The Second

Evidently, the present definition of the second is out of character with the rest of the definitions based on constants which could be called universal (with the possible exception of the Avogadro constant). In contrast, the hyperfine frequency of cesium is a property of a specific atom. 

A definition of the second that is consistent with those made in terms of universal constants could, in principle at least, be based on specifying a value for the Rydberg constant, which is also a universal constant. If the value of the Rydberg constant in inverse meters were specified, then since the speed of light c is exact, the corresponding frequency would be fixed. From this, the observed frequencies of particular atomic transitions could be known and used as time standards. 

The drawback, at the moment, is that the theory needed to relate the Rydberg constant to observable frequencies is not sufficiently accurate to make this modification without introducing an excessively large uncertainty. This could change in the future, but for now, such a redefinition would not be practical. 

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It is strictly for convenience that certain conventions have been adopted in the choice of a standard-state fugacity. These conventions, in turn, result from two important considerations (a) the necessity for an unambiguous thermodynamic treatment of noncondensable components in liquid solutions, and (b) the relation between activity coefficients given by the Gibbs-Duhem equation. The first of these considerations leads to a normalization for activity coefficients for nonoondensable components which is different from that used for condensable components, and the second leads to the definition and use of adjusted or pressure-independent activity coefficients. These considerations and their consequences are discussed in the following paragraphs. 

In a binary liquid solution containing one noncondensable and one condensable component, it is customary to refer to the first as the solute and to the second as the solvent. Equation (13) is used for the normalization of the solvent s activity coefficient but Equation (14) is used for the solute. Since the normalizations for the two components are not the same, they are said to follow the unsymmetric convention. The standard-state fugacity of the solvent is the fugacity of the pure liquid. The standard-state fugacity of the solute is Henry s constant. 

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... 

Bfi and 022- However, in the second binary, intermolecular forces between unlike molecules are much stronger than those between like molecules chloroform and ethyl acetate can strongly hydrogen bond with each other but only very weakly with them-... 

The third edition of "Properties of Gases and Liquids" by Reid et al. (1977) lists useful group contribution methods for predicting critical properties. Contributions to the second... 

In Equation (15), the third term is much more important than the second term. The third term gives the enthalpy of the ideal liquid mixture (corrected to zero pressure) relative to that of the ideal vapor at the same temperature and composition. The second term gives the excess enthalpy, i.e. the liquid-phase enthalpy of mixing often little basis exists for evaluation of this term, but fortunately its contribution to total liquid enthalpy is usually not large. 

The second term in Equation (15a) gives the enthalpy of mixing of the condensable components. It is difficult to estimate that enthalpy but fortunately it ma)ies only a small contri-... 

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. 

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 FREE CONTRIBUTION TO THE SECOND VIRIAL COEFFICIENT,... 

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. 

In the second model (Fig. 2.16) the continuous well-stirred model, feed and product takeoff are continuous, and the reactor contents are assumed to he perfectly mixed. This leads to uniform composition and temperature throughout. Because of the perfect mixing, a fluid element can leave at the instant it enters the reactor or stay for an extended period. The residence time of individual fluid elements in the reactor varies. 

The second class of distillation operation using an extraneous mass-separating agent is extractive distillation. Here, the extraneous mass-separating agent is relatively involatile and is known as a solvent. This operation is quite different from azeotropic distillation in that the solvent is withdrawn from the column bottoms and does not form an azeotrope with any of the components. A typical extractive distillation process is shown in Fig. 3.11. ... 

Another factor that can be important in the design of evaporators is the condition of the feed. If the feed is cold, then the backward-feed arrangement has the advantage that a smaller amount of liquid must be heated to the higher temperatures of the second and first stages. 

Consider a three-product separation as in Fig. 5.11a in which the lightest and heaviest components are chosen to be the key separation in the first column. Two further columns are required to produce pure products (see Fig. 5.11a). However, note from Fig. 5.11a that the bottoms and overheads of the second and third columns are both pure B. Hence the second and third columns could simply be connected and product B taken as a sidestream (see Fig. 5.116). The arrangement in Fig. 5.116 is known as a prefractionator arrangement. Note that the first column in Fig. 5.116, the prefractionator, has a partial condenser to reduce the overall energy consumption. Comparing the prefractionator arrangement in Fig. 5.116 with the conventional... 

First consider thermal coupling of the simple sequences from Fig. 5.1. Figure 5.14a shows a thermally coupled direct sequence. The reboiler of the first column is replaced by a thermal coupling. Liquid from the bottom of the first column is transferred to the second as before, but now the vapor required by the first column is supplied by the second column instead of by a reboiler on the first column. The four column sections are marked as 1, 2, 3, and 4 in Fig. 5.14a. In... 

The batch cycle time has been reduced from 2.6 to 1.3 hours. This means that a greater number of batches can be processed, and hence, if there are two reactors each with the original capacity, the process capacity has increased. However, the increase in capacity has been achieved at the expense of increased capital cost for the second reactor. An economic assessment is required before we can judge whether the tradeoff is justified. 

The second of the major hazards is explosion, which has a disaster potential usually considered to be greater than fire but lower than toxic release. Explosion is a sudden and violent release of energy. 

Wastewater leaves the process from the bottom of the second column and the decanter of the azeotropic distillation column. Although both these streams are essentially pure water, they will nevertheless contain small quantities of organics and must be treated before final discharge. This treatment can be avoided altogether by recycling the wastewater to the reactor inlet to substitute part of the freshwater feed (see Fig. 10.36). 

The crude phthalic anhydride is heated and held at 260 C to allow some byproduct reactions to go to completion. Purification is by continuous distillation in two columns. In the first column, maleic anhydride and benzoic and toluic acids are removed overhead. In the second column, pure phthalic anhydride is removed overhead. High boiling residues are removed from the bottom of the second column. 

The future worth of the second annual payment after (n - 2) years is... 

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