This page is about the physical properties of gas as a state of matter. For the uses of gases, and other meanings, see Gas (disambiguation).
Gas is one of three classical states of matter. Near absolute zero, a substance exists as a solid. As heat is added to this substance it melts into a liquid at its melting point (see phase change), boils into a gas at its boiling point, and if heated high enough would enter a plasma state in which the electrons are so energized that they leave their parent atoms from within the gas. A pure gas may be made up of individual atoms (e.g. a noble gas or atomic gas like neon), elemental molecules made from one type of atom (e.g. oxygen), or compound molecules made from a variety of atoms (e.g. carbon dioxide). A gas mixture would contain a variety of pure gases much like the air. What distinguishes a gas from liquids and solids is the vast separation of the individual gas particles. This separation usually makes a colorless gas invisible to the human observer. The interaction of gas particles in the presence of electric and gravitational fields are considered negligible as indicated by the constant velocity vectors in the image.
The gaseous state of matter is found 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 increased attention these days. High-density atomic gases super cooled to incredibly low temperatures are classified by their statistical behavior as either a Bose gas or a Fermi gas. For a comprehensive listing of these exotic states of matter see list of states of matter.
As most gases are difficult to observe directly with our senses, they are described through the use of four physical properties or macroscopic characteristics: the gas’s pressure, volume, number of particles (chemists group them by moles), and temperature. These four characteristics were repeatedly observed by men such as Robert Boyle, Jacques Charles, John Dalton, Joseph Gay-Lussac and Amedeo Avogadro for a variety of gases in a great many settings. Their detailed studies ultimately led to a mathematical relationship among these properties expressed by the ideal gas law (see simplified models section below).
Gas particles are widely separated from one another, and as such do not influence adjacent particles to the same degree as liquids or solids. This influence (intermolecular forces) results from the magnetic charges that these gas particles carry. Like charges repel, while oppositely charged particles attract one another. Gases made from ions carry permanent charges, as do compounds with their polar covalent bonds. These polar covalent bonds produce permanent charge concentrations within the molecule while the compound's net charge remains neutral. Transient charges exist in covalent bonds of molecules and are referred to as van der Waals forces. The interaction of these intermolecular forces varies within a substance which determines many of the physical properties unique to each gas. A quick 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 an incredibly low density and viscosity. Pressure 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.
When observing a gas, it is typical to specify a frame of reference or length scale. A larger length scale corresponds to a macroscopic 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. By way of contrast, a smaller length scale corresponds to a microscopic or particle point of view.
From this global vantage point, the gas characteristics measured are either in terms of the gas particles themselves (velocity, pressure, or temperature) or their surroundings (volume). By way of example, Robert Boyle studied pneumatic chemistry for a small portion of his career. One of his experiments related the macroscopic properties of pressure and volume of a gas. His experiment used a J-tube manometer which looks like a test tube 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 locking the number of particles and temperature. He observed that when the pressure was increased on the gas, by adding more mercury to the column, the trapped gas volume decreased. Mathematicians describe this situation as an inverse relationship. Furthermore, when Boyle multiplied the pressure and volume of each observation, the product (math) was always the same, a constant. This relationship held true for every gas that Boyle observed leading to the law, (PV=k), named to honor his work in this field of study.
There are many math tools to choose from when analyzing gas properties. As gases are subjected to extreme conditions, the math tools become a bit more complex, from the Euler equations (inviscid flow) to the Navier-Stokes equations that fully account for viscous effects. These equations are tailored to meet the unique conditions of the gas system in question. Boyle's lab equipment allowed the use of algebra 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 enable 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, to include statistics and multivariable calculus, makes possible the solution to such complex dynamic situations as space vehicle reentry. One such example might be the analysis of the image depicting space shuttle reentry to ensure the material properties under this loading condition are not exceeded. It is safe to say that in this flight regime, the gas is no longer behaving ideally.
- Main article: 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 (or absolute pressure) refers to the average force the gas exerts on the surface area 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 of the particle. As a reminder from classical mechanics, momentum, by definition, is the product of mass and velocity. Notice that during a collision only the normal component of velocity changes. A particle traveling parallel to the wall never changes its momentum. So the average force on a surface must be the average change in linear momentum from all of these gas particle collisions. To be more precise, 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. The image "Pressurized gases" depicts gas pressure and temperature spikes used in the entertainment industry.
