Gas

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OR:

Gas is one of the four fundamental
states 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 intermediate states are known to exist, such as ...
(the others being
solid Solid is one of the State of matter#Four fundamental states, four fundamental states of matter (the others being liquid, gas, and Plasma (physics), plasma). The molecules in a solid are closely packed together and contain the least amount o ...
,
liquid A liquid is a nearly Compressibility, incompressible fluid that conforms to the shape of its container but retains a (nearly) constant volume independent of pressure. As such, it is one of State of matter#Four fundamental states, the four fund ...
, and
plasma Plasma or plasm may refer to: Science * Plasma (physics) Plasma () 1, where \nu_ is the electron gyrofrequency and \nu_ is the electron collision rate. It is often the case that the electrons are magnetized while the ions are not. Magnetized ...
). A pure gas may be made up of individual
atoms Every atom is composed of a atomic nucleus, nucleus and one or more electrons bound to the nucleus. The nucleus is made of one or more protons and a number of neutrons. Only the most common variety of hydrogen has no neutrons. Every solid, l ...
(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 A chemical element is a species of atoms that have a given number of protons in their atomic nucleus, nuclei, including the pure Chemical substance, substance consisting only of that species. Unlike chemical com ...
), elemental 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 molecules made from a variety of atoms (e.g.
carbon dioxide Carbon dioxide ( chemical formula ) is a chemical compound made up of molecules that each have one carbon Carbon () is a chemical element with the chemical symbol, symbol C and atomic number 6. It is nonmetallic and tetravalence, tetraval ...
). A gas
mixture In chemistry, a mixture is a material made up of two or more different chemical substances which are not chemically bonded. A mixture is the physical combination of two or more substances in which the identities are retained and are mixed in the ...
, such as
air The atmosphere of Earth is the layer of gases, known collectively as air, retained by Earth's gravity that surrounds the planet and forms its planetary atmosphere. The atmosphere of Earth protects life on Earth by creating pressure allowing fo ...
, contains a variety of pure gases. What distinguishes a gas from liquids and solids is the vast separation of the individual gas particles. This separation usually makes a colourless 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 abide by Bose–Einstein statistics. The statistical mechanics of bosons were develo ...
es or
Fermi gas An ideal Fermi gas is a state of matter which is an ensemble of many non-interacting fermions. Fermions are subatomic particle, particles that obey Fermi–Dirac statistics, like electrons, protons, and neutrons, and, in general, particles with ...
es. For a comprehensive listing of these exotic states of matter see list of states of matter.

# Elemental gases

The only
chemical elements A chemical element is a species of atoms that have a given number of protons in their atomic nucleus, nuclei, including the pure Chemical substance, substance consisting only of that species. Unlike chemical compounds, chemical elements canno ...
that are stable
diatomic Diatomic molecules () are molecules composed of only two atoms, of the same or different chemical elements. If a diatomic molecule consists of two atoms of the same element, such as hydrogen () or oxygen (), then it is said to be homonuclear mol ...
homonuclear Homonuclear molecules, or homonuclear species, are molecules composed of only one Chemical element, element. Homonuclear molecules may consist of various numbers of atoms. The size of the molecule an element can form depends on the element's proper ...
molecular A molecule is a group of two or more atoms held together by attractive forces known as chemical bonds; depending on context, the term may or may not include ions which satisfy this criterion. In quantum physics, organic chemistry, and bioche ...
gases at STP are
hydrogen Hydrogen is the chemical element with the Symbol (chemistry), symbol H and atomic number 1. Hydrogen is the lightest element. At standard temperature and pressure, standard conditions hydrogen is a gas of diatomic molecules having the chemical ...
(H2),
nitrogen Nitrogen is the chemical element with the Symbol (chemistry), symbol N and atomic number 7. Nitrogen is a nonmetal and the lightest member of pnictogen, group 15 of the periodic table, often called the pnictogens. It is a common element in the ...
