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, 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. Noble gases, and mixtures such as air, have a considerable parameter range around standard temperature and pressure. Generally, a gas behaves more like an ideal gas at higher temperature and lower pressure, 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 22.71095464... L (exact value based on 2019 revision of the SI) at standard temperature and pressure (a temperature of 273.15 K and an absolute pressure of exactly 105 Pa). The ideal gas model tends to fail at lower temperatures or higher pressures, where intermolecular forces and molecular size become important. It also fails for most heavy gases, such as many refrigerants, 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:
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:
Ideal gas law
The ideal gas law is the equation of state for an ideal gas, given by:
P V = n R T {\displaystyle PV=nRT}
where
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: V ∝ 1 P {\displaystyle V\propto {\frac {1}{P}}} ; Charles's law: V ∝ T {\displaystyle V\propto T} ; Avogadro's law: V ∝ n {\displaystyle V\propto n} . After combining three laws we get
V ∝ n T P {\displaystyle V\propto {\frac {nT}{P}}}
That is:
V = R ( n T P ) {\displaystyle V=R\left({\frac {nT}{P}}\right)}
P V = n R T {\displaystyle PV=nRT} .
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