Equations of state. Other equations of state What is called the equation of state of the system
The state parameters are related to each other. The ratio that determines this connection is called the equation of state of this body. In the simplest case, the equilibrium state of the body is determined by the value of those parameters: pressure p, volume V and temperature, the mass of the body (system) is usually considered known. Analytically, the relationship between these parameters is expressed as a function of F:
Equation (1) is called the equation of state. This is a law that describes the nature of the change in the properties of a substance when external conditions change.
What is an ideal gas
Especially simple, but very informative is the equation of state of the so-called ideal gas.
Definition
An ideal gas is a gas in which the interaction of molecules with each other can be neglected.
Rarefied gases are considered ideal. Helium and hydrogen are especially close in their behavior to an ideal gas. An ideal gas is a simplified mathematical model of a real gas: the molecules are considered to move randomly, and the collisions between the molecules and the impact of the molecules on the walls of the vessel are elastic, such that they do not lead to energy losses in the system. Such a simplified model is very convenient, since it does not require taking into account the forces of interaction between gas molecules. Most real gases do not differ in their behavior from an ideal gas under conditions where the total volume of molecules is negligible compared to the volume of the vessel (i.e., at atmospheric pressure and room temperature), which makes it possible to use the ideal gas equation of state in complex calculations.
The equation of state for an ideal gas can be written in several forms (2), (3), (5):
Equation (2) is the Mendeleev-Claperon equation, where m is the gas mass, $\mu $ is the molar mass of the gas, $R=8.31\ \frac(J)(mol\cdot K)$ is the universal gas constant, $\nu \ $- the number of moles of the substance.
where N is the number of gas molecules in the mass m, $k=1.38\cdot 10^(-23)\frac(J)(K)$, the Boltzmann constant, which determines the "share" of the gas constant per molecule, and
$N_A=6.02\cdot 10^(23)mol^(-1)$ is Avogadro's constant.
If we divide both parts in (4) by V, then we obtain the following form of writing the equation of state for an ideal gas:
where $n=\frac(N)(V)$ is the number of particles per unit volume or the concentration of particles.
What is real gas
Let us now turn to more complex systems - to non-ideal gases and liquids.
Definition
A real gas is a gas, between the molecules of which there are noticeable interaction forces.
In non-ideal, dense gases, the interaction of molecules is large and must be taken into account. It turns out that the interaction of molecules complicates the physical picture so much that the exact equation of state of a nonideal gas cannot be written in a simple form. In such a case resort to approximate formulas found semi-empirical. The most successful such formula is the Van der Waals equation.
The interaction of molecules is complex. At relatively large distances between molecules, attractive forces act. As the distance decreases, the attractive forces first increase, but then decrease and turn into repulsive forces. The attraction and repulsion of molecules can be considered and taken into account separately. Van der Waals equation describing the state of one mole of a real gas:
\[\left(p+\frac(a)(V^2_(\mu ))\right)\left(V_(\mu )-b\right)=RT\ \left(6\right),\]
where $\frac(a)(V^2_(\mu ))$ is the internal pressure due to attractive forces between molecules, b is the correction for the intrinsic volume of molecules, which takes into account the action of repulsive forces between molecules, and
where d is the diameter of the molecule,
the value a is calculated by the formula:
where $W_p\left(r\right)\ $ is the potential energy of attraction of two molecules.
As the volume increases, the role of corrections in equation (6) becomes less significant. And in the limit equation (6) goes into equation (2). This is consistent with the fact that as the density decreases, real gases approach ideal gases in their properties.
The advantage of the van der Waals equation is the fact that at very high densities it also approximately describes the properties of a liquid, in particular, its poor compressibility. Therefore, there is reason to believe that the van der Waals equation will also make it possible to reflect the transition from a liquid to a gas (or from a gas to a liquid).
Figure 1 shows the van der Waals isotherm for some constant temperature T, constructed from the corresponding equation.
In the "gyrus" region (KM section), the isotherm crosses the isobar three times. In the section [$V_1$, $V_2$], the pressure increases with the increase in volume.