(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 (periodic table), group in the periodic table consisting of five or six chemically related chemical element, elements: fluorine (F), chlorine (Cl), bromine (Br), iodine (I), astatine (At), and tennessine (Ts). In the ...
:
fluorine Fluorine is a chemical element A chemical element is a species of atoms that have a given number of protons in their atomic nucleus, nuclei, including the pure Chemical substance, substance consisting only of that species. Unlike chemical c ...
(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 betwee ...
(Cl2). When grouped together with the
monatomic In physics and chemistry, "monatomic" is a combination of the words "mono" and "atomic", and means "single atom". It is usually applied to gases: a monatomic gas is a gas in which atoms are not bound to each other. Examples at Standard temperature ...
noble gases 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 ...
helium Helium (from el, ἥλιος, helios, lit=sun) is a chemical element with the symbol (chemistry), symbol He and atomic number 2. It is a colorless, odorless, tasteless, non-toxic, inert gas, inert, monatomic gas and the first in the noble gas gr ...
(He),
neon Neon is a chemical element A chemical element is a species of atoms that have a given number of protons in their atomic nucleus, nuclei, including the pure Chemical substance, substance consisting only of that species. Unlike chemical com ...
(Ne),
argon Argon is a chemical element with the Symbol (chemistry), symbol Ar and atomic number 18. It is in group 18 of the periodic table and is a noble gas. Argon is the third-most abundant gas in Earth's atmosphere, at 0.934% (9340 Parts-per notatio ...
(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, trace amount ...
(Kr),
xenon Xenon is a chemical element A chemical element is a species of atoms that have a given number of protons in their atomic nucleus, nuclei, including the pure Chemical substance, substance consisting only of that species. Unlike chemical c ...
(Xe), and
radon Radon is a chemical element A chemical element is a species of atoms that have a given number of protons in their atomic nucleus, nuclei, including the pure Chemical substance, substance consisting only of that species. Unlike chemical com ...
(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 dialect cluster of the Dutch language. It is sometimes referred to as Flemish Dutch (), Belgian Dutch ( ), or Southern Dutch (). Flemish is native to Flanders, a historical region in northern Belgium; i ...
chemist A chemist (from Greek ''chēm(ía)'' alchemy; replacing ''chymist'' from Medieval Latin ''alchemist'') is a scientist trained in the study of chemistry. Chemists study the composition of matter and its properties. Chemists carefully describe th ...
Jan Baptist van Helmont. He identified
carbon dioxide Carbon dioxide ( chemical formula ) is a chemical compound made up of molecules that each have one carbon Carbon () is a chemical element with the chemical symbol, symbol C and atomic number 6. It is nonmetallic and tetravalence, tetraval ...
, 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 (), Greek Dark ...
word χάος '' Chaos'' – the ''g'' in Dutch being pronounced like ''ch'' in "loch" (voiceless velar fricative, ) – in which case Van Helmont was simply following the established
alchemical Alchemy (from Arabic: ''al-kīmiyā''; from Ancient Greek: χυμεία, ''khumeía'') is an ancient branch of natural philosophy, a philosophical and protoscience, protoscientific tradition that was historically practiced in Chinese alchemy, C ...
usage first attested in the works of
Paracelsus Paracelsus (; ; 1493 – 24 September 1541), born Theophrastus von Hohenheim (full name Philippus Aureolus Theophrastus Bombastus von Hohenheim), was a Swiss physician, alchemist, lay theologian, and philosopher of the German Renaissance. He w ...
. 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 first and foundational historical dictionary of the English language, published by Oxford University Press (OUP). It traces the historical development of the English language, providing a com ...
''. 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 and cultural history. He wrote about a wide range of subjects, including baseball, mystery novels, and ...
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 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 scale, microscopic. Overview When applied to ph ...
characteristics:
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 e ...
,
volume Volume is a measure of occupied 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). ...
