechanics of bosons were developed b ...
es or
Fermi gas An ideal Fermi gas is a state of matter In physics, a state of matter is one of the distinct forms in which matter can exist. Four states of matter are observable in everyday life: solid, liquid, gas, and Plasma (physics), plasma. Many interme ...
es. For a comprehensive listing of these exotic states of matter see
list of states of matter States of matter are distinguished by changes in the properties of matter associated with external factors like pressure and temperature. States are usually distinguished by a discontinuity in one of those properties: for example, raising the tem ...
.

# Elemental gases

The only
chemical elements 400px, The periodic table of the chemical elements In chemistry Chemistry is the scientific discipline involved with Chemical element, elements and chemical compound, compounds composed of atoms, molecules and ions: their composition, s ...

that are stable
diatomic Diatomic molecules are molecule A scanning tunneling microscopy image of pentacene molecules, which consist of linear chains of five carbon rings. A molecule is an electrically neutral group of two or more atoms held together by chemical b ...
homonuclear Homonuclear molecules, or homonuclear species, are molecules composed of only one Chemical element, element. Homonuclear molecules may consist of various numbers of atoms, depending on the element's properties. Some elements form molecules of more t ...
molecules A scanning tunneling microscopy image of pentacene molecules, which consist of linear chains of five carbon rings. A molecule is an electrically neutral group of two or more atom An atom is the smallest unit of ordinary matter In ...

at STP are
hydrogen Hydrogen is the chemical element Image:Simple Periodic Table Chart-blocks.svg, 400px, Periodic table, The periodic table of the chemical elements In chemistry, an element is a pure substance consisting only of atoms that all have the same ...

(H2),
nitrogen Nitrogen is the chemical element with the Symbol (chemistry), symbol N and atomic number 7. It was first discovered and isolated by Scottish physician Daniel Rutherford in 1772. Although Carl Wilhelm Scheele and Henry Cavendish had independentl ...

(N2),
oxygen Oxygen is the chemical element with the chemical symbol, symbol O and atomic number 8. It is a member of the chalcogen Group (periodic table), group in the periodic table, a highly Chemical reaction, reactive nonmetal, and an oxidizing a ...

(O2), and two
halogens The halogens () are a group A group is a number A number is a mathematical object used to counting, count, measurement, measure, and nominal number, label. The original examples are the natural numbers 1, 2, 3, 4, and so forth. Numbers can b ...

:
fluorine Fluorine is a chemical element with the Chemical symbol, symbol F and atomic number 9. It is the lightest halogen and exists at Standard conditions for temperature and pressure, standard conditions as a highly toxic, pale yellow Diatomic molecule, ...

(F2) and
chlorine Chlorine is a chemical element with the Symbol (chemistry), symbol Cl and atomic number 17. The second-lightest of the halogens, it appears between fluorine and bromine in the periodic table and its properties are mostly intermediate betwe ...

(Cl2). When grouped together with the
monatomic In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related entities of energy and force. "Phy ...
noble gases The noble gases (historically also the inert gases; sometimes referred to as aerogens) make up a class of chemical element Image:Simple Periodic Table Chart-blocks.svg, 400px, Periodic table, The periodic table of the chemical elements In ...
helium Helium (from el, ἥλιος, helios Helios; Homeric Greek: ), Latinized as Helius; Hyperion and Phaethon are also the names of his father and son respectively. often given the epithets Hyperion ("the one above") and Phaethon ("the shining") ...

(He),
neon Neon is a chemical element Image:Periodic table (32-col, enwiki), black and white.png, upright=1.0, 500px, The chemical elements ordered by periodic table, link=Periodic table In chemistry, an element is a pure Chemical substance, substanc ...

(Ne),
argon Argon is a chemical element Image:Simple Periodic Table Chart-blocks.svg, 400px, Periodic table, The periodic table of the chemical elements In chemistry, an element is a pure substance consisting only of atoms that all have the same num ...

(Ar),
krypton Krypton (from grc, κρυπτός, translit=kryptos 'the hidden one') is a chemical element with the symbol (chemistry), symbol Kr and atomic number 36. It is a colorless, odorless, tasteless noble gas that occurs in trace element, tr ...

(Kr),
xenon Xenon is a chemical element with the Symbol (chemistry), symbol Xe and atomic number 54. It is a colorless, dense, odorless noble gas found in Atmosphere of Earth, Earth's atmosphere in trace amounts. Although generally unreactive, xe ...

(Xe), and
radon Radon is a chemical element Image:Simple Periodic Table Chart-blocks.svg, 400px, Periodic table, The periodic table of the chemical elements In chemistry, an element is a pure substance consisting only of atoms that all have the same numbe ...

(Rn) – these gases are referred to as "elemental gases".

# Etymology

The word ''gas'' was first used by the early 17th-century
Flemish Flemish (''Vlaams'') is a Low Franconian Low Franconian, Low Frankish, NetherlandicSarah Grey Thomason, Terrence Kaufman: ''Language Contact, Creolization, and Genetic Linguistics'', University of California Press, 1991, p. 321. (Calling it " ...
chemist A chemist (from Greek ''chēm(ía)'' alchemy; replacing ''chymist'' from Medieval Latin Medieval Latin was the form of Latin Latin (, or , ) is a classical language belonging to the Italic languages, Italic branch of the Indo-European la ...

Jan Baptist van Helmont Jan Baptist van Helmont (; ; 12 January 1580 – 30 December 1644) was a chemist, physiologist, and physician A physician (American English), medical practitioner (English in the Commonwealth of Nations, Commonwealth English), medic ...

. He identified
carbon dioxide Carbon dioxide (chemical formula ) is a colorless gas with a density about 53% higher than that of dry air. Carbon dioxide molecules consist of a carbon atom covalent bond, covalently double bonded to two oxygen atoms. It occurs naturally in At ...

, the first known gas other than air. Van Helmont's word appears to have been simply a phonetic transcription of the
Ancient Greek Ancient Greek includes the forms of the Greek language used in ancient Greece and the classical antiquity, ancient world from around 1500 BC to 300 BC. It is often roughly divided into the following periods: Mycenaean Greek (), Dark Ages () ...
word χάος ''
Chaos Chaos or CHAOS may refer to: Arts, entertainment and media Fictional elements * Chaos (Kinnikuman), Chaos (''Kinnikuman'') * Chaos (Sailor Moon), Chaos (''Sailor Moon'') * Chaos (Sesame Park), Chaos (''Sesame Park'') * Chaos (Warhammer), Chaos ('' ...
'' – the ''g'' in
Dutch Dutch commonly refers to: * Something of, from, or related to the Netherlands * Dutch people () * Dutch language () *Dutch language , spoken in Belgium (also referred as ''flemish'') Dutch may also refer to:" Castle * Dutch Castle Places * ...
being pronounced like ''ch'' in "loch" (voiceless velar fricative, ) – in which case Van Helmont was simply following the established
alchemical File:Aurora consurgens zurich 044 f-21v-44 dragon-pot.jpg, Depiction of Ouroboros from the alchemical treatise ''Aurora consurgens'' (15th century), Zentralbibliothek Zürich, Switzerland Alchemy (from Arabic: ''al-kīmiyā''; from Ancient Gree ...
usage first attested in the works of
Paracelsus Paracelsus (; c. 1493 – 24 September 1541), born Theophrastus von Hohenheim (full name Philippus Aureolus Theophrastus Bombastus von Hohenheim), was a Swiss physician, alchemist Depiction of Ouroboros from the alchemical treatise ''Aurora c ...