Such dependence is impossible. This may mean that something unusual is happening with the matter in this area. What exactly this is cannot be seen from the van der Waals equation. You need to turn to experience. Experience shows that in the region of the "gyrus" on the isotherm in a state of equilibrium, the substance separates into two phases: liquid and gaseous. Both phases coexist simultaneously and are in phase equilibrium. In phase equilibrium, the processes of liquid evaporation and gas condensation proceed. They go with such intensity that they completely compensate each other: the amount of liquid and gas remains unchanged over time. A gas in phase equilibrium with its liquid is called saturated vapor. If there is no phase equilibrium, there is no compensation for evaporation and condensation, then the gas is called unsaturated steam. How does the isotherm behave in the region of the two-phase state of matter (in the region of the "gyrus" of the van der Waals isotherm)? Experience shows that in this area, when the volume changes, the pressure remains constant. The isotherm graph runs parallel to the V axis (Fig. 2).
As the temperature increases, the area of two-phase states on the isotherms narrows until it turns into a point (Fig. 2). This is the singular point K, at which the distinction between liquid and vapor disappears. It's called the critical point. The parameters corresponding to the critical state are called critical (critical temperature, critical pressure, critical density of matter).
The parameters, the totality of which determines the state of the system, are related to each other. When one of them changes, at least one other changes. This interrelation of parameters finds expression in the functional dependence of thermodynamic parameters.
An equation relating the thermodynamic parameters of a system in an equilibrium state(for example, for a homogeneous body - pressure, volume, temperature) called the equation of state . The total number of equations of state of the system is equal to the number of its degrees of freedom(variants of the equilibrium system), those. the number of independent parameters characterizing the state of the system.
When studying the properties of equilibrium systems, thermodynamics primarily considers the properties of simple systems. simple system they call a system with a constant number of particles, the state of which is determined by only one external parameter "a" and temperature, i.e. a simple system is a single-phase system defined by two parameters.
So the equation
is an equation of state of pure matter in the absence of external electric, magnetic, gravitational fields. Graphically, the equation of state is expressed by the surface in coordinates P-V-T, which is called thermodynamic surface. Each state of the system on such a surface is represented by a point, which is called figurative dot . When the state of the system changes, the figurative point moves along the thermodynamic surface, describing a certain curve. The thermodynamic surface is the locus of points representing equilibrium state of the system in functions of thermodynamic parameters.
It is impossible to derive an equation of state based on the laws of thermodynamics; they are either established from experience or found by the methods of statistical physics.
Equations of state relate temperature T, external parameter a i(for example, volume) and some equilibrium internal parameter b k(e.g. pressure).
If the internal parameter b k is the internal energy U, then the equation
called the energy equation or caloric equation of state.
If the internal parameter b k is the conjugate of the external parameter a i force A i(e.g. pressure R is the volume force V), then the equation
is called the thermal equation of state.
Thermal and caloric equations of state for a simple system have the form:
If AND = R(pressure) and, therefore, a = V(volume of the system), then the equations of state of the system will be written accordingly:
For example, when studying the gaseous state, the concept of an ideal gas is used. Ideal gas is a collection of material points (molecules or atoms) that are in chaotic motion. These points are considered as absolutely elastic bodies with zero volume and not interacting with each other.
For a system as simple as an ideal gas thermal the equation of state is Clapeyron-Mendeleev equation
where R– pressure, Pa; V is the volume of the system, m3; n is the amount of substance, mol; T– thermodynamic temperature, K; R is the universal gas constant:
Caloric the equation of state of an ideal gas is Joule's law on the independence of the internal energy of an ideal gas from the volume at a constant temperature:
where C V is the heat capacity at constant volume. For a monatomic ideal gas C V does not depend on temperature, so
or if T 1 = 0 K, then .
More than 150 thermal equations of state have been empirically established for real gases. The simplest of them and qualitatively correctly conveying the behavior of real gases even when they pass into a liquid is van der Waals equation:
or for n moles of gas:
This equation differs from the Clapeyron-Mendeleev equation in two corrections: for the intrinsic volume of molecules b and internal pressure a/V 2 determined by mutual attraction of gas molecules ( a and b are constants independent of T and R, but different for different gases; in gases with more a at constant T and V less pressure, but with more b- more).
more accurate two-parameter thermal equations of state are:
the first and second Dieterici equations:
Berthelot equation:
Redlich-Kwong equation:
The given equations of Berthelot, Diterici and especially Redlich-Kwong have a wider range of applicability than the van der Waals equation. It should be noted, however, that constant a and b for a given substance do not depend on temperature and pressure only in small intervals of these parameters. Two-parameter van der Waals type equations describe both gaseous and liquid phases and reflect the liquid-vapor phase transition, as well as the presence of a critical point of this transition, although accurate quantitative results for a wide range of gaseous and liquid states using these equations at constant parameters a and b cannot be obtained.
Isotherms of ideal and real gases, as well as van der Waals gas, are shown in Figs. 1.1.