, number of particles (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, Alchemy, alchemist and inventor. Boyle is largely regarded today as the first modern chemist, and therefore one of the foun ...
,
Jacques Charles Jacques Alexandre César Charles (November 12, 1746 – April 7, 1823) was a French inventor, scientist, mathematician A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematica ...
,
John Dalton John Dalton (; 5 or 6 September 1766 – 27 July 1844) was an English chemist, physicist and meteorologist. He is best known for introducing the atomic theory into chemistry, and for his research into Color blindness, colour blindness, which ...
,
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 trained in the study of chemistry. ...
and
Amedeo Avogadro Lorenzo Romano Amedeo Carlo Avogadro, Count of Quaregna and Cerreto (, also , ; 9 August 17769 July 1856) was an Italian people, Italian scientist, most noted for his contribution to molecular theory now known as Avogadro's law, which states th ...
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 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 s ...
(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 Electromagnetism, electromagnetic forces of attraction or repulsion which act between atoms and other types of neighbouring ...
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 to be negative by convention and this charge is equal and opposite to the charge of a proton, which is considered to be po ...
are known as
plasma Plasma or plasm may refer to: Science * Plasma (physics) Plasma () 1, where \nu_ is the electron gyrofrequency and \nu_ is the electron collision rate. It is often the case that the electrons are magnetized while the ions are not. Magnetized ...
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 A chemical bond is a lasting attraction between atoms or ions that enables the formation of Molecule, molecules and crystals. The bond may result from the Coulomb's law, electrostatic force between oppos ...
s of molecules and electrostatic interactions caused by them are referred to as
Van der Waals force In molecular physics, the van der Waals force is a distance-dependent interaction between atoms or molecules. Unlike ionic bond, ionic or covalent bonds, these attractions do not result from a Chemical bond, chemical electronic bond; they are c ...
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 Density (volumetric mass density or specific mass) is the substance's mass per unit of volume. The symbol most often used for density is ''ρ'' (the lower case Greek language, Greek letter Rho (letter), rho), although the Latin letter ''D'' ca ...
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 quant ...
.
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 e ...
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 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, length scale is a particular length or distance determined with the precision of at most a few orders of magnitude. The concept of length scale is particularly important because physical phenomena of different length scales cannot aff ...
. 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 scale, microscopic. Overview When applied to ph ...
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 () is the scale of objects and events smaller than those that can easily be seen by the naked eye, requiring a lens (optics), lens or microscope to see them clearly. In physics, the microscopic scale is sometimes regarded a ...
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 In the history of science The history of science covers the development of science from ancient history, ancient times to the present. It encompasses all three major branches of science: natural science, natural, social science, social, a ...
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 scale, microscopic. Overview When applied to ph ...
properties of pressure and volume of a gas. His experiment used a J-tube
manometer Pressure measurement is the measurement of an applied force by a fluid (liquid or gas) on a surface. Pressure is typically measured in unit of measurement, units of force per unit of surface area. Many techniques have been developed for the me ...
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 s ...
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, 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 relationship). Furthermore, when Boyle multiplied the pressure and volume of each observation, the
product Product may refer to: Business * Product (business), an item that serves as a solution to a specific consumer problem. * Product (project management), a deliverable or set of deliverables that contribute to a business solution Mathematics * Pr ...
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 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 mathematician Sir G ...
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 () is one of the areas of mathematics, broad areas of mathematics. Roughly speaking, algebra is the study of mathematical symbols and the rules for manipulating these symbols in formulas; it is a unifying thread of almost all of mathem ...
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, 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 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 e ...
(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, momentum (more specifically linear momentum or translational momentum) is the Multiplication, product of the mass and velocity of an object. It is a Euclidean vector, vector quantity, possessing a magnitude and a dire ...
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, momentum (more specifically linear momentum or translational momentum) is the product of the mass Mass is an Intrinsic and extrinsic properties, intrinsic property of a body. It was traditionally believed to ...