. According to Paracelsus's terminology, ''chaos'' meant something like "ultra-rarefied water". An alternative story is that Van Helmont's term was derived from "''gahst'' (or ''geist''), which signifies a ghost or spirit". That story is given no credence by the editors of the ''
Oxford English Dictionary The ''Oxford English Dictionary'' (''OED'') is the principal historical dictionary of the English language, published by Oxford University Press (OUP). It traces the historical development of the English language, providing a comprehensive res ...
''. In contrast, French-American historian
Jacques Barzun Jacques Martin Barzun (; November 30, 1907 – October 25, 2012) was a French-American historian known for his studies of the history of ideas Intellectual history (also the history of ideas) is the study of the history of human thought and of in ...
speculated that Van Helmont had borrowed the word from the German ''Gäscht'', meaning the froth resulting from
fermentation Fermentation is a metabolism, metabolic process that produces chemical changes in organic Substrate (chemistry), substrates through the action of enzymes. In biochemistry, it is narrowly defined as the extraction of energy from carbohydrates in ...

.

# Physical characteristics

Because most gases are difficult to observe directly, they are described through the use of four
physical properties A physical property is any property Property (''latin: Res Privata'') in the Abstract and concrete, abstract is what belongs to or with something, whether as an attribute or as a component of said thing. In the context of this article, it is on ...
or
macroscopic The macroscopic scale is the length scale on which objects or phenomena are large enough to be visible with the naked eye, without magnifying optical instruments. It is the opposite of microscopic The microscopic scale (from , ''mikrós'', "sm ...
characteristics:
pressure Pressure (symbol: ''p'' or ''P'') is the force In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies ma ...

,
volume Volume is a scalar quantity (physics), scalar quantity expressing the amount of three-dimensional space enclosed by a closed surface. For example, the space that a substance (solid, liquid, gas, or Plasma (physics), plasma) or 3D shape occupies ...
,
number of particles The particle number (or number of particles) of a thermodynamic system A thermodynamic system is a body of matter and/or radiation, confined in space by walls, with defined permeabilities, which separate it from its surroundings. The surrounding ...
(chemists group them by moles) and temperature. These four characteristics were repeatedly observed by scientists such as
Robert Boyle Robert Boyle (; 25 January 1627 – 31 December 1691) was an Anglo-Irish natural philosopher, chemist, physicist, and inventor. Boyle is largely regarded today as the first modern chemist, and therefore one of the founders of modern che ...

,
Jacques Charles Jacques Alexandre César Charles (November 12, 1746 – April 7, 1823) was a French inventor, scientist, mathematician, and balloonist. Charles wrote almost nothing about mathematics, and most of what has been credited to him was due to mistaking h ...

,
John Dalton John Dalton (; 6 September 1766 – 27 July 1844) was an English chemist, physicist A physicist is a scientist A scientist is a person who conducts Scientific method, scientific research to advance knowledge in an Branches of science, ...

,
Joseph Gay-Lussac Joseph Louis Gay-Lussac (, , ; 6 December 1778  – 9 May 1850) was a French chemist A chemist (from Greek ''chēm(ía)'' alchemy; replacing ''chymist'' from Medieval Latin ''alchemist'') is a scientist A scientist is a person who con ...
and
Amedeo Avogadro Lorenzo Romano Amedeo Carlo Avogadro, Count of Quaregna and Cerreto (, also , ; 9 August 17769 July 1856) was an Italian scientist A scientist is a person who conducts Scientific method, scientific research to advance knowledge in an Branche ...

for a variety of gases in various settings. Their detailed studies ultimately led to a mathematical relationship among these properties expressed by the
ideal gas law Isotherms of an ideal gas. The curved lines represent the relationship between pressure Pressure (symbol: ''p'' or ''P'') is the force In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), k ...

(see simplified models section below). Gas particles are widely separated from one another, and consequently, have weaker intermolecular bonds than liquids or solids. These
intermolecular forces An intermolecular force (IMF) (or secondary force) is the force that mediates interaction between molecules, including the electromagnetic forces of attraction or repulsion which act between atoms and other types of neighboring particles, e.g. atom ...
result from electrostatic interactions between gas particles. Like-charged areas of different gas particles repel, while oppositely charged regions of different gas particles attract one another; gases that contain permanently charged
ions An ion () is an atom or molecule with a net electric charge, electrical charge. The charge of an electron is considered negative by convention and this charge is equal and opposite to charge of a proton, which is considered positive by convent ...

are known as
plasma Plasma or plasm may refer to: Science * Plasma (physics), one of the four fundamental states of matter * Plasma (mineral) or heliotrope, a mineral aggregate * Quark–gluon plasma, a state of matter in quantum chromodynamics Biology * Blood plasma ...
s. Gaseous compounds with polar covalent bonds contain permanent charge imbalances and so experience relatively strong intermolecular forces, although the molecule while the compound's net charge remains neutral. Transient, randomly induced charges exist across non-polar
covalent bond A covalent bond is a chemical bond that involves the sharing of electron pairs between atoms. These electron pairs are known as shared pairs or bonding pairs, and the stable balance of attractive and repulsive forces between atoms, when they sh ...
s of molecules and electrostatic interactions caused by them are referred to as
Van der Waals force Microfiber cloth makes use of London-dispersion force to remove dirt without scratches. In molecular physics Molecular physics is the study of the physical properties of molecule File:Pentacene on Ni(111) STM.jpg, A scanning tunneling micr ...
s. The interaction of these intermolecular forces varies within a substance which determines many of the physical properties unique to each gas. A comparison of ''boiling points'' for compounds formed by ionic and covalent bonds leads us to this conclusion. The drifting smoke particles in the image provides some insight into low-pressure gas behavior. Compared to the other states of matter, gases have low
density The density (more precisely, the volumetric mass density; also known as specific mass), of a substance is its mass per unit volume. The symbol most often used for density is ''ρ'' (the lower case Greek letter Rho (letter), rho), although the L ...

and
viscosity The viscosity of a fluid is a measure of its drag (physics), resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity can be ...

.
Pressure Pressure (symbol: ''p'' or ''P'') is the force In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies ma ...

and temperature influence the particles within a certain volume. This variation in particle separation and speed is referred to as ''compressibility''. This particle separation and size influences optical properties of gases as can be found in the following list of refractive indices. Finally, gas particles spread apart or
diffuse 250px, Diffusion from a microscopic and macroscopic point of view. Initially, there are solution, solute molecules on the left side of a barrier (purple line) and none on the right. The barrier is removed, and the solute diffuses to fill the wh ...

in order to homogeneously distribute themselves throughout any container.

