Gases

G. possess a number of characteristic properties. They completely fill the vessel, in which they are located, and takes its form. In contrast to solid bodies and liquids, the volume g. depends substantially on the pressure and the temperature. The coeff.s of volume expansion g. under the normal conditions (O -100°S) two orders are higher than in liquids, and it comprises in average 0,003663 deg^-1. In table are cited the data about phys. properties most common G.

Any substance can be converted to gaseous state by the proper selection of pressure and temperature. Therefore the possible domain of existence of gaseous state graphically is conveniently depicted in the variables: pressure r - rate -.pa T (in r, T- diagram, Fig. 1). At temperatures lower than critical T_to (see critical state) this region is limited by sublimation curves (sublimation) I and vaporization II. This means that at any pressure lower than critical r_k there is a temperature T (see Fig. 1), determined of sublimation curve or vaporization, higher than which substance becomes gaseous. In the states on the curve THE I (lower than the triple point T_r) gas is located in the equilibrium with the solid (solid phase), and on curved II (between the triple and crit. point K) - with the liquid phase. Gas in these states is usually called vapor of substance.

Fig. 1. r, T- diagram of the state of substance. The region of gaseous state is shaded. From the side of low temperatures and pressures it is limited by sublimation curves (I) and vaporization (II). Tr - triple point, k - critical point. Broken line showed the critical isochore of substance.

At temperatures below T_toit is possible to condense g. - to convert it to other state of aggregation (solid or liquid). In this case phase transformation g. into the liquid or solid body occurs spasmodically: a very small change in the pressure leads to final change in the number of the properties of substance (for example, PLOtto nosti, enthalpy, heat capacity , etc.). The processes of condensation g., especially the liquefaction of gases, have great technical value.

The boundary of gaseousregion is conditional with T>T _k, since the phase transformations do not occur at these temperatures. In a number of cases beyond the conditional boundary between g. and liquid with super-crit. rate -.pax and pressures assume crit.. the isochore of substance (curve of a constant density or specific volume, cm, Fig. 1), into neposredstv. of proximity of which the properties of substance change, although not abruptly, it is especially rapid.

In connection with the fact that the region of the gaseous state is very extensive, properties g. with a change in the temperature and pressure can change over wide limits. Thus, under normal conditions (with 0°S and atmospheric pressure) density g. is approximately 1000 times lower than the density of the same substance in the solid or liquid state. At room temperature, but pressure, in 10¹⁷ times of smaller than the atmospheric (limit, achieved by contemporary. by vacuum technology), density g. composes ok. 10^-20g/sm³. In kosmich. conditions the density g. can be 10 more orders less (~y0 ^-30g/sm³).

From other side, at high pressures the substance, which with super-crit. rate -.pax it is possible to consider g., possesses the enormous density (for example, in the center of some zvezd~y0⁹ g/sm³). Depending on conditions over wide limits change other properties g. - thermal conductivity, viscosity, etc.

Molecular-kinetic theory G. molekulyarno-kineticheskaya theory considers g. as the totality of the weakly interacting particles (molecules or atoms), find in the continuous chaotic (thermal) motion. On the basis of these simple ideas of kinet. theory it is possible to explain by osn phys. of property g., it is especially full - property rarefied G.

In sufficiently rarefied g. the medium intermolecular distances occur considerably more than the radius of action of intermolecular forces. Thus, for example, with the standard conditions into 1 sm^{of 3} g. are located ~ 10¹⁹ molecules and the average distance between them composes ~ 10^-6 sm, or ~y00A, whereas intermolecular interaction is not substantial at the distances more than shch-y0A. Consequently, under such conditions molecules interact only with the rapprochement up to the distance of the action of intermolecular forces. This rapprochement is accepted to treat as the collision of molecules. The radius of action of intermolecular forces in the example is 10-20 times examined lower than the medium intermolecular distance, so that the total volume, in which these forces can be shown (as "their own volume" of all molecules), composes 10~³ - 10~⁴ from the total volume Of g. eto it makes possible to count sobstv. the volume of molecules g. under normal conditions for negligible and to consider molecules as material points. Gas, whose the molecules are considered as the not interacting with each other material points, NAZ by ideal. With the thermal equilibrium

ideal g. all directions of the motion of its molecules are equally probable, and speeds are distributed in accordance with Maxwell by distribution. Fig. 2 gives the graph of this distribution for nitrogen at temperatures 20 and shch00°S. It is evident from the graph that the overwhelming majority

Fig. 2. Maxwellian distribution for the molecules of nitrogen at temperatures 20 and shch00°S. Along the Y-axis is postponed the share of the molecules (in %), which possess speeds between with and (with + 10) m/s; with_n - most probable speed, which possesses the greatest number of molecules at this temperature; - arithmetic mean speed of molecules;  - mean square velocity.

molecules has the close values of the speed (maximum of curve it corresponds to the speed most probable at this temperature), but there exists also the iznostnaya part of the molecules with the small and very high speeds. With the aid of the Maxwellian distribution can be determined by Vol. n. the mean square velocity of molecules  connected with the temperature T of gas by the relationship

(1)

Here k - Boltzmann constant, t - molecular mass. Equation (1) makes it possible to establish the connection between the average of kinetich. by energy of one molecule and with the temperature of the gas:

(2)

This dependence frequently considers as the molecular- kinet. interpretation of temperature - rate -.pa is a measure of kinetich. energy of molecules.