Rice. 1. Isotherms of various gases.
An exact description of the behavior of a real gas can be obtained using the equation proposed in 1901 by Kammerling-Onnes and Keesom and called equations of state with virial coefficients or virial equation of state:
which is written as compressibility factor decomposition
in powers of reciprocal volume. Odds AT 2 (T), AT 3 (T) etc. depend only on temperature, are called the second, third, etc. virial coefficient and describe the deviations of the properties of a real gas from an ideal one at a given temperature. Virial coefficients In i(T) are calculated from the experimental data on the dependence PV for a given temperature.
State equation called an equation that establishes the relationship between thermal parameters, i.e. ¦(P,V,T) = 0. The form of this function depends on the nature of the working fluid. Distinguish between ideal and real gases.
perfect is called a gas for which the intrinsic volume of the molecules and the forces of interaction between them can be neglected. The simplest equation of state for an ideal gas is the Mendeleev-Clapeyron equation = R = const, where R is a constant, depending on the chemical nature of the gas, and which is called the characteristic gas constant. From this equation follows:
Pu = RT (1 kg)
PV = mRT (m kg)
The simplest equation of state real gas is the van der Waals equation
(P + ) × (u - b) = RT
where is the internal pressure
where a, b are constants depending on the nature of the substance.
In the limiting case (for an ideal gas)
u >> b Pu = RT
To determine the characteristic gas constant R, we write the Mendeleev-Clapeyron equation (hereinafter M.-K.) for P 0 \u003d 760 mm Hg, t 0 \u003d 0.0 C
multiply both sides of the equation by the value m, which is equal to the mass of a kilomole of gas mP 0 u 0 = mRT 0 mu 0 = V m = 22.4 [m 3 / kmol]
mR \u003d R m \u003d P 0 V m / T 0 \u003d 101.325 * 22.4 / 273.15 \u003d 8314 J / kmol × K
R m - does not depend on the nature of the gas and is therefore called the universal gas constant. Then the characteristic constant is:
R=Rm/m=8314/m;[J/kg×K].
Let us find out the meaning of the characteristic gas constant. To do this, we write the equation M.-K. for two states of an ideal gas involved in an isobaric process:
P (V 2 -V 1) \u003d mR (T 2 -T 1)
R==; where L is the work of the isobaric process.
m(T 2 -T 1) m(T 2 -T 1)
Thus, the characteristic gas constant is the mechanical work (work of volume change) that 1 kg of gas performs in an isobaric process when its temperature changes by 1 K.
Lecture #2
Caloric state parameters
The internal energy of a substance is the sum of the kinetic energy of the thermal motion of atoms and molecules, the potential energy of interaction, the energy of chemical bonds, intranuclear energy, etc.
U \u003d U CIN + U POT + U CHEM + U POISON. +…
In such processes, only the first 2 quantities change, the rest do not change, since the chemical nature of the substance and the structure of the atom do not change in these processes.
In calculations, it is not the absolute value of the internal energy that is determined, but its change, and therefore it is accepted in thermodynamics that the internal energy consists only of the 1st and 2nd terms, because in the calculations, the rest are reduced:
∆U \u003d U 2 + U 1 \u003d U ORF + U POT ... For an ideal gas, U POT \u003d 0. In the general case
U ORF = f(T); UPOT = f(p, V)
U = f(p, T); U POT = f(p, V); U = f(V,T)
For an ideal gas, the following relation can be written:
Those. internal energy depends on
temperature and is independent of pressure and volume
u = U/m; [J/kg]-specific internal energy
Consider the change in the internal energy of the working body, performing a circular process or cycle
∆u 1m2 = u 2 - u 1; ∆U 1n2 \u003d u 1 - u 2; ∆u ∑ = ∆u 1m2 – ∆u 2n1 = 0 du = 0
From higher mathematics it is known that if the given integral is equal to zero, then the quantity du is the total differential of the function
u = u(T, u) and is equal to
All parameters, including temperature, depend on each other. This dependence is expressed by equations of the type
F(X 1 ,X 2 ,...,x 1 ,x 2 ,...,T) = 0,
where X 1 ,X 2 ,... are generalized forces, x 1 ,x 2 ,... are generalized coordinates, and T is temperature. Equations that establish the relationship between parameters are called equations of state.
The equations of state are given for simple systems, mainly for gases. For liquids and solids, which, as a rule, are assumed to be incompressible, the equations of state have practically not been proposed.
