Real gases thermodynamics

For real gases, thermodynamics defines a scaled pressure czlledfugacity,/, as... 

Van der Waals Johannes Diderik (1837-1923) Dutch phys., research on gaseous and liquid phases, determined so-called perfect and real gases, thermodynamic theory of capillarity, know for Van der Waals forces between dielectric molecules van t Hoff Jacobus Henricus (1852-1911) Dutch chem., father of phys. chem., relating thermodynamics to chem. 

For design calculations involving Refrigerant 500, a minimum-boiling azeotrope of 39.4 mol % of 1,1-difluoroethane and 60.4 mol % of difluorodichloromethane, reliable real gas thermodynamic properties are required which have been calculated from 0.2 to 100 bar and from 220 to 540 K using the recently proposed Boublik-Adler-Chen-Kreglewski equation of state and the PVT data reported in the literature. This equation of state has 21 universal constants and only five adjustable constants which have been calculated for R-500 from the PVT data, saturated vapor pressure and liquid density, and the critical constants. In order to calculate the absolute values of the real gas properties, the reference state properties, which are also reported here, are required. All properties are given in SI units. 

Real-gas thermodynamic properties may be expressed as functions of the variables of state, according to relations which may be developed from first principles. A comprehensive list of such relations has been given by Beattie and Stockmayer. For example, the molar enthalpy H, the molar entropy S, and the molar Gibbs energy G of a real gas can be written in terms of p, T, and p (the amount density) as follows ... 

The values of the thermodynamic properties of the pure substances given in these tables are, for the substances in their standard states, defined as follows For a pure solid or liquid, the standard state is the substance in the condensed phase under a pressure of 1 atm (101 325 Pa). For a gas, the standard state is the hypothetical ideal gas at unit fugacity, in which state the enthalpy is that of the real gas at the same temperature and at zero pressure. 

In mixtures of real gases the ideal gas law does not hold. The chemical potential of A of a mixture of real gases is defined in terms of the fugacity of the gas, fA. The fugacity is, as discussed in Chapter 2, the thermodynamic term used to relate the chemical potential of the real gas to that of the (hypothetical) standard state of the gas at 1 bar where the gas is ideal ... 

The standard state (and thus any standard thermodynamic property) of a pure solid refers to the pure substance in the solid phase under the pressure p of 1 bar (0.1 MPa). The standard state of a pure liquid refers to the pure substance in the liquid phase at p = 1 bar. When the substance is a pure gas, its standard state is that of an ideal gas at p = 1 bar (or, which is equivalent, that of a real gas at P = o). 

CHEMKIN REAL-GAS A Fortran Package for Analysis of Thermodynamic Properties and Chemical Kinetics in Nonideal Systems, Schmitt, R. G., Butler, P. B. and French, N. B. The University of Iowa, Iowa City, IA. Report UIME PBB 93-006,1993. A Fortran program (rglib.f and rgin-terp.f) used in connection with CHEMKIN-II that incorporates several real-gas equations of state into kinetic and thermodynamic calculations. The real-gas equations of state provided include the van der Waals, Redlich-Kwong, Soave, Peng-Robinson, Becker-Kistiakowsky-Wilson, and Nobel-Abel. 

Fugacity is a thermodynamic property related to the deviation of the p—V—T properties of the gas from those of an ideal gas. At very low pressures, the fugacity of a real gas tends to its partial pressure... 

Equation (2.2) is sometimes referred to as the ideal gas law. However, for our present purposes, we must recognize that this law [like those summarized in (2.3a-d)] is merely a crude approximation that never describes any real gas exactly, except in the idealized limit of zero pressure (to be discussed in Section 2.3). Hence, we must sharply distinguish between crude empirical laws (which are at most approximate rules of thumb) and true thermodynamic laws as summarized in Table 2.1. A difficulty for the beginning student of thermodynamics is to distinguish those equations that are based on the ideal gas approximation (and thus are practically never true) from those of rigorous thermodynamic quality. We shall often flag equations of the former type with IG (ideal gas), for example... 