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, symbol K, is the primary unit of temperature in the International System of Units (SI), used alongside its metric prefix, prefixed forms and the degree Celsius. It is named after the Belfast-born and University of Glasgow-based eng ...
s. The speed of a gas particle is proportional to its
absolute temperature Thermodynamic temperature is a quantity defined in thermodynamics as distinct from Kinetic theory of gases, kinetic theory or statistical mechanics. Historically, thermodynamic temperature was defined by William Thomson, 1st Baron Kelvin, Kelvin ...
. 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 ...
is related to the motions of the particles (molecules and atoms) which make up the assystem. In
statistical mechanics In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its motion and behavior through Spacetime, space and time, and the related entities of energy and force. "Physical scien ...
, 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 of the molecule itself ( energy modes). Thermal (kinetic) energy added to a gas or liquid (an
endothermic In thermochemistry, an endothermic process () is any thermodynamic process with an increase in the enthalpy (or internal energy ) of the system.Oxtoby, D. W; Gillis, H.P., Butler, L. J. (2015).''Principle of Modern Chemistry'', Brooks Cole. p. ...
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 Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its motion and behavior through Spacetime, space and time, and the related entities of energy and force. "Physical science ...
. Use of this distribution implies
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 The ideal gas law, also called the ge ...
es near
thermodynamic equilibrium Thermodynamic equilibrium is an axiomatic concept of thermodynamics. It is an internal State variables, state of a single thermodynamic system, or a relation between several thermodynamic systems connected by more or less permeable or impermeable ...
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 that deals with heat, Work (thermodynamics), work, and temperature, and their relation to energy, entropy, and the physical properties of matter and radiation. The behavior of these quantities is governed b ...
analysis, it is typical to speak of
intensive and extensive properties Physical properties of materials and system A system is a group of interacting or interrelated elements that act according to a set of rules to form a unified whole. A system, surrounded and influenced by its environment, is described by i ...
. 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 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 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 and fluid mechanics, the compressibility (also known as the coefficient of compressibility or, if the temperature is held constant, the isothermal compressibility) is a Measure (mathematics), measure of the instantaneous relativ ...
. Like pressure and temperature, density is a state variable 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 () is the scale of objects and events smaller than those that can easily be seen by the naked eye, requiring a lens (optics), lens or microscope to see them clearly. In physics, the microscopic scale is sometimes regarded a ...
view of gas is well-described by
statistical mechanics In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its motion and behavior through Spacetime, space and time, and the related entities of energy and force. "Physical scien ...
, but it can be described by many different theories. The ''kinetic theory of gases'', which makes the assumption that these collisions are perfectly elastic, 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, momentum (more specifically linear momentum or translational momentum) is the Multiplication, product of the mass and velocity of an object. It is a Euclidean vector, vector quantity, possessing a magnitude and a dire ...
and
kinetic energy In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its motion and behavior through Spacetime, space and time, and the related entities of energy and force. "Physical sci ...
, one can use the
conservation of momentum In Newtonian mechanics, momentum (more specifically linear momentum or translational momentum) is the Multiplication, product of the mass and velocity of an object. It is a Euclidean vector, vector quantity, possessing a magnitude and a dire ...
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 scale, a state at which the enthalpy and entropy of a cooled ideal gas reach their minimum value, taken as zero kelvin. The fundamental particles of nature have minimum vibration ...
(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 is the total energy contained within it. It is the energy necessary to create or prepare the system in its given internal state, and includes the contributions of potential energy and internal kinet ...
is above
zero-point energy Zero-point energy (ZPE) is the lowest possible energy that a quantum mechanical system may have. Unlike in classical mechanics, quantum systems constantly Quantum fluctuation, fluctuate in their lowest energy state as described by the Heisen ...