- Main article: Thermodynamic temperature The symbol used to represent temperature in equations is T with SI units of kelvins.
The speed of a gas particle is proportional to its absolute temperature. 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 is related to the motions of the particles (molecules and atoms) which make up the [gas] system. In statistical mechanics, temperature is the measure of the average kinetic energy stored in a particle. The methods of storing this energy are dictated by the degrees of freedom of the particle itself (energy modes). Kinetic energy added (endothermic process) to gas particles by way of collisions produces linear, rotational, and vibrational motion as well. By contrast, a molecule in a solid can only increase its vibration modes with the addition of heat as the lattice crystal structure prevents both linear and rotational motions. These heated gas molecules have a greater speed range which constantly varies due to constant collisions with other particles. The speed range can be described by the Maxwell-Boltzmann distribution. Use of this distribution implies ideal gases near thermodynamic equilibrium for the system of particles being considered.
- Main article: 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 analysis, it is typical to speak of intensive and extensive properties. 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 of protactinium as 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. When the seat ejection is initiated in the rocket sled image the specific volume increases with the expanding gases, while mass is conserved. Since a gas fills any container in which it is placed, volume is an extensive property.
- Main article: Density
The symbol used to represent density in equations is ρ (pronounced 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 mass per volume of a substance or simply, 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 or both. This variation of density is referred to as compressibility. 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 is a simple physical quantity that has a magnitude but no direction associated with it. 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.
If one could observe a gas under a powerful microscope, one would see a collection of particles (molecules, atoms, ions, electrons, etc.) without any definite shape or volume that are in more or less random motion. These neutral gas particles only change direction when they collide with another particle or the sides of the container. By stipulating that these collisions are perfectly elastic, this substance is transformed from a real to an ideal gas. This particle or microscopic view of a gas is described by the Kinetic-molecular theory. All of the assumptions behind this theory can be found in the postulates section of Kinetic Theory.
- Main article: Kinetic theory
Kinetic theory provides insight into the macroscopic properties of gases by considering their molecular composition and motion. Starting with the definitions of momentum and kinetic energy, one can use the conservation of momentum and geometric relationships of a cube to relate macro 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 theory also explains how the gas system responds to change. For example, as a gas is heated from absolute zero, when it is (in theory) perfectly still, its internal energy (temperature) is increased. As a gas is heated, the particles speed up and its temperature rise. This results in greater numbers of collisions with the container sides each second due to the higher particle speeds associated with elevated temperatures. As the number of collisions (per unit time) increase on the surface area of the container, the pressure increases in a proportional manner.
- Main article: 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). 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 as to how they move, but their motion is different from Brownian Motion. The reason is that 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 was examined.
- Main article: van der Waals force
As discussed earlier, momentary attractions (or repulsions) between particles have an effect on gas dynamics. In physical chemistry, the name given to these intermolecular forces is van der Waals force. These forces play a key role in determining physical properties of a gas such as viscosity and flow rate (see physical characteristics section). Ignoring these forces in certain conditions (see Kinetic-molecular theory) allows a real gas to be treated like an ideal gas. This assumption allows the use of ideal gas laws which greatly simplifies the path to a solution.
Proper use of these gas relationships requires us to take one more look at the Kinetic-molecular theory (KMT). When these gas particles possess a magnetic charge or Intermolecular force they gradually influence one another as the spacing between them is reduced (the hydrogen bond model illustrates one example). In the absence of any charge, at some point when the spacing between gas particles is greatly reduced they can no longer avoid collisions between themselves at normal gas temperatures found in a lab. Another case for increased collisions among gas particles would include a fixed volume of gas, which upon heating would contain very fast particles. What this means to us is that these ideal equations provide reasonable results except for extremely high pressure [compressible] or high temperature [ionized] conditions. Notice that all of these excepted conditions allow energy transfer to take place within the gas system. The absence of these internal transfers is what is referred to as ideal conditions (perfect - or well behaved) in which the energy exchange occurs only at the boundaries of the system. Real gases experience some of these collisions and intermolecular forces. When these collisions are statistically negligible [incompressible], results from these ideal equations are still valid. At the other end of the spectrum, when the gas particles are compressed into close proximity they behave more like a liquid, and hence another connection to fluid dynamics.