# Macroscopic view of gases

When observing a gas, it is typical to specify a frame of reference or
length scale In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, its Motion (physics), motion and behavior through Spa ...
. A larger length scale corresponds to a
macroscopic The macroscopic scale is the length scale on which objects or phenomena are large enough to be visible with the naked eye, without magnifying optical instruments. It is the opposite of microscopic The microscopic scale (from , ''mikrós'', "sm ...
or global point of view of the gas. This region (referred to as a volume) must be sufficient in size to contain a large sampling of gas particles. The resulting statistical analysis of this sample size produces the "average" behavior (i.e. velocity, temperature or pressure) of all the gas particles within the region. In contrast, a smaller length scale corresponds to a
microscopic The microscopic scale (from , ''mikrós'', "small" and σκοπέω, ''skopéō'' "look") is the scale of objects and events smaller than those that can easily be seen by the naked eye Naked eye, also called bare eye or unaided eye, is the pr ...

or particle point of view. Macroscopically, the gas characteristics measured are either in terms of the gas particles themselves (velocity, pressure, or temperature) or their surroundings (volume). For example, Robert Boyle studied
pneumatic chemistry Image:Boyle air pump.jpg, 150px, Robert Boyle's air pump In the history of science, pneumatic chemistry is an area of scientific research of the seventeenth, eighteenth, and early nineteenth centuries. Important goals of this work were an understa ...
for a small portion of his career. One of his experiments related the
macroscopic The macroscopic scale is the length scale on which objects or phenomena are large enough to be visible with the naked eye, without magnifying optical instruments. It is the opposite of microscopic The microscopic scale (from , ''mikrós'', "sm ...
properties of pressure and volume of a gas. His experiment used a J-tube
manometer Pressure measurement is the analysis of an applied force In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that st ...

which looks like a
test tube A test tube, also known as a culture tube or sample tube, is a common piece of laboratory glassware consisting of a finger-like length of glass or clear plastic tubing, open at the top and closed at the bottom. Test tubes are usually placed in spe ...

in the shape of the letter J. Boyle trapped an inert gas in the closed end of the test tube with a column of
mercury Mercury usually refers to: * Mercury (planet) Mercury is the smallest planet in the Solar System and the closest to the Sun. Its orbit around the Sun takes 87.97 Earth days, the shortest of all the Sun's planets. It is named after the Roman g ...

, thereby making the number of particles and the temperature constant. He observed that when the pressure was increased in the gas, by adding more mercury to the column, the trapped gas' volume decreased (this is known as an
inverse Inverse or invert may refer to: Science and mathematics * Inverse (logic), a type of conditional sentence which is an immediate inference made from another conditional sentence * Additive inverse (negation), the inverse of a number that, when add ...
relationship). Furthermore, when Boyle multiplied the pressure and volume of each observation, the product was constant. This relationship held for every gas that Boyle observed leading to the law, (PV=k), named to honor his work in this field. There are many mathematical tools available for analyzing gas properties. As gases are subjected to extreme conditions, these tools become more complex, from the Euler equations for inviscid flow to the
Navier–Stokes equations In physics, the Navier–Stokes equations () are a set of partial differential equations which describe the motion of viscous fluid substances, named after French engineer and physicist Claude-Louis Navier and Anglo-Irish physicist and mathematic ...
that fully account for viscous effects. These equations are adapted to the conditions of the gas system in question. Boyle's lab equipment allowed the use of
algebra Algebra (from ar, الجبر, lit=reunion of broken parts, bonesetting, translit=al-jabr) is one of the areas of mathematics, broad areas of mathematics, together with number theory, geometry and mathematical analysis, analysis. In its most ge ...

to obtain his analytical results. His results were possible because he was studying gases in relatively low pressure situations where they behaved in an "ideal" manner. These ideal relationships apply to safety calculations for a variety of flight conditions on the materials in use. The high technology equipment in use today was designed to help us safely explore the more exotic operating environments where the gases no longer behave in an "ideal" manner. This advanced math, including statistics and
multivariable calculus Multivariable calculus (also known as multivariate calculus) is the extension of calculus in one Variable (mathematics), variable to calculus with function of several variables, functions of several variables: the Differential calculus, different ...
, makes possible the solution to such complex dynamic situations as space vehicle reentry. An example is the analysis of the space shuttle reentry pictured to ensure the material properties under this loading condition are appropriate. In this flight regime, the gas is no longer behaving ideally.

## Pressure

The symbol used to represent pressure in equations is "p" or "P" with SI units of pascals. When describing a container of gas, the term
pressure Pressure (symbol: ''p'' or ''P'') is the force In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies ma ...

(or absolute pressure) refers to the average force per unit area that the gas exerts on the surface of the container. Within this volume, it is sometimes easier to visualize the gas particles moving in straight lines until they collide with the container (see diagram at top of the article). The force imparted by a gas particle into the container during this collision is the change in
momentum In Newtonian mechanics, linear momentum, translational momentum, or simply momentum is the product of the mass Mass is both a property Property (''latin: Res Privata'') in the Abstract and concrete, abstract is what belongs to or w ...

of the particle. During a collision only the normal component of velocity changes. A particle traveling parallel to the wall does not change its momentum. Therefore, the average force on a surface must be the average change in
linear momentum In Newtonian mechanics, linear momentum, translational momentum, or simply momentum ( pl. momenta) is the product of the mass Mass is both a property Property (''latin: Res Privata'') in the Abstract and concrete, abstract is what ...
from all of these gas particle collisions. Pressure is the sum of all the normal components of force exerted by the particles impacting the walls of the container divided by the surface area of the wall.

## Temperature

The symbol used to represent ''temperature'' in equations is ''T'' with SI units of
kelvin The kelvin is the base unit of temperature Temperature is a physical quantity that expresses hot and cold. It is the manifestation of thermal energy, present in all matter, which is the source of the occurrence of heat, a flow of energy, ...

