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An ideal gas is a theoretical gas composed of many randomly moving point particles that are not subject to interparticle interactions.^[1] The ideal gas concept is useful because it obeys the ideal gas law, a simplified equation of state, and is amenable to analysis under statistical mechanics. The requirement of zero interaction can often be relaxed if, for example, the interaction is perfectly elastic or regarded as point-like collisions.

Under various conditions of temperature and pressure, many real gases behave qualitatively like an ideal gas where the gas molecules (or atoms for monatomic gas) play the role of the ideal particles. Many gases such as nitrogen, oxygen, hydrogen, noble gases, some heavier gases like carbon dioxide and mixtures such as air, can be treated as ideal gases within reasonable tolerances^[2] over a considerable parameter range around standard temperature and pressure. Generally, a gas behaves more like an ideal gas at higher temperature and lower pressure,^[2] as the potential energy due to intermolecular forces becomes less significant compared with the particles' kinetic energy, and the size of the molecules becomes less significant compared to the empty space between them. One mole of an ideal gas has a volume of 22.710 954 64... litres (exact value based on 2019 redefinition of the SI base units)^[3] at standard temperature and pressure (a temperature of 273.15 K and an absolute pressure of exactly 10⁵ Pa).^{[note 1]}

The ideal gas model tends to fail at lower temperatures or higher pressures, when intermolecular forces and molecular size becomes important. It also fails for most heavy gases, such as many refrigerants,^[2] and for gases with strong intermolecular forces, notably water vapor. At high pressures, the volume of a real gas is often considerably larger than that of an ideal gas. At low temperatures, the pressure of a real gas is often considerably less than that of an ideal gas. At some point of low temperature and high pressure, real gases undergo a phase transition, such as to a liquid or a solid. The model of an ideal gas, however, does not describe or allow phase transitions. These must be modeled by more complex equations of state. The deviation from the ideal gas behavior can be described by a dimensionless quantity, the compressibility factor, Z.

The ideal gas model has been explored in both the Newtonian dynamics (as in "kinetic theory") and in quantum mechanics (as a "gas in a box"). The ideal gas model has also been used to model the behavior of electrons in a metal (in the Drude model and the free electron model), and it is one of the most important models in statistical mechanics.

If the pressure of an ideal gas is reduced in a throttling process the temperature of the gas does not change. (If the pressure of a real gas is reduced in a throttling process, its temperature either falls or rises, depending on whether its Joule–Thomson coefficient is positive or negative.)

Types of ideal gas

There are three basic classes of ideal gas:^{[citation needed]}

• the classical or Maxwell–Boltzmann ideal gas,
• the ideal quantum Bose gas, composed of bosons, and
• the ideal quantum Fermi gas, composed of fermions.

The classical ideal gas can be separated into two types: The classical thermodynamic ideal gas and the ideal quantum Boltzmann gas. Both are essentially the same, except that the classical thermodynamic ideal gas is based on classical statistical mechanics, and certain thermodynamic parameters such as the entropy are only specified to within an undetermined additive constant. The ideal quantum Boltzmann gas overcomes this limitation by taking the limit of the quantum Bose gas and quantum Fermi gas in the limit of high temperature to specify these additive constants. The behavior of a quantum Boltzmann gas is the same as that of a classical ideal gas except for the specification of these constants. The results of the quantum Boltzmann gas are used in a number of cases including the Sackur–Tetrode equation for the entropy of an ideal gas and the Saha ionization equation for a weakly ionized plasma.

Classical thermodynamic ideal gas

The classical thermodynamic properties of an ideal gas can be described by two equations of state:^[6][7]

Ideal gas law

The ideal gas law is the equation of state for an ideal gas, given by:

$${\displaystyle PV=nRT}$$

• P is the pressure
• V is the volume
• n is the amount of substance of the gas (in moles)
• T is the absolute temperature
• R is the gas constant, which must be expressed in units consistent with those chosen for pressure, volume and temperature. For example, in SI units R = 8.3145 J⋅K⁻¹⋅mol⁻¹ when pressure is expressed in pascals, volume in cubic meters, and absolute temperature in kelvin.

The ideal gas law is an extension of experimentally discovered gas laws. It can also be derived from microscopic considerations.

Real fluids at low density and high temperature approximate the behavior of a classical ideal gas. However, at lower temperatures or a higher density, a real fluid deviates strongly from the behavior of an ideal gas, particularly as it condenses from a gas into a liquid or as it deposits from a gas into a solid. This deviation is expressed as a compressibility factor.

This equation is derived from

• Boyle's law: ${\displaystyle V\propto {\frac {1}{P}}}$;
• Charles's law: ${\displaystyle V\propto T}$;
• Avogadro's law: ${\displaystyle V\propto n}$.

After combining three laws we get

${\displaystyle V\propto {\frac {nT}{P}}}$

That is:

${\displaystyle V=R\left({\frac {nT}{P}}\right)}$

${\displaystyle PV=nRT}$.

Internal energy

The other equation of state of an ideal gas must express Joule's second law, that the internal energy of a fixed mass of ideal gas is a function only of its temperature, with ${\displaystyle U=U(n,T)}$. For the present purposes it is convenient to postulate an exemplary version of this law by writing:

${\displaystyle U={\hat {c}}_{V}nRT}$

where

• U is the internal energy
• ĉ_V is the dimensionless specific heat capacity at constant volume, approximately 3/2 for a monatomic gas, 5/2 for diatomic gas, and 3 for non-linear molecules if we treat translations and rotations classically and ignore quantum vibrational contribution and electronic excitation. These formulas arise from application of the classical equipartition theorem to the translational and rotational degrees of freedom. ^[8]

That U for an ideal gas depends only on temperature is a consequence of the ideal gas law, although in the general case ĉ_V depends on temperature and an integral is needed to compute U.

Microscopic model

In order to switch from macroscopic quantities (left hand side of the following equation) to microscopic ones (right hand side), we use

${\displaystyle nR=Nk_{\mathrm {B} }}$

where

• ${\displaystyle N}$ is the number of gas particles
• ${\displaystyle k_{\mathrm {B} }}$ is the Boltzmann constant (1.381×10⁻²³ J·K⁻¹).

The probability distribution of particles by velocity or energy is given by the Maxwell speed distribution.

The ideal gas model depends on the following assumptions:

• The molecules of the gas are indistinguishable, small, hard spheres
• All collisions are elastic and all motion is frictionless (no energy loss in motion or collision)
• Newton's laws apply
• The average distance between molecules is much larger than the size of the molecules
• The molecules are constantly moving in random directions with a distribution of speeds
• There are no attractive or repulsive forces between the molecules apart from those that determine their point-like collisions
• The only forces between the gas molecules and the surroundings are those that determine the point-like collisions of the molecules with the walls
• In the simplest case, there are no long-range forces between the molecules of the gas and the surroundings.

The assumption of spherical particles is necessary so that there are no rotational modes allowed, unlike in a diatomic gas. The following three assumptions are very related: molecules are hard, collisions are elastic, and there are no inter-molecular forces. The assumption that the space between particles is much larger than the particles themselves is of paramount importance, and explains why the ideal gas approximation fails at high pressures.

Heat capacity

The dimensionless heat capacity at constant volume is generally defined by

${\displaystyle {\stackrel{^<!--\; ^\; -->}{c}}_V=\frac{1}{nR}T{\left(\frac{\mathrm{\partial <!--\; \partial \; -->}S}{\mathrm{\partial <!--\; \partial \; -->}T}\right)}_V=}$Zdroj:https://en.wikipedia.org?pojem=Ideal_gas
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