Covolume term

Van der Waals Equations of State. A logical step to take next is to consider equations of state that contain both a covolume term and an attractive force term, such as the van der Waals equation. De Boer [4] and Ross and Olivier [55] have given this type of equation much emphasis. 

The allowance for polarization in the DH model obviates the need for separation of long-range and short-range attractive forces and for inclusion of additional repulsive interactions. Belief in the necessity to include some kind of covolume term stems from the confused analysis of Onsager (13), and is compounded by a misunderstanding of the standard state concept. Reference to a solvated standard state in which there are no interionic effects can in principle be made at any arbitrary concentration, and the only repulsive or exclusion term required is that described by the DH theory which puts limits on the ionic atmosphere size and hence on the lowering of electrical free energy. The present work therefore supports the view of Stokes (34) that the covolume term should not be included in the comparison of statistical-mechanical results with experimental ones. 

First we consider the virial expansion in density originally due to Boltzmann and derived from the kinetic theory of gases for hard-sphere molecules. This equation was modified by Hirschfelder and Roseveare, and covolume terms for product species were adjusted to high temperature by setting them equal to the high-temperature second virial coeflficientz. The equation is... 

It is generally recognized that the average dimensions of a macromolecule are dependent on two factors one related to short distance interactions, those to which conformational analysis is applied, and one concerned with long distance interactions that are often considered in terms of excluded volume effects or covolume effects. One may, therefore, put ... 

The term b was introduced by vanderWaals and named covolume (See Vol 3 of Encycl, p C550, under "Covolume ). Actually b does not represent the Sum of the volumes occupied by the individual molecules (exclusive of the voids between them) but four times its value. The reason for this is explained in Ref 3, pp... 

Could be applied to deton of condensed expls. Here the coefficient /3 was included in the exponential term to secure constancy of the k with respect to density of gases, and in which T 4 dependence of the covolume... 

Cg) Covolume Equations of State. Any equation of state which uses "covolume as one of its terms may be so-called. Cook (Ref 12, pp 63-4) adopted the "covolume approximation ... 

Equation (4) is a variable covolume departure from the hard-sphere-molecule Eq. (1), for if /3=0.625, k=1, and a—0 the K-W equation would be identical with the Boltzmann equation to the third virial term, and the ki s would be just the bi of the hard-sphere-molecule model. If 0 were 0.625, with a about 0.25 to 0.5, one might consider the K-W equation to be a soft-sphere equation of state. In applying Eq. (4) to the calculation of detonation velocities it was quickly found, however, that 0 could not be as large as 0.625,... 

As used herein, the term RUBY includes the results of computations at tbe Los Alamos Scientific Laboratory by the STRETCH BKW computer code and at NOL by the Lawrence Radiation Laboratory s RUBY code. For the purposes of present discussions, these codes differ only in minor regards and, unless otherwise specified, RUBY computations shall he considered as based on Mader s most recent covolume factors and the more appropriate of his dual K-W parameter sets (Ref. 11 of Part I), with the heat of formation of solid carbon taken as zero. See Part I for other leading references. 

Covolume (Covolumen in Ger).This is a term applied in certain equations of state to correct the vol of gas for the effect of the vol o the molecules. This term is not the molecular vol itself (Ref 12)... 

At pressures up to 40 tons/in2, corresponding to density of 0.35 g/cc, only the first 3 terms in the equation need be kept. Thus the pressure dependence of the thermodynamic props can be evaluated from a knowledge of the 2nd 3rd virial coeffs of the various gaseous products. Tables are presented which cover the range 1600° - 4000° K, and which have found considerable application in internal ballistics. These tables give covolumes of propellants with a systematic error of less than 5%- The basis of Corner s theory is the expression of the 2nd virial coefficient of a gas as a simple function of the parameters of the intermolecular field... 

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