By the middle of the twentieth century. a significant number of equations of state for gases were known. However, the development of science has gone in such a way that almost all of them have not found application. The only equation of state that continues to be widely used in thermodynamics is the ideal gas equation of state.
Ideal gas is called a gas that approaches in properties the gas of a low molecular weight substance at a very low pressure and a relatively high temperature (quite far from the condensation temperature).
For an ideal gas:
Boyle's Law - Mariotte(at a constant temperature, the product of the pressure of a gas and its volume remains constant for a given amount of substance)
Gay-Lussac's law(at constant pressure, the ratio of gas volume to temperature remains constant)
Charles' law(at constant volume, the ratio of gas pressure to temperature remains constant)
.
S. Carnot combined the above relations into a single equation of the type
.
B. Clapeyron gave this equation a form close to the modern one:
The volume V included in the equation of state for an ideal gas refers to one mole of the substance. It is also called molar volume.
The generally accepted name for the constant R is the universal gas constant (it is very rare to find the name "Clapeyron's constant" ). Its value is
R=8.31431J/mol TO.
Approximation of a real gas to an ideal one means achieving such large distances between molecules, at which one can completely neglect their own volume and the possibility of interaction, i.e. the existence of forces of attraction or repulsion between them.
Van der Waals proposed an equation that takes these factors into account in the following form:
,
where a and b are constants determined for each gas separately. The remaining quantities included in the van der Waals equation have the same meaning as in the Clapeyron equation.
The possibility of the existence of an equation of state means that to describe the state of the system, not all parameters can be indicated, but their number, less than one, since one of them can be determined (at least hypothetically) from the equation of state. For example, to describe the state of an ideal gas, it is enough to indicate only one of the following pairs: pressure and temperature, pressure and volume, volume and temperature.
Volume, pressure and temperature are sometimes called the external parameters of the system.
If a simultaneous change in volume, pressure and temperature is allowed, then the system has two independent external parameters.
A system located in a thermostat (a device that ensures a constant temperature) or a manostat (a device that ensures a constant pressure) has one independent external parameter.
EQUATIONS OF STATE, ur-tion, expressing the relationship between the parameters of the state of a physically homogeneous system at thermodynamic. balance . The thermal equation of state relates the pressure p to the volume V and the temperature T, and for multicomponent systems, also to the composition (molar fractions of the components). The caloric equation of state expresses the internal. the energy of the system as a function of V, T and composition. Usually, under the equation of state, unless otherwise specified, they mean thermal. equation of state. From it you can directly get the coefficient. thermal extensions, coefficient isothermal compression, thermal coefficient pressure (elasticity). The equation of state is a necessary addition to thermodynamic. laws. Using the equations of state, you can reveal the dependence of thermodynamic. f-tions from V and p, integrate the differential. thermodynamic ratios, calculate the volatility (fugacity) of the components of the system, through which the conditions of phase equilibrium are usually written down. Thermodynamics establishes a connection between the equations of state and any of the thermodynamic potentials of the system, expressed as a function of its natural variables. For example, if the Helmholtz energy (free energy) F is known as a function of T and V, thenthe equation of state cannot be obtained using the laws of thermodynamics alone, it is determined from experience or derived by statistical methods. physics. The last task is very difficult and might. solved only for simplified models of the system, for example, for an ideal gas. The equations of state used for real systems have an empirical or semiempirical. character. Some of the most well-known and promising equations of state are considered below.
At the equation of state for an ideal gas is pV=RT, where V is the molar volume, R is the universal gas constant. This equation is subject to real gases at high rarefaction (see Clapeyron - Mendeleev equation).
Properties of real gases at low and medium pressures are well described by the virial equation: pV / RT \u003d 1 + B 2 / V + B 3 / V 2 + ..., where B 2, B 3 - second, third, etc. . virial coefficients. For a given in-va they depend only on t-ry. The virial equation of state is justified theoretically; it is shown that the coefficient B 2 is determined by the interaction. pairs of molecules, B 3 - interaction. three particles, etc. At high densities in the islands, the above expansion in powers of the inverse volume diverges, so the virial equation is unsuitable for describing liquids. It only serves forcalculation of volatilities of gaseous components B-B. Usually limited to B 2 /V (rarely B 3 /V 2). In lit. lead experiment. values of virial coefficients., developed and theoretical. methods for their determination. The equation of state with the second virial coefficient. B 2 is widely used to model the gas phase in the calculation of phase equilibria in the case of not too high pressures (up to 10 atm). It is also used to describe St. in dilute p-ditch high mol. in-in (see Solutions of polymers).