, 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 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 (linguistic), meaning of a #Source and target languages, source-language text by means of an Dynamic and formal equivalence, equivalent #Source and target languages, target-language text. The ...
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 oscillations occur about an equilibrium point. The word comes from Latin ''vibrationem'' ("shaking, brandishing"). The oscillations may be periodic function, periodic, such as the motion of a pendulum ...
. This finite range of possible motions, along with the finite set of molecules in the system, leads to a finite number of '' microstates'' within the system; we call the set of all microstates an '' ensemble.'' Specific to atomic or molecular systems, we could potentially have three different kinds of ensemble, depending on the situation:
microcanonical ensemble In statistical mechanics, the microcanonical ensemble is a statistical ensemble (mathematical physics), statistical ensemble that represents the possible states of a mechanical system whose total energy is exactly specified. The system is assum ...
,
canonical ensemble In statistical mechanics In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its motion and behavior through Spacetime, space and time, and the related entities of ene ...
, or
grand canonical ensemble In statistical mechanics, the grand canonical ensemble (also known as the macrocanonical ensemble) is the statistical ensemble (mathematical physics), statistical ensemble that is used to represent the possible states of a mechanical system of pa ...
. 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 In classical statistical mechanics In physics Physics is the natural science that studies matter, its Elementary particle, fundamental constituents, its motion and behavior through Spacetime, space and time, and the related enti ...
, which greatly-simplifies calculation. However, this method assumes all molecular degrees of freedom 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 quantity, physical property of matter, defined as the amount of heat to be supplied to an object to produce a unit change in its temperature. The International System of Units, SI unit of heat ca ...
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 thermodynam ...
). These events are also described by particle theory. 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 scale, macroscopic and Microscopic scale, microscopic phenomena in chemistry, chemical systems in terms of the principles, practices, and concepts of physics such as Motion (physics), motion, energy ...
, one of the most prominent intermolecular forces throughout physics, are ''
van der Waals forces In molecular physics, the van der Waals force is a distance-dependent interaction between atoms or molecules. Unlike ionic bond, ionic or covalent bonds, these attractions do not result from a Chemical bond, chemical electronic bond; they are c ...
''. Van der Waals forces play a key role in determining nearly all physical properties 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 quant ...
, flow rate, and
gas dynamics Compressible flow (or gas dynamics) is the branch of fluid mechanics that deals with flows having significant changes in fluid density. While all flows are compressibility, compressible, flows are usually treated as being incompressible flow, incom ...
(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 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 The ideal gas law, also called the ge ...
, 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, which is one of the most extensively studied of all interatomic potentials describing the
potential energy In physics, potential energy is the energy held by an object because of its position relative to other objects, stresses within itself, its electric charge, or other factors. Common types of potential energy include the gravitational potentia ...
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 intermolecular force An intermolecul ...
, and a short-range repulsion due to electron-electron exchange interaction (which is related to the
Pauli exclusion principle In quantum mechanics, the Pauli exclusion principle states that two or more identical particles with half-integer spin (physics), spins (i.e. fermions) cannot occupy the same quantum state within a quantum system simultaneously. This principle ...
). 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) 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, chemistry, and thermodynamics, an equation of state is a thermodynamic equations, thermodynamic equation relating state variables, which describe the state of matter under a given set of physical conditions, such as pressure, Volume ( ...
for an ideal or perfect gas is 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 s ...
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, expressed in units of energy per temperature, temperature i ...
, 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 gas, 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, 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 to ...
''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 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 s ...
. 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 or IC engine) is a heat engine in which the combustion of a fuel occurs with an oxidizer (usually air) in a combustion chamber that is an integra ...
of a
jet engine A jet engine is a type of reaction engine discharging a fast-moving jet (fluid), jet of heated gas (usually air) that generates thrust by jet propulsion. While this broad definition can include Rocket engine, rocket, Pump-jet, water jet, and ...
