The degenerate gas

Gas degeneracy ensues with a decrease in its temperature to the some value, called degeneration temperature. Complete degeneration corresponds to the absolute of zero temperatures.

The influence of the identity of particles is shown the more essential, the less the average distance between particles R in comparison with the De Broglie wavelength the particles of lyamda = h/mv (t - mass of particle, v - its speed, h - Planck constant). This explains by the fact that the classical mechanics is applicable to the particle motion of the gas only with condition R > > of lyamda. Since the velocity of the particles of the gas is connected with the temperature (the greater the speed, the higher the rate -.pa), then the rate -.pa of degeneration, that determines the limit of the applicability of classical theory, the higher, the less the mass of the particles of the gas and the greater its density (i.e. the less the average distance between the particles). Therefore the rate -.pa of degeneration it is especially great (order 10 000 k) for the electron gas in the metals: the mass of electrons is very small (~ 10^-27 g), and their density in the metals is very great (10²² electrons in 1 cm³). Electron gas in the metals is degenerated with all rate -.pax, with which the metal remains in the solid state.

For the usual atomic and molecular gases the rate -.pa of degeneration it is close to abs. zero, so that this gas practically always behaves as classical (with such low rate -.pax all substances they find in the solid state, except helium, which is been quantum liquid with as as desired close ones to abs. zero temperatures).

Since the nature of the non-load-bearing influence of identical particles on each other is various for the particles with the integral (bosons) and half-integral (fermions) spin, behavior of gas from the fermions (Fermi gas) and from the bosons (Bose gas) will be also different during the degeneration.

All lower energ. levels up to some maximum, called Fermi level are filled in Fermi gas ( which includes the electron gas in the metal) during the complete degeneration (with T = o k), and all subsequent remain empty. An increase in the temperature only insignificantly changes this distribution of the electrons of metal along the levels: the small share of electrons, which are located on the levels, close to the Fermi level, passes to the empty levels with the larger energy, freeing thus the levels lower than Fermi, from which was perfected the passage.

With the gas degeneracy of bosons from the particles with the different from zero masses (such bosons they can be atoms and molecule) a some fraction of the particles of the system must convert to state with the zero pulse; these are phenomenon NAZ. Base- Einstein by condensation. The nearer the rate -.pa to abs. zero, the greater the particles must prove to be in this state. However, as has already been spoken, the systems of such particles with a temperature decrease to the very low values convert to the solid or liquid (for helium) states, in which power interactions between the particles are significant and therefore the approximation of perfect gas is not applicable to which. The phenomenon of the Boses - Einstein condensation in liquid helium, whom can be considered as imperfect gas from Vol. n. quasi-particles, it leads to the appearance of superfluidity.

For the gas from the bosons of the zero mass, which include the photons (spin 1), degeneration temperature is equal to infinity; therefore photon gas - always degenerated and classical statistics to it is applicable not with what conditions. Photon gas is the only degenerate ideal Bose gas of stable particles. However, Bose- Einstein condensations in it does not occur, since there does not exist photons with the zero pulse (photons always tyuey dvizhutsya with the speed of light). Photon gas ceases to exist at a zero abs. temperature.

See also statistical physics, metals, semiconductors and lit. with these articles. G. 4. Myakishev.