Covolume constant

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. 

The detonation velocity is insensitive to the composition of the explosion products, and calculations based upon the conventional decomposition scheme differ little from the much more elaborate calculations which include the determination of the equilibrium composition. The covolume constants can be detd from exptl values of deton velocities of selected expls by an extensive series of successive approximations which were outlined in Ref 32. The hydrothermodynamic theory described in the same Rept was used in ealens. The final values of the constants for the individual gas species were found to be closely proportional to the high temp values of the vandetWaals b as evaluated by Hirschfelder et al (Ref 29c)... 

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 As there was no report issued at that time but just an unpublished letter of E.M. Boggs F.J. Martin addressed to Brinkley, a brief description of the method was given by him in Ref 39, p 87 In the ERL method, the general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,... 

By 1946, the best exptl values of the deton velocities had become somewhat different from 1943 values employed by Boggs Martin and this resulted in a somewhat different value of the covolume constant. A small residual variation in the covolume constant with density of expl suggested that the parameter of eq 23 should be re-evaluated. It was felt that the use of a T (jn lieu of T ) dependence of the covolume on temperature (which, would necessitate the re-evaluation of both the covolume constant and /S) would improve the agreement betw theory and experiment for cold expls (expls with. low temp of deton, like NGu) without sacrificing the excellent agreement obtd by Boggs Martin for the expls with higher deton temps (Ref 39, p 87). The hydrothermodynamic theory of detonation described in Ref 32 was used in calculation of expl properties of Amatex, 50/50-Amatol, 60/40-Amatol, TNT Composition B... 

The empirical parameters a, P, k, 6, and k,- were adjusted so that (for RDX, TNT, and their mixtures at various bulk densities) computed D-po curves and C-J pressures would match experimental values [120]. In order to extend the predictive capability of the EOS to a wider range of explosives, Mader employed two different sets of values for a, P, and k, depending on whether the explosive is moderately or highly oxygen deficient [122]. Moreover, he replaced the covolume constants k, of N2, CO2, and H2O with values which, when used in the C-F EOS, reproduced their shock Hugoniot F-F curves in the condensed phase. As for graphite, the EOS... 

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 ... 

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). 

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 ... 

It may be questioned whether the rapid increase of the pressure with the density of loading, rather than being the consequence of a constant reaction giving place to a considerable covolume, is not due simply to the mode of de-... 

Many attempts have been made to develop PVT relations for detonation products of condensed expls. These product gases, even in the absence of any condensed phase products, are very far from ideal. Thus most EOS for detonation products have included correction factors to account for non-ideality. Most product EOS are semi-empirical because they have to be adjusted to fit expti data. Usually the Abel equation, pv=nRT+atp, is used as a starting point. In the original Abel equation a is a constant covolume, but a constant a does not agree with observation. Therefore various attempts have been made to modify the Abel equation by inclusion of a = a(v) or a = a(p) and so on. The various attempts at obtaining a true EOS are summarized in Vol 4, D268-L to D298-R. Below we will briefly describe a new EOS which was developed recently... 

Here a and b are constants, b and a/V o, considering the covolume of the molecules and the inter molecular forces of attraction, respectively, p is the pressiue exerted by the gas on the walls of the vessel, and F ,oi is Ihe molecular volume. But even the van der Waals equation of state does not apply exactly to any particular substance since the intermolecular forces do not obey so simple a law as assumed in... 

The covolume b depends on state condition and on the kinds of molecules. To obtain a value for b, van der Waals devised an argument based in kinetic theory [23]. In practice, the covolume is usually taken to be a constant for a particular substance, with its value obtained by a fit to experimental data. If we do take b to be constant, if the molecules can be approximated as spheres, and if we want the equation of state to reliably reproduce Z at low densities, then the covolxune can be taken to be the hard-sphere second virial coefficient. 

Figure 3.1.2 shows the influence of pressure on z for different gases (Figure 3.1.2a) and the influence of temperature and pressure for the example of nitrogen (Figure 3.1.2b). At moderate temperatures z initially decreases with increasing pressure for most gases as the influence of the attractive forces dominates. Exceptions are H2 and He, where even at room temperature z increases with p as the parameter for the attractive force (value of constant a in Table 3.1.1) is very small. At high pressures, the influence of the covolume has an increasingly strong influence for all gases - as for H2 already at...

The Krypton Floride heat of formation from its elements at zero K is 8.114 kcalo-ries/mole. The covolume used for Krypton was 400. It was estimated using the corresponding states model and critical constants of Argon and Krypton as described in reference 52 as were the Krypton potential values for the ESP equation of state calculations . 

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