s. The speed of a gas particle is proportional to its
absolute temperature Thermodynamic temperature is the measure of ''absolute temperature'' and is one of the principal parameters of thermodynamics. A thermodynamic temperature reading of zero denotes the point at which the fundamental physical property that imbues mat ...
. The volume of the balloon in the video shrinks when the trapped gas particles slow down with the addition of extremely cold nitrogen. The temperature of any
physical system A physical system is a collection of physical objects. In physics, it is a portion of the physical universe chosen for analysis. Everything outside the system is known as the environment (systems), environment. The environment is ignored except f ...
is related to the motions of the particles (molecules and atoms) which make up the system. In
statistical mechanics In physics, statistical mechanics is a mathematical framework that applies Statistics, statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural laws, but explains the ma ...
, temperature is the measure of the average kinetic energy stored in a molecule (also known as the thermal energy). The methods of storing this energy are dictated by the
degrees of freedom In many scientific fields, the degrees of freedom of a system is the number of parameters of the system that may vary independently. For example, a point in the plane has two degrees of freedom for translation Translation is the communicatio ...
of the molecule itself (). Thermal (kinetic) energy added to a gas or liquid (an
endothermic An endothermic process is any process with an increase in the enthalpy Enthalpy is a property of a thermodynamic system A thermodynamic system is a body of matter and/or radiation, confined in space by walls, with defined permeabilities, whic ...
process) produces translational, rotational, and vibrational motion. In contrast, a solid can only increase its internal energy by exciting additional vibrational modes, as the crystal lattice structure prevents both translational and rotational motion. These heated gas molecules have a greater speed range (wider distribution of speeds) with a higher average or ''mean'' speed. The variance of this distribution is due to the speeds of individual particles constantly varying, due to repeated collisions with other particles. The speed range can be described by the
Maxwell–Boltzmann distribution In physics (in particular in statistical mechanics), the Maxwell–Boltzmann distribution is a particular probability distribution named after James Clerk Maxwell and Ludwig Boltzmann. It was first defined and used for describing particle speeds i ...
. Use of this distribution implies
ideal gas An ideal gas is a theoretical gas Gas is one of the four fundamental states of matter (the others being solid, liquid A liquid is a nearly incompressible fluid In physics, a fluid is a substance that continually Deformation (mecha ...
es near
thermodynamic equilibrium Thermodynamic equilibrium is an axiomatic An axiom, postulate or assumption is a statement that is taken to be true True most commonly refers to truth Truth is the property of being in accord with fact or reality.Merriam-Webster's Online ...
for the system of particles being considered.

## Specific volume

The symbol used to represent specific volume in equations is "v" with SI units of cubic meters per kilogram. The symbol used to represent volume in equations is "V" with SI units of cubic meters. When performing a
thermodynamic Thermodynamics is a branch of physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its Motion (physics), motion and behavior through Spacetime, space and time, and the related ent ...
analysis, it is typical to speak of
intensive and extensive propertiesIn grammar, an intensive word form is one which denotes stronger, more forceful, or more concentrated action relative to the root on which the intensive is built. Intensives are usually lexical formations, but there may be a regular process for formi ...
. Properties which depend on the amount of gas (either by mass or volume) are called ''extensive'' properties, while properties that do not depend on the amount of gas are called intensive properties. Specific volume is an example of an intensive property because it is the ratio of volume occupied by a ''unit of mass'' of a gas that is identical throughout a system at equilibrium. 1000 atoms a gas occupy the same space as any other 1000 atoms for any given temperature and pressure. This concept is easier to visualize for solids such as iron which are
incompressible In fluid mechanics or more generally continuum mechanics, incompressible flow (isochoric process, isochoric flow) refers to a fluid flow, flow in which the material density is constant within a fluid parcel—an infinitesimal volume that moves w ...
compared to gases. However, volume itself --- not specific --- is an extensive property.

## Density

The symbol used to represent density in equations is ρ (rho) with SI units of kilograms per cubic meter. This term is the
reciprocal Reciprocal may refer to: In mathematics * Multiplicative inverse, in mathematics, the number 1/''x'', which multiplied by ''x'' gives the product 1, also known as a ''reciprocal'' * Reciprocal polynomial, a polynomial obtained from another poly ...

of specific volume. Since gas molecules can move freely within a container, their mass is normally characterized by density. Density is the amount of mass per unit volume of a substance, or the inverse of specific volume. For gases, the density can vary over a wide range because the particles are free to move closer together when constrained by pressure or volume. This variation of density is referred to as
compressibility In thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, radiation, and physical properties of matter. The behavior of these quantities is governed ...
. Like pressure and temperature, density is a
state variable A state variable is one of the set of variables that are used to describe the mathematical "state"of a dynamical system In mathematics, a dynamical system is a system in which a Function (mathematics), function describes the time dependence of ...
of a gas and the change in density during any process is governed by the laws of thermodynamics. For a static gas, the density is the same throughout the entire container. Density is therefore a scalar quantity. It can be shown by kinetic theory that the density is inversely proportional to the size of the container in which a fixed mass of gas is confined. In this case of a fixed mass, the density decreases as the volume increases.

# Microscopic view of gases

If one could observe a gas under a powerful microscope, one would see a collection of particles without any definite shape or volume that are in more or less random motion. These gas particles only change direction when they collide with another particle or with the sides of the container. This
microscopic The microscopic scale (from , ''mikrós'', "small" and σκοπέω, ''skopéō'' "look") is the scale of objects and events smaller than those that can easily be seen by the naked eye Naked eye, also called bare eye or unaided eye, is the pr ...
view of gas is well-described by
statistical mechanics In physics, statistical mechanics is a mathematical framework that applies Statistics, statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural laws, but explains the ma ...
, but it can be described by many different theories. The ''kinetic theory of gases'', which makes the assumption that these collisions are perfectly , does not account for intermolecular forces of attraction and repulsion.

## Kinetic theory of gases

Kinetic theory provides insight into the macroscopic properties of gases by considering their molecular composition and motion. Starting with the definitions of
momentum In Newtonian mechanics, linear momentum, translational momentum, or simply momentum is the product of the mass Mass is both a property Property (''latin: Res Privata'') in the Abstract and concrete, abstract is what belongs to or w ...

and
kinetic energy In physics, the kinetic energy of an object is the energy that it possesses due to its motion (physics), motion. It is defined as the work (physics), work needed to accelerate a body of a given mass from rest to its stated velocity. Having gaine ...
, one can use the
conservation of momentum In Newtonian mechanics, linear momentum, translational momentum, or simply momentum is the product of the mass and velocity of an object. It is a Euclidean vector, vector quantity, possessing a magnitude and a direction. If is an object's ma ...
and geometric relationships of a cube to relate macroscopic system properties of temperature and pressure to the microscopic property of kinetic energy per molecule. The theory provides averaged values for these two properties. The ''kinetic theory of gases'' can help explain how the system (the collection of gas particles being considered) responds to changes in temperature, with a corresponding change in ''kinetic energy''. For example: Imagine you have a sealed container of a fixed-size (a ''constant'' volume), containing a fixed-number of gas particles; starting from
absolute zero Absolute zero is the lowest limit of the thermodynamic temperature Thermodynamic temperature is the measure of ''absolute temperature'' and is one of the principal parameters of thermodynamics. A thermodynamic temperature reading of zero deno ...
(the theoretical temperature at which atoms or molecules have no thermal energy, i.e. are not moving or vibrating), you begin to add energy to the system by heating the container, so that energy transfers to the particles inside. Once their
internal energy The internal energy of a thermodynamic system A thermodynamic system is a body of matter In classical physics and general chemistry, matter is any substance that has mass and takes up space by having volume. All everyday objects that can ...
is above
zero-point energy Zero point may refer to: *Origin (mathematics), a fixed point of reference for a coordinate system *Zero Point (film), ''Zero Point'' (film), an Estonian film *Zero point (photometry), a calibration mechanism for magnitude in astronomy *Zero Point ...
, meaning their ''kinetic'' energy (also known as ''thermal'' energy) is non-zero, the gas particles will begin to move around the container. As the box is further heated (as more energy is added), the individual particles increase their average speed as the system's total internal energy increases. The higher average-speed of all the particles leads to a greater rate at which
collisions In physics, a collision is any event in which two or more bodies exert Force, forces on each other in a relatively short time. Although the most common use of the word ''collision'' refers to incidents in which two or more objects collide with gr ...

happen (i.e. greater number of collisions per unit of time), between particles and the container, as well as between the particles themselves. The ''macro''scopic, measurable quantity of ''pressure,'' is the direct result of these ''micro''scopic particle collisions with the surface, over which, individual molecules exert a small force, each contributing to the total force applied within a specific area. (''Read "''Pressure''" in the above section "''Macroscopic view of gases''".)'' Likewise, the macroscopically measurable quantity of ''temperature'', is a quantification of the overall amount of ''motion, or kinetic energy'' that the particles exhibit. (''Read "''Temperature''" in the above section "''Macroscopic view of gases''".)''

