Equations of State General

Substituting the general equation of state and the definition of the aeous-tie veloeity, the following equation is obtained ... 

The formulation above allows a more general equation of state for the combustion products (Kuhl 1983). The method described breaks down for low piston velocities, where the leading shock Mach number approaches unity. In such cases, the numerical integration marches into the point (F = 0, Z = 1), which is a singularity. 

Kuhl, A. L. 1983. On the use of general equations of state in similarity, analysis of flame-... 

Figure 1. The relation between central density and the mass of various degenerate star models. Chandrasekhar s curve is for white dwarfs with a mean molecular weight 2 of atomic mass units. Rudkjobing s curve is the same except for inclusion of the relativistic spin-orbit effects Rudkjobing (1952). The curve labeled Oppenheimer and Volkoff is for a set of neutron star models. The solid line marked Wheeler is a set of models computed with a generalized equation of state, from Cameron (1959).

Generalized Equation of State for Real Gases, which can be applied from low densities to about twice the critical density is ... 

V2) ViriaJ Equations of State. Any equation of state which contains constants known as virial coefficients, is known as a virial equation, or sometimes "general equation of state (See item j2)... 

Rankine-Hugoniot equations 181-87 (Equations of state which include among others the following Jones Miller, Lennard-Jones Devonshire, Halford-Kistiakowsky-Wilson, Joffe its modification by Su Chang, Taylor, Kihara Hikita, Travers, Cook, Kistiakowsky-Wilson-Brinkley and Polytropic equations) 194 (Landau-Stanyukovich and Hirschfelder et al equations of state 11) J.F. Roth, Explosiv-stoffe 1958, 50 (Abel sche Zustandsgleichung fur die Detonation) 12) Cook (1958), 37 (General equation of state) 62-3 [Halford-Kistiakowsky-W ilson-Brinkley equation of state, (listed as K-H-W-B equation of state)] ... 

Kistiakowsky, 8c Wilson (Ref 29a) calcd deton velocities of some gaseous and condensed expls using a modification of Becker s semiempirical eq of state. The calcd values were, in most cases, in fair agreement with, exptl values. In their final rept (Ref 29b) a more general equation of state fiv if... 

A sample calculation was given in Ref 29b for shock waves in air employing the general equation of state (See eq 23) for the expln products and the ideal gas adiabatic eq of state for air. Employing the method of calculation based on the hydrodynamic theory, good agreement was obtd for expls investigated (PETN Tetryl) between calculated and experimentally detd explosive properties... 

About 1943, a simplified method for ealen of deton velocities of solid organic expls was developed at the Explosives Research.Laboratory (ERL), Bruceton, Pennsylvania. As there was no report issued at that time but just an unpublished letter of E.M. Boggs F.J. Martin addressed to Brinkley, a brief description of the method was given by him in Ref 39, p 87 In the ERL method, the general equation of state (See our eq 23), with a single covolume constant per unit mass of gaseous expln product, was used and the decompn scheme which leads to quantitative formation of water,... 

Cook (Ref 96), continuing his discussion on p 61, stated after equation (4.5) that if. one adopts a general equation of state in the forms ... 

Solution of these three equations for the three unknowns Tc, Pc, Vc leads, as before, to (2.46)-(2.48). (Note, however, that this trick of equating algebraic coefficients does not work for more general equations of state, so the calculus-based derivation is clearly preferred.)... 

For an ideal gas the general equation of state or overall relationship connecting the possible variables P, pressure, T,... 

The Lee-Kesler (7) generalized equation of state, which also applies to both phases, is the basis for the sixth thermodynamic properties method. As originally developed, the Lee-Kesler equation was for predicting bulk properties (densities, enthalpies etc.) for the entire mixture and not for calculating partial properties for the components of mixtures. Phase equilibrium was not one of the uses that the authors had in mind when they developed the equation. Recognizing the other possibilities of the Lee-Kesler equation, Ploecker, Knapp, and... 

The specific energy of an explosive is defined as its working performance per kg, calculated theoretically from the general equation of state for gases ... 

The Virial Equation of State The most general equation of state for real gases is the virial equation, proposed by Kammertirghones. 

The effects of large pressure changes upon the thermodynamic functions can, of course, be examined by using the more general equation of state (12.12) a rather more interesting discussion of this case follows, however, if we regard the volume instead of the pressure as independent variable. 

A more convenient and accurate waythat has-been-developed to-tie together the concepts of the law of corresponding states and the ideal gas law is to revert to a correction of the ideal gas law, that is, a generalized equation of state expressed in the following manner ... 

The critical compressibility factor, Z, calculated from the relation pV = nZ KT., is 0.282. A parameter representing the number of associated molecules of a fluid at the critical composition, and derived from a generalized equation of state, has been described as the cohesive weight [288a]. Under such conditions the cohesive weight of phosgene is said to correspond to the stoicheiometry, (COCi,). ... 

Ap97 was the first annual report to record a majority of papers favoring non-zero A. Ap98 registered both the word "quintessence" and the idea of a more general equation of state, with P = -wp, and w potentially a... 

A general equation of state may be written as PV=zRT or z = PV/RT, where V is the molar volume and z is the compressibility factor. In accordance with the partial property equation, the partial molar volume and the partial compressibility factor are expressed as follows ... 

The value of z from the general equation of state and its derivative with respect to u, is substituted in the partial compressibility factor equation to give... 

Just as we arrived at the equation of state (148) with the aid of the hypothesis (138), we should be able to obtain a generalized equation of state for gases, in other words, a... 

To describe the adsorption behaviour of such systems the chemical potentials of the solvent and all configurations of the protein are set equal in bulk and at the surface. For non-ideal adsorption layers (in respect to enthalpy and entropy) a more general equation of state is obtained (cf. Equations (22) and (27) in ref. 3) ... 

Although the discussion of the previous section focused on the van der Waals equation and corresponding-states charts for both the compressibility factor Z and the thermodynamic departure functions, the modem application of the corresponding states idea is to use generalized equations of state. The concept is most easily demonstrated by again using the van der Waals equation of state. From Eqs. 6.2-38,... 

The combination of Eqs. 6.2-38b and 6.6-4a is an example of a generalized equation of. state,. since we now have an equation of state that is presumed to be valid for a class of fluids with parameters ( and b) that have not been fitted to a whole collection of experimental data, but rather are obtained only from the fluid critical properties. The important content of these equations is that they permit the calculation of the PVT behavior of a fluid knowing only its critical properties, as was the case in corresponding-states theory. 

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