Since the molecules ideal g. possess only kinetich. by energy, internal energy such a g. does not depend on the occupied by it volume (Joule's law).

Molecular- kinet. theory examines pressure g. on the walls of the vessel, in which it is located as the action of the impacts of molecules, averaged on the surface and the time. Pressure r is quantitatively determined by the pulse, transferred by molecules per unit time to the unit of the area of the wall:

(3)

where p - number of molecules per unit of volume. Equ. (2) and (3) make it possible to write down equation of state ideal g. in the form

(4)

Equ. (4), recorded for 1 moles g., containing N = of ',0è*y0^{of 23} molecules (see Avogadro's number), call Clapeyron the equation:

(5)

Here R = kN - universal gas constant, v - volume, which falls on 1 mole. Clapeyron's equ. generalizes empirich. the gas laws of Boyle - Mariotte and Gay-Lussac (see Boyle - Mariotte law, Gay-Lussac laws). It follows also from equ.( 5) that at identical to temperature and pressure ideal g., undertaken in a quantity 1 maboutl4, have equal volumes and in any such g. per unit of volume an equal quantity of molecules (see Avogadro's law) is contained.

Under the conditions of thermal equilibrium the rate -.pa and pressure g. throughout entire its volume are identical, molecules dvizhutsya chaotically, in g. there are no regulated flows. Appearance in g. of drops (gradients) in the temperature or pressure leads to disruption of equilibrium and transfer in the direction of the gradient of energy, mass or other phys. of values.

Kinet. property g. - thermal conductivity, diffusion, viscosity - molecular- kinet. theory examines from unity of opinion: diffusion as transfer by the molecules of mass, thermal conductivity as transfer by them energy, viscosity as the transfer of momentum. Model ideal g. for the analysis of the transport phenomena is unfit, since in these processes play the significant role the collisions of molecules (with which occurs the transfer of some of the transferable quantities, for example, energy) and the "size" of molecules (influencing collision rate). Therefore in the simplest case of transport phenomenon in g. they are examined for rarefied g., whose the molecules in the first approximation, are considered elastic balls the specific diameter and, these balls interacting with each other only at the moment of collision. In this approximation the diameter of molecule is connected with simple correlation with its mean free path

(6)

Sizesubstantially affects the processes of the transfer in rarefied G, in particular, if the significant dimension of the volume, occupied by g., is greater, then thermal conductivity and viscosity g. do not depend on pressure. On the contrary, when  it is more than significant dimension, thermal conductivity and viscosity g. with the decrease of the pressure (but it means, and the collision frequencies) begin to fall. On this phenomenon, in particular, are based the teshyuizoliruyushchiye properties of vessels with the double walls, air between which is evacuated (see Dewar vessel vessels). In a stricter molecular theory with the analysis of transport phenomena in the rarefied gases interaction of molecules with any distances between them is considered. The nature of interaction is determined by Vol. n. by the potential of interaction (see intermolecular interaction). A strict examination of the dynamics of pairwise interactions (collisions) leads to the fact that in the formulas for calculating the transfer coefficients the integrals of collisions, which are been the functions only of reduced temperature, appear by Vol. n. . This rate -.pa characterizes the relation of kinetich. energy of molecules (~.kT) to their potential energy (- potential well depth with this potential of interaction). The integrals of collisions consider the circumstance that the colliding molecules depending on their kinetich. of energy, and it means temperatures g., they can converge up to different distances, i.e. seemingly change their effective size.

Properties real g. with an increase in the density change property g., they cease to be ideal. Equation of state (5) proves to be inapplicable, since the medium intermolecular distances g. become comparable with a radius of intermolecular interaction. For describing the thermo-dynamic properties of imperfect, or as they more frequently are called, real, g. use different equation of states, which have more or less strict teo-retpch. substantiation. By the simplest example of equation, which qualitatively correctly describes osn of difference real g. from the ideal, serves Van der Waals equ.. It considers, from one side, existence of attracting forces between the molecules (their action leads to the decrease of pressure G.), from other side - repulsive forces, which impede limitless compression g. (see Van der Waals equation).