The perfect gas is an abstraction to which any real gas approximates according to the nature of the gas and the conditions. For a given temperature and composition, the perfect gas condition is approached when tile density tends to zero. From a molecular point of view, the perfect gas laws correspond to the behavior of a system of molecules whose interactions may be neglected in expressing the thermodynamic equilibrium properties. However, even at a low density, the transport properties depend essentially on the interactions. 

The thermodynamic property of the real gas is extrapolated to zero pressure. 

As shown in Chap. 6, ideal-gas heat capacities, rather than the actual heat capacities of gases, are used in the evaluation of thermodynamic properties such as internal energy and enthalpy. The reason is that thermodynamic-property evaluation is conveniently accomplished in two steps first, calculation of ideal-gas values from ideal-gas heat capacities second, calculation from PVT data of the differences between real-gas and ideal-gas values. A real gas becomes ideal in the limit as P - 0 if it were to remain ideal when compressed to a finite pressure, its state would remain that of an ideal-gas. Gases in these hypothetical ideal-gas states have properties that reflect their individuality just as do real gases. Ideal-gas heat capacities (designated by Cf and Cy) are therefore different for different gases although functions of temperature, they are independent of pressure. 

The denominator on the right side of Eq. (4) is the heat capacity at constant pressure Cp. The numerator is zero for an ideal gas [see Eq. (1)]. Accordingly, for an ideal gas the Joule-Thomson coefficient is zero, and there should be no temperature difference across the porous plug. Eor a real gas, the Joule-Thomson coefficient is a measure of the quantity [which can be related thermodynamically to the quantity involved in the Joule experiment, Using the general thermodynamic relation ... 

Rudzinski W. and Panczyk T., Phenomenological Kinetics of Real Gas-Adsorption-Systems Isothermal Adsorption, Journal of Non-EqmHbrium Thermodynamics, 27 (2002)pp.l49-204. 

The thermodynamics of a l-d Fermi system can be perfectly mapped onto the thermodynamics of a two-component classical real gas on the surface of a cylinder. The relationship between these two infrared problems (cf. Zittartz s contribution) is exploited as follows. We treat the classical plasma by a modified Mayer cluster expansion method (the lowest order term corresponding to the Debye Hiickel theory), and obtain an exponentially activated behavior of the specific heat (cf. Luther s contribution) of the original quantum gas by simply reinterpreting the meaning of thermodynamic variables. 

Repeat Problem 3.25, now considering nitrogen to be a real gas with the thermodynamic properties given in Fig. 3.3-3. 

Equation (7-106) is the Lewis and Randall rule for computing the fugacity of a pure real gas. (Further methods of calculation are discussed in Gilbert Newton Lewis and Merle Randall, Thermodynamics and the Free Energy of Chemical Substances, chap. 17, McGraw-Hill Book Company, Inc., New York, 1923.)... 

Equation (7-162) implies that p, approaches zero as p approaches zero and thus the limits in Eqs. (7-154) and (7-157) may be taken as p approaches zero. The Gibbs-Dalton law is an empirical law that cannot be obtained from the general formalism of thermodynamics it is an additional piece of information. Equation (7-162) follows from Dalton s law and the fact that real-gas mixtures behave like ideal-gas mixtures in the zero-pressure limit. Dalton s law states that, for an ideal-gas mixture, the following equations hold ... 

This completes our discussion of the thermodynamic properties of real-gas mixtures. 

Significant errors in thermodynamic properties calculated as previously described may arise from the uncertainty in the specific-heat data. These errors may be reduced significantly by using zero-pressure specific heats calculated by the methods of statistical mechanics with spectroscopic data, since ideal-gas properties are generally about an order of magnitude more accurately known than the real-gas properties determined by calorimetric methods. ... 

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