For practical calculations of phase equilibria in a wide range of t-r and pressures, the equations of state are important, capable of describing simultaneously the properties of the liquid and gas phases. For the first time, such an equation was proposed by I. van der Waals in 1873:
p \u003d RT (V-b) -a / V 2,
where a and b are the van der Waals constants characteristic of a given in-va (see the van der Waals equation). This equation of state has the third order with respect to the volume V, any isotherm with state parameters less than critical. values (in the subcritical region), has three valid. put, the root at fixed. pressure . Naib, from the roots of the equation corresponds to the gas phase, the smallest - to the liquid; the average root of the ur-niya nat. doesn't make sense. In supercritical areas of the isotherm state parameters have only one valid. root.
Kubich. the dependence of pressure on volume is preserved in MH. empirical modifications of the van der Waals equation. More often than others, a two-parameter is used. ur-tion Peng - Robinson (1976) and Redlich - Kwong - Soave (1949, 1972). Empirical the constants of these equations of state can be determined from the critical. parameters in-va (see. Critical condition). To expand the circle of the described equations of state of systems, the set of considered CB-B, the range of t-p and pressures, developed cubic. State equations containing three or more empiric. permanent. An important advantage of cubic. equations of state - their simplicity, due to which the calculations with the help of a computer do not require too much computer time. For many systems formed by non-polar or weakly polar in-you, these equations of state provide the required for practical. goals accuracy.
If detailed experiments are known. data on p-V-T-dependencies, for their generalization, multiparameters are involved. empirical equations of state. One of the most common equations of state of this type is the Benedict-Webb Rubin equation (BVR equation), developed in 1940 on the basis of the virial equation of state. In this equation, the pressure p is represented as a density polynomial in the islands with coefficients depending on the t-ry. The terms of a series of high orders are neglected, and for compensation, an exponential term is included in the equation. This leads to the appearance of S-shaped isotherms and makes it possible to describe the liquid phase and liquid-gas equilibria.
For non-polar and weakly polar v-v, the BVR equation gives very accurate results. For an individual substance, it contains eight adjustable parameters; for a mixture, the parameters of a mixed ("binary") interaction are additionally introduced. Estimating a large number of fitting parameters is a very complex task, requiring numerous and varied experiments. data. The parameters of the BVR equation are known only for a few. tens of in-in, ch. arr. hydrocarbons and inorg. gases. Modifications of the equation, aimed, in particular, at improving the accuracy of the description of St. in specific substances, contain an even greater number of adjustable parameters. Despite this, it is not always possible to achieve satisfactory results for the polar regions. The complexity of the form makes it difficult to use equations of state of this type in the calculation of distillation processes, when it is necessary to repeatedly evaluate the volatilities of the components, the volume and enthalpy of the system.
When describing mixtures in-in empiric. the constant equations of state are assumed to be dependent on the composition. For cubic. equations of state of the van der Waals type, quadratic mixing rules are generally accepted, according to which the constants a and b for the mixture are determined from the relationships:
where x i , x j are the molar fractions of the components, the values a ij and b ij are associated with constants for individual in-in a ii , a jj and b ii , b jj according to the combination rules:
a ij = (a ii a jj) 1/2 (1-k ij); 6 ij = (b ii +b jj)/2,
where k ij - adjustable parameters of the mixed interaction., determined by experiment. data. However, the quadratic mixing rules do not allow one to obtain satisfactory results for the so-called. asymmetric systems, the components of which are very different in polarity and pier. sizes, e.g. for mixtures of hydrocarbons with water.
M. Huron and J. Vidal in 1979 formulated mixing rules of a new type, based on local composition models, which successfully convey the asymmetry of concentrations. dependences of the excess Gibbs potential G E for liquid mixtures and can significantly improve the description of phase equilibria. The essence of the approach is that the values of G E of the liquid solution are equated, obtained from the equations of state and calculated according to the selected local composition model [Wilson equations, NRTL (Non-Random Two Liquids equation), UNIQAC (UNIversal QUAsi-Chemical equation) , UNIFAC (UNIque Functional group Activity Coefficients model); CM. Solutions of non-electrolytes]. This direction is developing intensively.