To those most theoretically substantiated, in any case for the states, removed from the crit. point, relates virial"noye equation of state:

(7)

The values of virial coefficients v, etc. are determined by molecular collisions: paired (c), triple of (S) and higher order for the subsequent coefficients. It is significant that the virial coeff.s are the functions only of temperature.

In g. of low density are most probable the paired collisions of molecules, i.e. for such a g. in expansion (7) it is possible to disregard all terms after term coeff.. In. In accordance with the temperature change v, with Vol. n. to Boyle temperature T_v (see Boyle point) in it becomes zero, and moderately dense g. behaves as ideal, i.e. it is subordinated to equ. (5). Physically this means that with T_by the intermolecular attracting forces and repulsion practically they compensate each other. Existence of intermolecular interaction to one degree or another affects all properties real g. vnutr. energy real g. proves to be depending on its volume (from the intermolecular distances), since potential energy of molecules is determined by their relative distances.

With intermolecular interaction is connected also a change in the temperature real g. with its flow with the small constant velocity through the porous diaphragm (this process NAZ. by throttling). As the measure for a change in the temperature g. during the throttling it serves joule - Thomson coeff.., which depending on conditions can be positive (cooling G.), negative (heating G.) or equal to zero with Vol. n. to inversion temperature (see joule - Thomson phenomenon). The effect of cooling g. during the throttling widely adapts in the technology as one of the methods of the liquefaction of gases.

The internal structure of molecules g. weakly influences their therm. properties (pressure, temperature, density and the connection between them). For these svrystv in the first approximation, is essential only molecular weight G. naprotiv, kalorich. of property g. (heat capacity, entropy, etc.), and also his elektrich. and magnetic properties depend substantially on vnutr. of the structure of molecules. For example, for calculating (in the first approximation) the heat capacity g. at a constant volume c_v it is necessary to know the number vnutr. of the degrees of freedom of molecule (i.e. the number of possible vnutr. of motions) i_vn. In accordance with equipartition the law of the classical of statistical physics to each degree of freedom of molecule g. (progressive, oscillating, rotatory) is the energy, equal to 1/2 *kT. Hence the heat capacity of 1 moles

(8)

For the precise calculation of kalorich. of properties g. it is necessary to know the energy levels of the molecules, the information about which in the majority of the cases are obtained from the analysis of spectra g. for the large number of substances in the state ideal g. of kalorich. of property they are calculated with the high accuracy and their values are represented in the form of tables to temperatures of 10-22 thousand degrees.

Elec. properties g. are connected first of all with the possibility of the ionization of molecules or atoms, i.e. with the advent of in g. of the electrically charged particles (ions and electrons). In the absence of the charged particles g. they are good dielectrics. With an increase in the concentration of charges the electrical conductivity g. increases. The dependence of electrical conductivity g. on different the phys. of factors is examined in st. Electrical discharge through gases.

With rate -.pax beginning from several thousand degrees any g. partially it is ionized and it is converted into the plasma. If the concentration of charges in the plasma is small, then its properties differ little from the properties usual G.

According to the magnetic properties g. they are divided into the diamagnetic (to them they relate, for example, inert gases, N₂, N₂, CO₂, N₂o) and paramagnetic (for example, about₂). Are diamagnetic those g., whose the molecules do not have a constant magnetic moment and acquire it only under the effect of the external field (see diamagnetism). The same g., in which the molecules possess a constant magnetic moment, in the external magnetic field behave as the paramagnetic materials (see paramagnetism).

The calculation of intermolecular interaction and vnutr. of the structure of molecules is necessary with the solution of many problems of physics g., for example, with a study of the influence of upper of those rarefied it is layer the atmosphere to the motion of rockets and satellites (see gas dynamics, aerodynamics of the rarefied gases).

In the contemporary physicist g. is called not only one of the state of aggregation of substances. To g. with the special properties carries, for example, the totality of free electrons in the metal (electronic g.), phonons in liquid helium (phonon G.) and so forth G. elementary particles and the quasi-particles, which possess integral spin, Vol. n. bozonOV (for example, photons, 4- mesons, phonons), NAZ by Bose gas. Its properties examines quantum of the statistician of the Boses - Einstein. Properties of particles g. with the half-integral spin - fermions (for example, electrons, neutrons, neutrino, the holes of conductivity and others.) examines quantum of statistician Fermi - Dirac (see statistical physics).

Lit.: Kirillin V. A., Sychev V. V. and Sh of eyndlin AU, technical thermodynamics, M., 1969; Kikoin I. K. n of kikoin A. K., molecular physics, M., 1963; Hirschfelder Dzh., Curtiss Ch., Baird r., the molecular theory of gases n of liquids, translated from English, M., 1961; Thermodynamic properties of individual substances. Reference book, under red. In. P. Glushko, 2 izd., Vol. 1-2, M., 1962.

3. 3. Shpil'reyn.