Virial second

Equation (10a) is somewhat inconvenient first, because we prefer to use pressure rather than volume as our independent variable, and second, because little is known about third virial coefficients It is therefore more practical to substitute... 

At moderate densities. Equation (3-lOb) provides a very good approximation. This approximation should be used only for densities less than (about) one half the critical density. As a rough rule, the virial equation truncated after the second term is valid for the present range... 

Figure 1 shows second virial coefficients for four pure fluids as a function of temperature. Second virial coefficients for typical fluids are negative and increasingly so as the temperature falls only at the Boyle point, when the temperature is about 2.5 times the critical, does the second virial coefficient become positive. At a given temperature below the Boyle point, the magnitude of the second virial coefficient increases with... 

Figure 3-1. Second virial coefficients for four fluids.

In the generalized method of Hayden and O Connell (1975), the pure-component and cross second virial coefficients are given by the sum of two contributions... 

Individual contributions to the second virial coefficient are calculated from temperature-dependent correlations ... 

As discussed in Chapter 3, the virial equation is suitable for describing vapor-phase nonidealities of nonassociating (or weakly associating) fluids at moderate densities. Equation (1) gives the second virial coefficient which is used directly in Equation (3-lOb) to calculate the fugacity coefficients. 

Equilibrium constants,, for all possible dimerization reactions are calculated from the metastable, bound, and chemical contributions to the second virial coefficients, B , as given by Equations (6) and (7). The equilibrium constants, K calculated using Equation (3-15). 

The total free contribution to the second virial coeffi-F... 

The Lewis fugacity rule is used for calculating the fugacity coefficients of the true species, and (2) the second virial co-... 

VPLQFT is a computer program for correlating binary vapor-liquid equilibrium (VLE) data at low to moderate pressures. For such binary mixtures, the truncated virial equation of state is used to correct for vapor-phase nonidealities, except for mixtures containing organic acids where the "chemical" theory is used. The Hayden-0 Connell (1975) correlation gives either the second virial coefficients or the dimerization equilibrium constants, as required. 

CALCULATE URE COMPONENT ANO CROSS SECOND VIRIAL COEPFICfENTS C... 

PARAMETER USED TO CALCULATE PART OF CHEMICAL CONTRIBUTION TO THE SECOND VIRIAL COEFFICIENT. CALCULATED ONE OF TWO WAYS DEPENDING ON THE VALUE OF ETA(IJ). 

CALCULATE THE TEMPERATURE DEPENDENT SECOND VIRIAL COEFFICIENTS. 

CALCULATE THE FREE CONTRIBUTION TO THE SECOND VIRIAL COEFFICIENT,... 

TEMP UNCHANGED. 8IJS2 NOT CALLED. SECOND VIRIAL... 

IF BINARY SYSTEM CONTAINS NO ORGANIC ACIDS. THE SECOND VIRTAL coefficients ARE USED IN A VOLUME EXPLICIT EQUATION OF STATE TO CALCULATE THE FUGACITY COEFFICIENTS. FOR ORGANIC ACIDS FUGACITY COEFFICIENTS ARE PREDICTED FROM THE CHEMICAL THEORY FOR NQN-IOEALITY WITH EQUILIBRIUM CONSTANTS OBTAINED from METASTABLE. BOUND. ANO CHEMICAL CONTRIBUTIONS TO THE SECOND VIRIAL COEFFICIENTS. 

GET SECOND VIRIAL COEFFICIENTS BIJ IN /VIRIAL/ llO CALL BlJS(N,ID,KEY,T,eR8)... 

CALCULATE EFF SECOND VIRIAL COEFFICIENT FOR COMP I IN MIXTURE, SS(I)... 

BUS calculated second virial coefficients for pure compoments and all binary pairs in a mixture of N components (N 20) at specified temperature. These coefficients are placed in common storage /VIRIAL/. 

Second virial coefficients are calculated using the equations for the Hayden-0 Connell correlation (see Appendix A). 

Stigter and Dill [98] studied phospholipid monolayers at the n-heptane-water interface and were able to treat the second and third virial coefficients (see Eq. XV-1) in terms of electrostatic, including dipole, interactions. At higher film pressures, Pethica and co-workers [99] observed quasi-first-order phase transitions, that is, a much flatter plateau region than shown in Fig. XV-6. 

The viscosity, themial conductivity and diffusion coefficient of a monatomic gas at low pressure depend only on the pair potential but through a more involved sequence of integrations than the second virial coefficient. The transport properties can be expressed in temis of collision integrals defined [111] by... 

Hu C H and Thakkar A J 1996 Potential energy surface for interactions between N2 and He ab initio calculations, analytic fits, and second virial coefficients J. Chem. Phys. 104 2541... 

Fender B E F and Halsey G D Jr 1962 Second virial coefficients of argon, krypton and argon-krypton mixtures at low temperatures J. Chem. Phys. 36 1881... 

Buckingham R A and Corner J 1947 Tables of second virial and low-pressure Joule-Thompson coefficients for intermolecular potentials with exponential repulsion Proc. R. Soc. A 189 118... 

Corner J 1948 The second virial coefficient of a gas of non-spherical molecules Proc. R. Soc. A 192 275... 

Figure A2.1.7. The second virial coefficient 5 as a fiinction of temperature T/T. (Calculated for a gas satisfying the Leimard-Jones potential [8].)...

Gas mixtures are subject to the same degree of non-ideality as the one-component ( pure ) gases that were discussed in the previous section. In particular, the second virial coefficient for a gas mixture can be written as a quadratic average... 

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