- Main article: Equation of state
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. The image of first powered flight at Kitty Hawk, North Carolina illustrates one example on the successful application of these relationships in 1903. More recent examples include the 2009 maiden flights of the first solar powered aircraft, the Solar Impulse, and the first commercial airliner to be constructed primarily from composite materials, the Dreamliner.
- Main article: Perfect gas
By definition, a perfect gas is one in which intermolecular forces are negligible due to the separation of the molecules and any particle collisions are elastic.
Perfect gas equation of state
The symbol n represents the number of particles grouped by moles of a substance. All other symbols in these equations use notation described earlier in the Macroscopic Section. These relationships are valid only when used with absolute temperatures and pressures.
- Chemist's version – PV = nRT
The gas constant, R, in this expression has different units than the Gas Dynamicist's version. The Chemist's version emphasizes numbers of particles (n), while the latter emphasizes the particle mass in the density term ρ.
- Gas Dynamicist's version- P = ρRT
There are two subclassifications to a perfect gas although various textbooks either omit or combine the following simplifications into a general "perfect gas" definition. For sake of clarity, these simplifications are defined separately in the following two subsections.
- Main article: Calorically perfect gas
The Calorically perfect gas model is the most restrictive from a temperature perspective, as it adds the following condition:
- Constant specific heats (valid for most gases below 1000 K)
- u = CvT, h = CpT
Although this may be the most restrictive model from a temperature perspective, it is accurate enough to make reasonable predictions within the limits specified. A comparison of calculations for one compression stage of an axial compressor (one with variable Cp, and one with constant Cp) produces a deviation small enough to support this approach. As it turns out, other factors come into play and dominate during this compression cycle. These other effects would have a greater impact on the final calculated result than whether or not Cp was held constant. (examples of these real gas effects include compressor tip-clearance, separation, and boundary layer/frictional losses, etc.)
- Main article: Thermally perfect gas
A thermally perfect gas is:
- in thermodynamic equilibrium
- not chemically reacting (chemical equilibrium)
- cp - cv = R (still valid even though specific heats vary with temperature)
- Internal energy, enthalpy, and specific heats are functions of temperature only.
- u = u(T), h = h(T), du = CvdT, dh = CpdT
This type of approximation is useful for modeling, for example, a turbine where temperature fluctuations are usually not large enough to cause any significant deviations from the thermally perfect gas model. Heat capacity is still allowed to vary, though only with temperature and the molecules are not permitted to dissociate.
An "ideal gas" is a simplified "real gas" with the assumption that the compressibility factor 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.
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 of a jet engine. It may also be useful to keep the elementary reactions and chemical dissociations for calculating emissions.
- Main article: 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 pressure rises, 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). 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 processes 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 (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 reactions 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 re-entry where extremely high temperatures and pressures are present or the gases produced during geological events as in the image of the 1990 eruption of Mount Redoubt.
- Main article: Boyle's Law
- Boyle's Law was perhaps the first expression of an equation of state. In 1662 Robert Boyle, an Irishman, 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. Through these experiments, Boyle noted that the gas volume varied inversely with the pressure. The image of Boyle's Equipment shows some of the exotic tools used by Boyle during his study of gases.
- Boyle's Law - describes a gas in which the number of particles and Temperature are constant.
- PV = constant in this situation constant = nRT from the ideal gas law.
Law of volumesEdit
- Main article: Charles Law
In 1787, the French physicist and balloon pioneer, Jacques Charles, found that oxygen, nitrogen, hydrogen, carbon dioxide, and air expand to the same extent over the same 80 kelvin interval.
In 1802, Joseph Louis Gay-Lussac published results of similar, though more extensive experiments, indicating a linear relationship between volume and temperature. Gay-Lussac credited Charle's earlier work by naming the law in his honor. In the absence of this linkage, Dalton could have been in contention for this honor for his previously published work on partial pressures.
