Covolume

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. 

Van Deemter rate theory analychem A theory that the sample phase in gas chromatography flows continuously, not stepwise. van dam tar rat. the a re ) van der Waals adsorption physchem Adsorption in which the cohesion between gas and solid arises from van der Waals forces. van dar, w6lz ad.sorp shan ) van der Waals attraction See van der Waals force. van dar, w6lz a.trak shan ) van der Waals covolume physchem The constant b in the van der Waals equation, which is approximately four times the volume of an atom of the gas in question multiplied by Avogadro s number. van dar, w6lz ko val yam ) van der Waals equation phys chem An empirical equation of state which takes into account the finite size of the molecules and the attractive forces between them p = RT/(v — b) - (a/v ). where p is the pressure, v is the volume per mole, T is the absolute temperature, R is the gas constant, and a and b are constants. van dar, w6lz i,kwa-zhan ... 

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 ... 

Covolume. See Vol 3 of Encycl p C550-R and under Detonation (and Explosion), Equations of State, in this Volume. See also the following ... 

Addnl Refs A) Cook (1958), 64-5, 265 287 (Covolume) 63-5 (Covolume equation of state)... 

Covolume and the Condition of Gases of Decomposition in the Detonotion Zone of Brisant Explosives. The Engl translation of Ger paper "Ueber das Covolumen und den Zustand der Schwaden in der Detonationszone brisanter Sprengstoffe by J.F. Roth, SS 34, 193-97 (1939) CA 33, 8406(1939)... 

Covolume Theory as Applied to Propellants in Interior Ballistics was discussed by Corner in Ballistics (1950), pp 102-14... 

The distance between chemically bound atoms in many molecules is shorter than the sum of the radii of the same atoms when free, and the specific volume of the compound may be actually smaller than the total covolume of its gaseous products. If, as seems plausible, the drastic compression within the detonation front ruptures chemical bonds, many atoms suddenly expand, exerting forces like those by which solids resist compression. Such forces could result in a spike pressure much higher than the peak pressure of the non-reactive shock front, exert a brisant effect on the surroundings, and expedite the progress of the detonation wave. This view accords with observations of cases in which... 

In order to obtain even reasonable agreement with experiment, as Zel dovlch and Kompaneecs pointed out (Ref 12a, p 293), it is necessary to treat the covolume as a variable quantity depending on the volume. This means that the molecules cannot be con-... 

Cook also found the covolume to be function of specific volume only, and this was also discussed in Ref 6, p 183. In this connection (Ref 13, p 15d), it may seem to make no difference whether covolume depends on specific volume or [as in the MacLeod Equation of State, described and Detonation... 

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... 

Cowan Fickett (Addnl Ref E) added the 6 to T to prevent pressure from tending to infinity as the temperature tends to zero and to keep (dp/e T)v positive over the range of volumes of interest. They found that the values a =0.5 and /3 = 0.09 were satisfactory for reporducing experimental detonation velocity-density curve and C-J pressure of Comp B. The value of 6 they used was 400 k was defined as /tSx -k(, where K was 11,85, x was the mole fraction and kz- were the individual geometrical covolumes. The final version of Cowan-Fickett equation is given here under Kistiakowsky-Wilson Equation of State... 

In a parameter study of the BKW equation of state one may adjust parameters alpha, beta and kappa, as well as the covolumes of the deton products... 

Cj) Caldirola Paterson Equation of State. Dunkle (Ref 10, p 183), stated that Cook (Ref 2c) found by working backward from experimental detonation rates to Corresponding values of covolume, that for all expls at very high pressures the Covolume is a function of the specific volume only. At these pressures all molecules have the same covolume per unit weight the dependence of a(T,v) on temperature is exceedingly small. The equation of state can be written pV = nRT +a(v)p... 

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 ... 

Equations of Jones, of Halford-Kistia-kowsky-Wilson-Brinkley and of Noble-Abel are also covolume equations of state... 

T = absolute temperature, d=an arbitrary value in °K, k=covolume constant, T2 =absol temp of detonation and p2 —pressure of detonation, a=constant originally assigned as —1/3, but later changed to -1/4 b 0.3 d=0 and e = base of natural logarithm. The covolume constant k was taken as an additive covolume constant by summing the values for each type of molecule weighted by its mole fraction. 

Vg = molar gas volume R=gas constant T = absolute temperature F = function X =mole fraction of component i, and the sum extends over all chemical components of the gaseous mixture. The quantities a, /3, k, Q, kj are empirical constants, the k having the nature of covolumes (ie, a sort of excluded volume). 

Vj) VanderWaals Equation of State. It is listed in Vol 3 of Encycl, p C550-R, under "Covolume and fully described in the "Introduction to this section on Equations... 

Pure shock waves) 4) G.B. Kistiakowsky, p 951 in Kirk Othmer 5 (1950), pp given in the text (Not included in the 2nd edition) 5) Corner, Ballistics (1950), 100-01 (Corner Noble-Abel equations of state) 6) SAC MS, Ballistics (1951), 18 (Covolume and equation of state of propint gases) 7) Taylor(1952), 34 (Boltzmann and Hirschfelder Roseveare equation of state for the expln products) 69-72 (Rankine-Hugoniot equation of state) 87-98 (Abel, Boltzmann and other equations of state applicable to deton of condensed expls yielding only gaseous products) 114 (Equations of state applicable to deton of condensed expls whose products contain a condensed phase)... 

Cook equation of state, using covolume approximation) 63-4 (Other coyolume equations of state) 65 (Jones, Jones-Miller and Lennard-Jones equations of state) 66 (Cot-trell-Paterson equation of state) 12aj) W. Fickett W.W. Wood, Physics of Fluids 1, 528(1958 (A Detonation-Product Equation of State Observed from Hydrodynamic Data)... 

There were two steps in Jones determination of equations of his theory. He first solved the perturbed hydrodynamic equations for D, using a constant covolume equation of state. Then, using an expression for the ideal deton velocity D, he obtd the equation ... 

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