## Thermal motion and statistical mechanics

In the ''kinetic theory of gases'', kinetic energy is assumed to purely consist of linear translations according to a speed distribution of ''particles'' in the system. However, in ''real gases'' and other real substances, the motions which define the kinetic energy of a system (which collectively determine the temperature), are much more complex than simple linear
translation Translation is the communication of the meaning Meaning most commonly refers to: * Meaning (linguistics), meaning which is communicated through the use of language * Meaning (philosophy), definition, elements, and types of meaning discussed ...
due to the more complex structure of molecules, compared to single atoms which act similarly to point-masses. In real thermodynamic systems, quantum phenomena play a large role in determining thermal motions. The random, thermal motions (kinetic energy) in molecules is a combination of a finite set of possible motions including translation, rotation, and
vibration Vibration is a mechanical phenomenon whereby oscillation Oscillation is the repetitive variation, typically in time, of some measure about a central value (often a point of equilibrium) or between two or more different states. The term '' vib ...
. This finite range of possible motions, along with the finite set of molecules in the system, leads to a finite number of ''
microstates Image:BlankMap-World-v6 small states.png, upright=1.4, Map of the smallest states in the world by land area. Note many of these are not considered microstates A microstate or ministate is a sovereign state having a very small population or very ...
'' within the system; we call the set of all microstates an ''
ensemble Ensemble may refer to: Art * Musical ensemble * Ensemble cast (drama, comedy) * Ensemble (musical theatre), also known as the chorus * Ensemble (band), a project of Olivier Alary * Ensemble (album), ''Ensemble'' (album), Kendji Girac 2015 album ...
.'' Specific to atomic or molecular systems, we could potentially have three different kinds of ensemble, depending on the situation:
microcanonical ensemble In statistical mechanics In physics, statistical mechanics is a mathematical framework that applies Statistics, statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natu ...
,
canonical ensemble In statistical mechanics, a canonical ensemble is the statistical ensemble (mathematical physics), statistical ensemble that represents the possible states of a mechanical system in thermal equilibrium with a heat bath at a fixed temperature. Th ...
, or
grand canonical ensemble In statistical mechanics In physics, statistical mechanics is a mathematical framework that applies Statistics, statistical methods and probability theory to large assemblies of microscopic entities. It does not assume or postulate any natural ...
. Specific combinations of microstates within an ensemble are how we truly define ''macrostate'' of the system (temperature, pressure, energy, etc.). In order to do that, we must first count all microstates though use of a '' partition function.'' The use of statistical mechanics and the partition function is an important tool throughout all of physical chemistry, because it is the key to connection between the microscopic states of a system and the macroscopic variables which we can measure, such as temperature, pressure, heat capacity, internal energy, enthalpy, and entropy, just to name a few. (''Read'': Partition function Meaning and significance) Using the partition function to find the energy of a molecule, or system of molecules, can sometimes be approximated by the
Equipartition theorem peptide. The jittery motion is random and complex, and the energy of any particular atom can fluctuate wildly. Nevertheless, the equipartition theorem allows the ''average'' kinetic energy In physics, the kinetic energy of an object is the e ...
, which greatly-simplifies calculation. However, this method assumes all molecular
degrees of freedom In many scientific fields, the degrees of freedom of a system is the number of parameters of the system that may vary independently. For example, a point in the plane has two degrees of freedom for translation Translation is the communicatio ...
are equally populated, and therefore equally utilized for storing energy within the molecule. It would imply that internal energy changes linearly with temperature, which is not the case. This ignores the fact that
heat capacity Heat capacity or thermal capacity is a physical property A physical property is any property Property is a system of rights that gives people legal control of valuable things, and also refers to the valuable things themselves. Depending on t ...
changes with temperature, due to certain degrees of freedom being unreachable (a.k.a. "frozen out") at lower temperatures. As internal energy of molecules increases, so does the ability to store energy within additional degrees of freedom. As more degrees of freedom become available to hold energy, this causes the molar heat capacity of the substance to increase.

## Brownian motion

Brownian motion is the mathematical model used to describe the random movement of particles suspended in a fluid. The gas particle animation, using pink and green particles, illustrates how this behavior results in the spreading out of gases (
entropy Entropy is a scientific concept as well as a measurable physical property that is most commonly associated with a state of disorder, randomness, or uncertainty. The term and the concept are used in diverse fields, from classical thermodynamics ...

). These events are also described by . Since it is at the limit of (or beyond) current technology to observe individual gas particles (atoms or molecules), only theoretical calculations give suggestions about how they move, but their motion is different from Brownian motion because Brownian motion involves a smooth drag due to the frictional force of many gas molecules, punctuated by violent collisions of an individual (or several) gas molecule(s) with the particle. The particle (generally consisting of millions or billions of atoms) thus moves in a jagged course, yet not so jagged as would be expected if an individual gas molecule were examined.

## Intermolecular forces - the primary difference between ''Real'' and ''Ideal'' gases

Forces between two or more molecules or atoms, either attractive or repulsive, are called ''intermolecular forces''. Intermolecular forces are experienced by molecules when they are within physical proximity of one another. These forces are very important for properly modeling molecular systems, as to accurately predict the microscopic behavior of molecules in ''any'' system, and therefore, are necessary for accurately predicting the physical properties of gases (and liquids) across wide variations in physical conditions. Arising from the study of
physical chemistry Physical chemistry is the study of macroscopic The macroscopic scale is the length scale on which objects or phenomena are large enough to be visible with the naked eye, without magnifying optical instruments. It is the opposite of microscopi ...
, one of the most prominent intermolecular forces throughout physics, are ''
van der Waals forces Microfiber cloth makes use of London-dispersion force to remove dirt without scratches. In molecular physics, the van der Waals force, named after Dutch physicist Johannes Diderik van der Waals, is a distance-dependent interaction between atoms ...
''. Van der Waals forces play a key role in determining nearly all
physical properties A physical property is any property Property (''latin: Res Privata'') in the Abstract and concrete, abstract is what belongs to or with something, whether as an attribute or as a component of said thing. In the context of this article, it is on ...
of fluids such as
viscosity The viscosity of a fluid is a measure of its drag (physics), resistance to deformation at a given rate. For liquids, it corresponds to the informal concept of "thickness": for example, syrup has a higher viscosity than water. Viscosity can be ...