. 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) Plasma () 1, where \nu_ is the electron gyrofrequency and \nu_ is the electron collision rate. It is often the case that the electrons are magnetized while the ions are not. Magnetized ...
). 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 Thermodynamic process is a process in which the thermodynamic state of a system is change ...
es by adjusting the equation to read ''pVn = constant'' and then varying the ''n'' through different values such as the specific heat ratio, ''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 quantity, physical property of matter, defined as the amount of heat to be supplied to an object to produce a unit change in its temperature. The International System of Units, SI unit of heat ca ...
(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 reaction An elementary reaction is a chemical reaction in which one or more chemical species react directly to form Product (chemistry), products in a single reaction step and with a single transition state. In practice, a reaction is assumed to be element ...
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. National Aeronautics and Space Administration (NASA) as part of the Space Shuttle program. I ...
re-entry 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 Redoubt Volcano, or Mount Redoubt (Denaʼina language, Dena'ina: ''Bentuggezh K’enulgheli''), is an active volcano, active stratovolcano in the largely volcanic Aleutian Range of the U.S. state of Alaska. Located at the head of the Chigmit ...
.

## 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, Alchemy, alchemist and inventor. Boyle is largely regarded today as the first modern chemist, and therefore one of the foun ...
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 A mathematician is someone who uses an extensive knowledge of mathematics in their work, typically to solve mathematica ...
, 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 people, 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), ...
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 physical constant that bears his name (the Avogadro constant) is the number of atoms per mole of elemental carbon-12 (). 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 ratio of the volume occupied by a substance to the amount of substance, usually given at a given temperature and pressure. It is equal to the molar ...
. Avogadro's law states that the volume occupied by an ideal gas is proportional to the
amount of substance In chemistry, the amount of substance ''n'' in a given sample of matter is defined as the countable quantity, quantity or particle number, number of discrete atomic-scale particles in it divided by the Avogadro constant ''N''A. The particles or ent ...
in the volume. 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 ratio of the volume occupied by a substance to the amount of substance, usually given at a given temperature and pressure. It is equal to the molar ...
of a gas, which at STP is 22.4 dm3/mol (liters per mole). The relation is given by $\frac=\frac ,$ where ''n'' is the amount of substance of gas (the number of molecules divided by the Avogadro constant).

## Dalton's law

In 1801,
John Dalton John Dalton (; 5 or 6 September 1766 – 27 July 1844) was an English chemist, physicist and meteorologist. He is best known for introducing the atomic theory into chemistry, and for his research into Color blindness, colour blindness, which ...
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 shaped in the form of a triangle. It is named for its similarity in shape to the Greek uppercase letter delta (letter), delta (Δ). Although long studied, it did not find significant applications until the Jet Age, when i ...
in the Schlieren 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 A microstate or ministate is a sovereign state having a very small population or very small land area, usually both. However, the meanings of "state" and "very small" are not well-defined in international law.Warrington, E. (1994). "Lilliputs ...
". 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.

*
Greenhouse gas A greenhouse gas (GHG or GhG) is a gas that Absorption (electromagnetic radiation), absorbs and Emission (electromagnetic radiation), emits radiant energy within the thermal infrared range, causing the greenhouse effect. The primary greenhouse ...
* List of gases *
Natural gas Natural gas (also called fossil gas or simply gas) is a naturally occurring mixture of gaseous hydrocarbons consisting primarily of methane in addition to various smaller amounts of other higher alkanes. Low levels of trace gases like carbon di ...
*
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 rocks, dissolved or dissociated gases in magma and lava, or gases emanating from lava, from vol ...
*
Breathing gas A breathing gas is a mixture of gaseous chemical elements and compounds used for 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 and enclosed ...
*
Wind Wind is the natural movement of atmosphere of Earth, air or other gases relative to a planetary surface, planet's surface. Winds occur on a range of scales, from thunderstorm flows lasting tens of minutes, to local breezes generated by heating ...

* * *