Many two-parameter equations of state (van der Waals, virial with a third virial coefficient, etc.) can be represented as the reduced equation of state:
f(p pr, T pr, V pr)= 0,
where p pr \u003d p / p crit, T pr \u003d T / T crit, V pr \u003d V / V crit - reduced state parameters. V-va with the same values of p CR and T CR have the same reduced volume V np ; the compressibility factors Z = pV/RT also coincide, coefficient. volatility and some other thermodynamic. f-tions (see. Respective states law). A more general approach, which makes it possible to expand the circle of considered substances, is associated with the introduction of additional parameters into the above equation of state. Naib, simple among them - the critical factor. compressibility Z crit = p crit V crit /RT crit. and acentric. factor w = -Ig p pr -1 (at T pr = 0.7). Acentric the factor is an indicator of the non-sphericity of the intermol field. forces of a given island (for noble gases it is close to zero).
K. Pitzer proposed to use linear expansion to calculate the compressibility factor
Z(T crit, p crit) \u003d Z 0 (T crit, p crit) + w Z "(T crit, p crit),
where Z 0 means the compressibility factor of a "simple" liquid, for example, argon, and Z "characterizes deviations from the model of a simple liquid (see Liquid). Correlation relations are proposed that determine the dependences Z ° (T crit, р crit)
and Z "(T crit, p crit). Naib, the correlations of Lee and Kessler are known, in which the dependence of Z 0 on T crit and p crit is transmitted using the BVR equation for argon. The dependence of Z" on T crit and p Creteset when n-octane is selected as the "reference" fluid. It is assumed that Z "(T crit, p crit) \u003d / w *, where w * is the acentricity factor of n-octane, Z * is its compressibility factor according to the BVR equation. A technique has been developed for applying the Lee-Kessler equation and for liquid mixtures... This equation of state most accurately describes thermodynamic properties and phase equilibria for non-polar substances and mixtures.
Along with the above empirical Equations of state have become important equations that have the ability to take into account the features of the structure of molecules and intermoles. interaction They rely on the provisions of statistics. theory and results of numerical experiments for model systems. According to the mol.-statistic. interpretation, the van der Waals equation describes a fluid of solid attracting spheres considered in the mean field approximation. In the new equations, first of all, the term of the van der Waals equation, which is determined by the forces of interparticle repulsion, is specified. Much more accurate is the Cariahan-Starling approximation based on the results of numerical modeling of hard sphere fluid in a wide range of densities. It is used in many equations of state, but the equations of state of model systems of solid particles have great potential, in which the asymmetry of the pier is taken into account. forms. For example, in the BACK (Boublik-Alder-Chen-Kre-glewski) equation, the contribution of repulsive forces is estimated using the equation of state for a fluid of dumbbell-shaped solid particles. To take into account the contribution of attractive forces, an expression is used that approximates the results obtained by the mol. dynamics for a fluid with interparticle potentials of the rectangular well type (see Molecular Dynamics). The BACK equation and its analogues make it possible to describe with sufficient accuracy mixtures that do not contain high-boiling components.
A feature of the description of mixtures of high-boiling org. B-B - the need to take into account additional rotational vibrations. degrees of freedom associated with displacements of segments of chain molecules (eg C 8 alkenes). For these systems, naib, the PHCT (Perturbed Hard Chain Theory) equation proposed by J. Prausnitz and M. Donahue in 1978 has become widespread. parameters in the PHCT equation. Combination rules for a mix contain one mix interaction parameter. Further improvement of the PHCT equation is based on replacing the rectangular well potential, which describes the attraction of molecules, with the Lennard-Jones potential [PSCT (Perturbed Soft Chain Theory) equation] and taking into account the anisotropy of the intermoles. forces [equation PACT (Perturbed Anisotropic Chain Theory)]. The last equation well describes phase equilibria in systems with polar components even without using the adjustable pair interaction parameters.
component molecules.
The ever-increasing interest in the equations of state is primarily due to practical. development needs. modern technologies associated with the absorption separation of substances, the exploitation of oil and gas fields, etc., since in these cases quantities, description and prediction of phase equilibria are required in a wide range of t-r and pressures. However, there is not yet enough universality. state equations. All the mentioned equations of state turn out to be inaccurate when describing states near the critical. points and are not designed to deal with critical phenomena. For these purposes, special equations of state are being developed, but even they are still poorly adapted for specific practical applications. applications.
, including dense plasma.
Lit .: R. Reed, J. Prausnitz, T. Sherwood, Properties of gases and liquids, trans. from English, L., 1982; Ailes S., Head equilibria in chemical engineering, trans. from English, part 1, M., 1989; Viktorov A.I. (and others), "Journal of Applied Chemistry", 1991, vol. 64, no. 5, p. 961-78. G. L. Kuranov.
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