, flow rate, and
gas dynamics Compressible flow (or gas dynamics) is the branch of fluid mechanics Fluid mechanics is the branch of physics concerned with the mechanics Mechanics (Ancient Greek, Greek: ) is the area of physics concerned with the motions of physical objec ...
(see physical characteristics section). The van der Waals interactions between gas molecules, is the reason why modeling a "real gas" is more mathematically difficult than an "''ideal'' gas". Ignoring these proximity-dependent forces allows a
real gas Real gases are nonideal 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 effects; ...
to be treated like an
ideal gas An ideal gas is a theoretical gas Gas is one of the four fundamental states of matter (the others being solid, liquid A liquid is a nearly incompressible fluid In physics, a fluid is a substance that continually Deformation (mecha ...
, which greatly simplifies calculation. The intermolecular attractions and repulsions between two gas molecules are dependent on the amount of distance between them. The combined attractions and repulsions are well-modelled by the
Lennard-Jones potential The Lennard-Jones potential (also termed the LJ potential or 12-6 potential) is an intermolecular pair potential. Among the Interatomic potential, intermolecular potentials, the Lennard-Jones potential is the potential that has been studied most e ...
, which is one of the most extensively studied of all interatomic potentials describing the
potential energy In physics, potential energy is the energy In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter ...

of molecular systems. The Lennard-Jones potential between molecules can be broken down into two separate components: a long-distance attraction due to the
London dispersion force London dispersion forces (LDF, also known as dispersion forces, London forces, instantaneous dipole–induced dipole forces, Fluctuating Induced Dipole Bonds or loosely as van der Waals forces) are a type of force acting between atom An atom ...
, and a short-range repulsion due to electron-electron
exchange interactionIn chemistry Chemistry is the scientific discipline involved with Chemical element, elements and chemical compound, compounds composed of atoms, molecules and ions: their composition, structure, properties, behavior and the changes they undergo ...
(which is related to the
Pauli exclusion principle The Pauli exclusion principle is the quantum mechanical principle which states that two or more identical fermion In particle physics Particle physics (also known as high energy physics) is a branch of physics Physics (from grc ...
). When two molecules are relatively distant (meaning they have a high ''potential'' energy), they experience a weak attracting force, causing them to move toward each other, lowering their potential energy. However, if the molecules are ''too far'' away, then they would not experience attractive force of any significance. Additionally, if the molecules get ''too close'' then they will collide, and experience a ''very high'' repulsive force (modelled by
Hard spheres Hard spheres are widely used as model particles in the statistical mechanical theory of fluids and solids. They are defined simply as impenetrable spheres that cannot overlap in space. They mimic the extremely strong ("infinitely elastic bouncing") ...
) which is a ''much stronger force'' than the attractions, so that any attraction due to proximity is disregarded. As two molecules approach each other, from a distance that is ''neither'' too-far, ''nor'' too-close, their attraction increases as the magnitude of their potential energy increases (becoming more negative), and lowers their total internal energy. The attraction causing the molecules to get closer, can only happen if the molecules remain in proximity for the duration of time it takes to physically ''move'' closer. Therefore, the attractive forces are strongest when the molecules move at ''low speeds''. This means that the attraction between molecules is ''significant'' when gas temperatures is ''low''. However, if you were to isothermally compress this cold gas into a small volume, ''forcing'' the molecules into close proximity, and raising the pressure, the repulsions will begin to dominate over the attractions, as the rate at which collisions are happening will increase significantly. Therefore, at low temperatures, and low pressures, ''attraction'' is the dominant intermolecular interaction. If two molecules are moving at high speeds, in arbitrary directions, along non-intersecting paths, then they will not spend enough time in proximity to be affected by the attractive London-dispersion force. If the two molecules collide, they are moving too fast and their kinetic energy will be much greater than any attractive potential energy, so they will only experience repulsion upon colliding. Thus, attractions between molecules can be neglected at ''high temperatures'' due to high speeds. At high temperatures, and high pressures, ''repulsion'' is the dominant intermolecular interaction. Accounting for the above stated effects which cause these attractions and repulsions, real gases, delineate from the ''ideal gas'' model by the following generalization: * At low temperatures, and low pressures, the volume occupied by a real gas, is ''less than'' the volume predicted by the ideal gas law. * At high temperatures, and high pressures, the volume occupied by a real gas, is ''greater than'' the volume predicted by the ideal gas law.

# Mathematical models

An ''equation of state'' (for gases) is a mathematical model used to roughly describe or predict the state properties of a gas. At present, there is no single equation of state that accurately predicts the properties of all gases under all conditions. Therefore, a number of much more accurate equations of state have been developed for gases in specific temperature and pressure ranges. The "gas models" that are most widely discussed are "perfect gas", "ideal gas" and "real gas". Each of these models has its own set of assumptions to facilitate the analysis of a given thermodynamic system. Each successive model expands the temperature range of coverage to which it applies.

## Ideal and perfect gas

The
equation of state In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, its Motion (physics), motion and behavior through S ...
for an ideal or perfect gas is the
ideal gas law Isotherms of an ideal gas. The curved lines represent the relationship between pressure Pressure (symbol: ''p'' or ''P'') is the force In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), k ...

and reads :$PV=nRT,$ where ''P'' is the pressure, ''V'' is the volume, ''n'' is amount of gas (in mol units), ''R'' is the
universal gas constant The molar gas constant (also known as the gas constant, universal gas constant, or ideal gas constant) is denoted by the symbol or . It is the molar equivalent to the Boltzmann constant The Boltzmann constant ( or ) is the proportionality fac ...
, 8.314 J/(mol K), and ''T'' is the temperature. Written this way, it is sometimes called the "chemist's version", since it emphasizes the number of molecules ''n''. It can also be written as :$P=\rho R_s T,$ where $R_s$ is the specific gas constant for a particular gas, in units J/(kg K), and ρ = m/V is density. This notation is the "gas dynamicist's" version, which is more practical in modeling of gas flows involving acceleration without chemical reactions. The ideal gas law does not make an assumption about the specific heat of a gas. In the most general case, the specific heat is a function of both temperature and pressure. If the pressure-dependence is neglected (and possibly the temperature-dependence as well) in a particular application, sometimes the gas is said to be a
perfect gasIn physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), knowledge of nature, from ''phýsis'' 'nature'), , is the natural science that studies matter, its Motion (physics), motion and behavior through Spac ...
, although the exact assumptions may vary depending on the author and/or field of science. For an ideal gas, the ideal gas law applies without restrictions on the specific heat. An ideal gas is a simplified "real gas" with the assumption that the
compressibility factor In thermodynamics Thermodynamics is a branch of physics that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, radiation, and physical properties of matter. The behavior of these quantities is governe ...
''Z'' is set to 1 meaning that this pneumatic ratio remains constant. A compressibility factor of one also requires the four state variables to follow the
ideal gas law Isotherms of an ideal gas. The curved lines represent the relationship between pressure Pressure (symbol: ''p'' or ''P'') is the force In physics Physics (from grc, φυσική (ἐπιστήμη), physikḗ (epistḗmē), k ...