- Law of Volumes - Both Charles and Gay-Lussac played a role in developing this relationship
- V/T = constant - notice that constant = nR/P from the ideal gas law.
- Main article: Avogadro's law
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 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 and is referred to as the molar volume.
- Avogadro's Law - describes a gas in a container in which the pressure and temperature are constant. The simplified form for the ideal gas law follows:
- V/n = constant – notice that constant = RT/P from the ideal gas law.
- Main article: Dalton's law
In 1801, John Dalton published the Law of Partial Pressures from his work with ideal gas law relationship: The pressure of a mixture of 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 + ... + Pressuren
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).
- Main article: Compressibility factor
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.
- Main article: 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 Reynold's number provides the link between modeling results (design) and the full scale actual conditions. It can also be used to characterize the flow.
- Main article: 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. From the image of air flowing past a delta wing, it is clear that the gas particles stick to one another (see discussion on boundary layer below).
- Main article: 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 just one example.
- Main article: 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 image below and to the right clearly shows the boundary layer thickening as the flow moves past the point from right to left along the leading edge.
Maximum entropy principleEdit
- Main article: Principle of maximum entropy
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." 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.
- Main article: 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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- ↑ Considering when this text was published, it thoroughly covers the three phases of matter "known" at the time. McPherson, pp.104-10
- ↑ This early 1900's discussion infers what is regarded as the plasma state. See page 137 of American Chemical Society, Faraday Society, Chemical Society (Great Britain)'s The Journal of physical chemistry, Volume 11 (Cornell - 1907).
- ↑ The work by T. Zelevinski provides another link to latest research about Strontium in this new field of study. See Tanya Zelevinsky (2009). "84Sr—just right for forming a Bose-Einstein condensate". Physics 2: 94, http://physics.aps.org/articles/v2/94.
- ↑ ScienceDaily 4 November 2009 provides a link to more material on the Bose-Einstein condensate.
- ↑ The authors make the connection between molecular forces of metals and their corresponding physical properties. By extension, this concept would apply to gases as well, though not universally. (Cornell - 1907) pp. 164-5.
- ↑ One noticeable exception to this physical property connection is conductivity which varies depending on the state of matter (ionic compounds in water) as described by Michael Faraday in the 1833 when he noted that ice does not conduct a current. See page 45 of John Tyndall's Faraday as a Discoverer (1868).
- ↑ John S. Hutchinson (2008). Concept Development Studies in Chemistry. p. 67, http://cnx.org/content/col10264/latest/.
- ↑ Anderson, p.501
- ↑ J. Clerk Maxwell (1904). Theory of Heat. Mineola: Dover Publications. pp. 319–20. ISBN 0486417352.
- ↑ See pages 137-8 of Society (Cornell - 1907).
- ↑ Kenneth Wark (1977). Thermodynamics (3 ed.), McGraw-Hill. p. 12. ISBN 0-07-068280-1.
- ↑ For assumptions of Kinetic Theory see McPherson, pp.60-61
- ↑ Anderson, pp.289-291
- ↑ Anderson, p.291
- ↑ Implies temperature limited to 1500 K. See John p.256
- ↑ John p.205
- ↑ John pp.247-56
- ↑ McPherson, pp.52-55
- ↑ McPherson, pp.55-60
- ↑ John P. Millington (1906). John Dalton. pp. 72, 77–78.
- ↑ Online Etymology Dictionary
- John D. Anderson (1984). Fundamentals of Aerodynamics, McGraw-Hill Higher Education. ISBN 0070016569.
- James John (1984). Gas Dynamics, Allyn and Bacon. ISBN 0-205-08014-6.
- William McPherson and William Henderson (1917). An Elementary study of chemistry.
- Philip Hill and Carl Peterson. Mechanics and Thermodynamics of Propulsion: Second Edition Addison-Wesley, 1992. ISBN 0-201-14659-2
- National Aeronautics and Space Administration (NASA). Animated Gas Lab. Accessed February, 2008.
- Georgia State University. HyperPhysics. Accessed February, 2008.
- Antony Lewis WordWeb. Accessed February, 2008.
- Northwestern Michigan College The Gaseous State. Accessed February, 2008.af:Gas
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