Gas
The gaseous state of matter occurs between the liquid and plasma states,[2] the latter of which provides the upper-temperature boundary for gases. Bounding the lower end of the temperature scale lie degenerative quantum gases[3] which are gaining increasing attention.[4] High-density atomic gases super-cooled to very low temperatures are classified by their statistical behavior as either Bose gases or Fermi gases. For a comprehensive listing of these exotic states of matter, see list of states of matter.
Elemental gases
The only
(Rn) – these gases are referred to as "elemental gases".Etymology
The word gas was first used by the early 17th-century
An alternative story is that Van Helmont's term was derived from "gahst (or geist), which signifies a ghost or spirit".[8] That story is given no credence by the editors of the Oxford English Dictionary.[9] In contrast, the French-American historian Jacques Barzun speculated that Van Helmont had borrowed the word from the German Gäscht, meaning the froth resulting from fermentation.[10]
Physical characteristics
Because most gases are difficult to observe directly, they are described through the use of four
Gas particles are widely separated from one another, and consequently, have weaker intermolecular bonds than liquids or solids. These
Compared to the other states of matter, gases have 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.
Macroscopic view of gases
When observing a gas, it is typical to specify a frame of reference or
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
There are many mathematical tools available for analyzing gas properties. As gases are subjected to extreme conditions, these tools become more complex, from the
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 is the sum of all the
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
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
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
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 view of gas is well-described by statistical mechanics, but it can be described by many different theories. The kinetic theory of gases, which makes the assumption that these collisions are perfectly elastic
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
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 (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 is above zero-point energy, 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 macroscopic, measurable quantity of pressure, is the direct result of these microscopic 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
Using the partition function to find the energy of a molecule, or system of molecules, can sometimes be approximated by the Equipartition theorem, 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 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.[19]
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 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
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 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, and a short-range repulsion due to electron-electron exchange interaction (which is related to the Pauli exclusion 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.[20] 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:[21]
- 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.[22] Each successive model expands the temperature range of coverage to which it applies.
Ideal and perfect gas
The equation of state for an ideal or perfect gas is the ideal gas law and reads
where P is the pressure, V is the volume, n is amount of gas (in mol units), R is the
where 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 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.[23] 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).[24] 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
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.[25]
Historical research
Boyle's law
Boyle's law was perhaps the first expression of an equation of state. In 1662 Robert Boyle 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.[26] 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:
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:
Charles's 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. He noted that, for an ideal gas at constant pressure, the volume is directly proportional to its temperature:
Gay-Lussac's law
In 1802, Joseph Louis Gay-Lussac published results of similar, though more extensive experiments.[27] 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.
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 physical constant that bears his name (the Avogadro constant) is the number of atoms per mole of elemental carbon-12 (6.022×1023 mol−1). This specific number of gas particles, at standard temperature and pressure (ideal gas law) occupies 22.40 liters, which is referred to as the molar volume.
Avogadro's law states that the volume occupied by an ideal gas is proportional to the amount of substance in the volume. This gives rise to the molar volume of a gas, which at STP is 22.4 dm3/mol (liters per mole). The relation is given by
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 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 + ... + 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:[28]
- 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 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
Maximum entropy principle
As the total number of degrees of freedom approaches infinity, the system will be found in the
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.
To From
|
Solid | Liquid | Gas | Plasma |
---|---|---|---|---|
Solid | Melting | Sublimation | ||
Liquid | Freezing | Vaporization | ||
Gas | Deposition | Condensation | Ionization | |
Plasma | Recombination |
See also
Notes
- ^ "Gas". Merriam-Webster. 7 August 2023.
- ^ This early 20th century discussion infers what is regarded as the plasma state. See page 137 of American Chemical Society, Faraday Society, Chemical Society (Great Britain) The Journal of Physical Chemistry, Volume 11 Cornell (1907).
- S2CID 14321276.
- ^ "Quantum Gas Microscope Offers Glimpse Of Quirky Ultracold Atoms". ScienceDaily. Retrieved 2023-02-06.
- ^ Helmont, Jan Baptist Van (1652). Ortus medicine, id est initial physicae inaudita... authore Joanne Baptista Van Helmont,... (in Latin). apud L. Elzevirium. The word "gas" first appears on page 58, where he mentions: "... Gas (meum scil. inventum) ..." (... gas (namely, my discovery) ...). On page 59, he states: "... in nominis egestate, halitum illum, Gas vocavi, non longe a Chao ..." (... in need of a name, I called this vapor "gas", not far from "chaos" ...)
- ^ Ley, Willy (June 1966). "The Re-Designed Solar System". For Your Information. Galaxy Science Fiction. pp. 94–106.
- ^ Harper, Douglas. "gas". Online Etymology Dictionary.
- ^ Draper, John William (1861). A textbook on chemistry. New York: Harper and Sons. p. 178.
- ^ ""gas, n.1 and adj."". OED Online. Oxford University Press. June 2021.
There is probably no foundation in the idea (found from the 18th cent. onwards, e.g. in J. Priestley On Air (1774) Introd. 3) that van Helmont modelled gas on Dutch geest spirit, or any of its cognates
- ^ Barzun, Jacques (2000). For Dawn to Decadence: 500 Years of Western Cultural Life. New York: HarperCollins Publishers. p. 199.
- ^ 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 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.
- ^ Anderson, p.501
- ISBN 978-0-486-41735-6.
- ^ See pages 137–8 of Society, Cornell (1907).
- ISBN 978-0-07-068280-1.
- ^ For assumptions of kinetic theory see McPherson, pp.60–61
- ^ Jeschke, Gunnar (26 November 2020). "Canonical Ensemble". Archived from the original on 2021-05-20.
- ^ "Lennard-Jones Potential - Chemistry LibreTexts". 2020-08-22. Archived from the original on 2020-08-22. Retrieved 2021-05-20.
- ^ "14.11: Real and Ideal Gases - Chemistry LibreTexts". 2021-02-06. Archived from the original on 2021-02-06. Retrieved 2021-05-20.
- ^ Anderson, pp. 289–291
- ^ John, p.205
- ^ John, pp. 247–56
- ^ "Permanent gas". www.oxfordreference.com. Oxford University Press. Retrieved 3 April 2021.
- ^ McPherson, pp.52–55
- ^ McPherson, pp.55–60
- ^ John P. Millington (1906). John Dalton. pp. 72, 77–78.
References
- ISBN 978-0-07-001656-9.
- John, James (1984). Gas Dynamics. Allyn and Bacon. ISBN 978-0-205-08014-4.
- McPherson, William; Henderson, William (1917). An Elementary study of chemistry.
Further reading
- 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.
- Lewes, Vivian Byam; Lunge, Georg (1911). Encyclopædia Britannica. Vol. 11 (11th ed.). p. 481–493. .