. This approximation is more suitable for applications in engineering although simpler models can be used to produce a "ball-park" range as to where the real solution should lie. An example where the "ideal gas approximation" would be suitable would be inside a
combustion chamber A combustion chamber is part of an internal combustion engine An internal combustion engine (ICE) is a heat engine in which the combustion of a fuel occurs with an oxidizer (usually air) in a combustion chamber that is an integral part of the ...
of a
jet engine A jet engine is a type of reaction engine A reaction engine is an engine or motor that produces thrust by expelling reaction mass, in accordance with Newton's third law of motion. This law of motion is most commonly paraphrased as: "For ...

. It may also be useful to keep the elementary reactions and chemical dissociations for calculating emissions.

## Real gas

Each one of the assumptions listed below adds to the complexity of the problem's solution. As the density of a gas increases with rising pressure, the intermolecular forces play a more substantial role in gas behavior which results in the ideal gas law no longer providing "reasonable" results. At the upper end of the engine temperature ranges (e.g. combustor sections – 1300 K), the complex fuel particles absorb internal energy by means of rotations and vibrations that cause their specific heats to vary from those of diatomic molecules and noble gases. At more than double that temperature, electronic excitation and dissociation of the gas particles begins to occur causing the pressure to adjust to a greater number of particles (transition from gas to
plasma Plasma or plasm may refer to: Science * Plasma (physics), one of the four fundamental states of matter * Plasma (mineral) or heliotrope, a mineral aggregate * Quark–gluon plasma, a state of matter in quantum chromodynamics Biology * Blood plasma ...
). Finally, all of the thermodynamic processes were presumed to describe uniform gases whose velocities varied according to a fixed distribution. Using a non-equilibrium situation implies the flow field must be characterized in some manner to enable a solution. One of the first attempts to expand the boundaries of the ideal gas law was to include coverage for different
thermodynamic process Classical thermodynamics considers three main kinds of thermodynamic process: (1) changes in a system, (2) cycles in a system, and (3) flow processes. (1) A change in a system is defined by a passage from an initial to a final state of thermodyna ...
es by adjusting the equation to read ''pVn = constant'' and then varying the ''n'' through different values such as the
specific heat ratio In thermal physics and thermodynamics, the heat capacity ratio, also known as the adiabatic index, the ratio of specific heats, or Laplace's coefficient, is the ratio of the heat capacity at constant pressure () to heat capacity at constant volume ...
, ''γ''. Real gas effects include those adjustments made to account for a greater range of gas behavior: * Compressibility effects (''Z'' allowed to vary from 1.0) *Variable
heat capacity Heat capacity or thermal capacity is a physical property A physical property is any property Property is a system of rights that gives people legal control of valuable things, and also refers to the valuable things themselves. Depending on t ...
(specific heats vary with temperature) *Van der Waals forces (related to compressibility, can substitute other equations of state) * Non-equilibrium thermodynamic effects *Issues with molecular dissociation and
elementary reactionAn elementary reaction is a chemical reaction A chemical reaction is a process that leads to the chemical transformation of one set of chemical substances to another. Classically, chemical A chemical substance is a form of matter having cons ...
s with variable composition. For most applications, such a detailed analysis is excessive. Examples where real gas effects would have a significant impact would be on the
Space Shuttle The Space Shuttle is a retired, partially reusable launch system, reusable low Earth orbital spacecraft system operated from 1981 to 2011 by the U.S. NASA, National Aeronautics and Space Administration (NASA) as part of the Space Shuttle progra ...

re-entry (MER) aeroshell, artistic rendition Atmospheric entry is the movement of an object from outer space Outer space is the expanse that exists beyond Earth and between astronomical object, celestial bodies. Outer space is not completely empt ...
where extremely high temperatures and pressures were present or the gases produced during geological events as in the image of the 1990 eruption of Mount Redoubt.

## Permanent gas

Permanent gas is a term used for a gas which has a critical temperature below the range of normal human-habitable temperatures and therefore cannot be liquefied by pressure within this range. Historically such gases were thought to be impossible to liquefy and would therefore permanently remain in the gaseous state. The term is relevant to ambient temperature storage and transport of gases at high pressure.

# Historical research

## Boyle's law

Boyle's law was perhaps the first expression of an equation of state. In 1662
Robert Boyle Robert Boyle (; 25 January 1627 – 31 December 1691) was an Anglo-Irish natural philosopher, chemist, physicist, and inventor. Boyle is largely regarded today as the first modern chemist, and therefore one of the founders of modern che ...

performed a series of experiments employing a J-shaped glass tube, which was sealed on one end. Mercury was added to the tube, trapping a fixed quantity of air in the short, sealed end of the tube. Then the volume of gas was carefully measured as additional mercury was added to the tube. The pressure of the gas could be determined by the difference between the mercury level in the short end of the tube and that in the long, open end. The image of Boyle's equipment shows some of the exotic tools used by Boyle during his study of gases. Through these experiments, Boyle noted that the pressure exerted by a gas held at a constant temperature varies inversely with the volume of the gas. For example, if the volume is halved, the pressure is doubled; and if the volume is doubled, the pressure is halved. Given the inverse relationship between pressure and volume, the product of pressure (''P'') and volume (''V'') is a constant (''k'') for a given mass of confined gas as long as the temperature is constant. Stated as a formula, thus is: :$PV = k$ Because the before and after volumes and pressures of the fixed amount of gas, where the before and after temperatures are the same both equal the constant ''k'', they can be related by the equation: $\qquad P_1 V_1 = P_2 V_2.$

## Charles's law

In 1787, the French physicist and balloon pioneer,
Jacques Charles Jacques Alexandre César Charles (November 12, 1746 – April 7, 1823) was a French inventor, scientist, mathematician, and balloonist. Charles wrote almost nothing about mathematics, and most of what has been credited to him was due to mistaking h ...

, found that oxygen, nitrogen, hydrogen, carbon dioxide, and air expand to the same extent over the same 80 kelvin interval. He noted that, for an ideal gas at constant pressure, the volume is directly proportional to its temperature: : $\frac = \frac$

## Gay-Lussac's law

In 1802,
Joseph Louis Gay-Lussac Joseph Louis Gay-Lussac (, , ; 6 December 1778  – 9 May 1850) was a French chemist and physicist. He is known mostly for his discovery that water is made of two parts hydrogen and one part oxygen (with Alexander von Humboldt Friedric ...

published results of similar, though more extensive experiments. Gay-Lussac credited Charles' earlier work by naming the law in his honor. Gay-Lussac himself is credited with the law describing pressure, which he found in 1809. It states that the pressure exerted on a container's sides by an ideal gas is proportional to its temperature. :$\frac=\frac \,$

In 1811, Amedeo Avogadro verified that equal volumes of pure gases contain the same number of particles. His theory was not generally accepted until 1858 when another Italian chemist Stanislao Cannizzaro was able to explain non-ideal exceptions. For his work with gases a century prior, the number that bears his name
Avogadro's constant The Avogadro constant (''N''A or ''L'') is the proportionality factor that relates the number of constituent particles (usually molecule File:Pentacene on Ni(111) STM.jpg, A scanning tunneling microscopy image of pentacene molecules, which ...
represents the number of atoms found in 12 grams of elemental carbon-12 (6.022×1023 mol−1). This specific number of gas particles, at standard temperature and pressure (ideal gas law) occupies 22.40 liters, which is referred to as the
molar volume In chemistry and related fields, the molar volume, symbol ''V''m, or \tilde V of a substance is the occupied volume divided by the amount of substance at a given temperature and pressure. It is equal to the molar mass (''M'') divided by the mass de ...
. Avogadro's law states that the volume occupied by an ideal gas is proportional to the number of moles (or molecules) present in the container. This gives rise to the
molar volume In chemistry and related fields, the molar volume, symbol ''V''m, or \tilde V of a substance is the occupied volume divided by the amount of substance at a given temperature and pressure. It is equal to the molar mass (''M'') divided by the mass de ...
of a gas, which at STP is 22.4 dm3 (or liters). The relation is given by :$\frac=\frac \,$ where n is equal to the number of moles of gas (the number of molecules divided by
Avogadro's number The Avogadro constant (''N''A or ''L'') is the proportionality factor that relates the number of constituent particles (usually molecule File:Pentacene on Ni(111) STM.jpg, A scanning tunneling microscopy image of pentacene molecules, which ...
).

## Dalton's law

In 1801,
John Dalton John Dalton (; 6 September 1766 – 27 July 1844) was an English chemist, physicist A physicist is a scientist A scientist is a person who conducts Scientific method, scientific research to advance knowledge in an Branches of science, ...

published the law of partial pressures from his work with ideal gas law relationship: The pressure of a mixture of non reactive gases is equal to the sum of the pressures of all of the constituent gases alone. Mathematically, this can be represented for ''n'' species as: : Pressuretotal = Pressure1 + Pressure2 + ... + Pressure''n'' The image of Dalton's journal depicts symbology he used as shorthand to record the path he followed. Among his key journal observations upon mixing unreactive "elastic fluids" (gases) were the following: *Unlike liquids, heavier gases did not drift to the bottom upon mixing. *Gas particle identity played no role in determining final pressure (they behaved as if their size was negligible).

# Special topics

## Compressibility

Thermodynamicists use this factor (''Z'') to alter the ideal gas equation to account for compressibility effects of real gases. This factor represents the ratio of actual to ideal specific volumes. It is sometimes referred to as a "fudge-factor" or correction to expand the useful range of the ideal gas law for design purposes. ''Usually'' this ''Z'' value is very close to unity. The compressibility factor image illustrates how Z varies over a range of very cold temperatures.

## Reynolds number

In fluid mechanics, the Reynolds number is the ratio of inertial forces (''vsρ'') to viscous forces (''μ/L''). It is one of the most important dimensionless numbers in fluid dynamics and is used, usually along with other dimensionless numbers, to provide a criterion for determining dynamic similitude. As such, the Reynolds number provides the link between modeling results (design) and the full-scale actual conditions. It can also be used to characterize the flow.

## Viscosity

Viscosity, a physical property, is a measure of how well adjacent molecules stick to one another. A solid can withstand a shearing force due to the strength of these sticky intermolecular forces. A fluid will continuously deform when subjected to a similar load. While a gas has a lower value of viscosity than a liquid, it is still an observable property. If gases had no viscosity, then they would not stick to the surface of a wing and form a boundary layer. A study of the
delta wing A delta wing is a wing A wing is a type of fin that produces lift while moving through air or some other fluid. Accordingly, wings have streamlined Cross section (geometry), cross-sections that are subject to aerodynamic forces and act as ...
in the
Schlieren Schlieren (; singular: ''schliere'', meaning "streak") are optical inhomogeneities in transparent medium that are not necessarily visible to the human eye The human eye is a organ (anatomy), sense organ that reacts to light and allows Visual ...

image reveals that the gas particles stick to one another (see Boundary layer section).

## Turbulence

In fluid dynamics, turbulence or turbulent flow is a flow regime characterized by chaotic, stochastic property changes. This includes low momentum diffusion, high momentum convection, and rapid variation of pressure and velocity in space and time. The satellite view of weather around Robinson Crusoe Islands illustrates one example.

## Boundary layer

Particles will, in effect, "stick" to the surface of an object moving through it. This layer of particles is called the boundary layer. At the surface of the object, it is essentially static due to the friction of the surface. The object, with its boundary layer is effectively the new shape of the object that the rest of the molecules "see" as the object approaches. This boundary layer can separate from the surface, essentially creating a new surface and completely changing the flow path. The classical example of this is a stalling airfoil. The delta wing image clearly shows the boundary layer thickening as the gas flows from right to left along the leading edge.

## Maximum entropy principle

As the total number of degrees of freedom approaches infinity, the system will be found in the macrostate that corresponds to the highest multiplicity. In order to illustrate this principle, observe the skin temperature of a frozen metal bar. Using a thermal image of the skin temperature, note the temperature distribution on the surface. This initial observation of temperature represents a "
microstate upright=1.4, Map of the smallest states in the world by land area. Note many of these are not considered microstates A microstate or ministate is a sovereign state A sovereign state is a political entity that is represented by one centralize ...
". At some future time, a second observation of the skin temperature produces a second microstate. By continuing this observation process, it is possible to produce a series of microstates that illustrate the thermal history of the bar's surface. Characterization of this historical series of microstates is possible by choosing the macrostate that successfully classifies them all into a single grouping.

## Thermodynamic equilibrium

When energy transfer ceases from a system, this condition is referred to as thermodynamic equilibrium. Usually, this condition implies the system and surroundings are at the same temperature so that heat no longer transfers between them. It also implies that external forces are balanced (volume does not change), and all chemical reactions within the system are complete. The timeline varies for these events depending on the system in question. A container of ice allowed to melt at room temperature takes hours, while in semiconductors the heat transfer that occurs in the device transition from an on to off state could be on the order of a few nanoseconds.

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Greenhouse gas A greenhouse gas (GHG or GhG) is a gas Gas is one of the four fundamental states of matter (the others being solid, liquid A liquid is a nearly incompressible fluid In physics, a fluid is a substance that continually Deformat ...
* List of gases *
Natural gas Natural gas (also called fossil gas; sometimes just gas) is a naturally occurring hydrocarbon gas mixture consisting of methane and commonly including varying amounts of other higher alkanes, and sometimes a small percentage of carbon dioxide ...

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Volcanic gas Volcanic gases are gases given off by active (or, at times, by dormant) volcanoes. These include gases trapped in cavities ( vesicles) in volcanic rock Volcanic rock (often shortened to volcanics in scientific contexts) is a Rock (geo ...
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Breathing gas A breathing gas is a mixture of gaseous chemical elements and compounds used for breathing, respiration. Air is the most common, and only natural, breathing gas. But other mixtures of gases, or pure oxygen, are also used in breathing equipment a ...
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