Rule Assumption

Lewis rule assumes that (1) the densities of the adsorbates are the same as the densities of the liquid-phase adsorptive and (2) the volumes of the adsorbates add to yield the pore volume. Both assumptions could be incorrect, but for mixing liquid phases, assumption (2) is usually fairly good. These assumptions yield 

The analysis of binary adsorption in micropores depends somewhat upon the analysis of adsorption of the pure adsorptives. The ideal situation would be to analyze the adsorption of the pure adsorptives and from this information predict the adsorption of the binary adsorptives. The analysis of the pure adsorbates is given in Chapter 6. Some of the results of the analysis will be used here to demonstrate a few points. 

It is not completely necessary to do a thorough investigation of the pure adsorbates, if one is wilhng to make a few measurements for the binary system. The following analysis wiU demonstrate this. 

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Does this person tend to question established rules, assumptions, and structures ... 

A viable alternative for small systems is variational transition state theory or VTST (see Truhlar et al. 1985). Recall that TST makes use of the non-recrossing rule assumption. When recrossing does occur, the assumption results in the over-counting of transitions from reactants to products that is, the TST rate constant is an upper bound. In VTST, a divide is sought that minimizes these transitions resulting in a minimum rate constant and this divide becomes the basis for the VTST rate constant. We consider, as the simplest example, canonical variational ensemble transition state theory (CVT). 

In both cases, part of the functions will be executed in a more predictable way (under a stronger failure or timeliness model), while other functions, the complex ones, will execute in a less predictable part of the system. The system separation in two parts makes it easier to enforce the properties assumed for the better part, while safety is ensured by making the system adjustable at run-time the complex functions will only be used for control when a certain set of assumptions is satisfied. For that, the system must encompass a safety manager that observes relevant variables, verifies if predefined safety rules (assumptions) are met, and adjusts the system configuration and operation whenever necessary. 

Unfortunately, the ideal-gas assumption can sometimes lead to serious error. While errors in the Lewis rule are often less, that rule has inherent in it the problem of evaluating the fugacity of a fictitious substance since at least one of the condensable components cannot, in general, exist as pure vapor at the temperature and pressure of the mixture. 

The maximum temperature cross which can be tolerated is normally set by rules of thumb, e.g., FrSQ,75 °. It is important to ensure that Ft > 0.75, since any violation of the simplifying assumptions used in the approach tends to have a particularly significant effect in areas of the Ft chart where slopes are particularly steep. Any uncertainties or inaccuracies in design data also have a more significant effect when slopes are steep. Consequently, to be confident in a design, those parts of the Ft chart where slopes are steep should be avoided, irrespective of Ft 0.75. 

Many experimental techniques now provide details of dynamical events on short timescales. Time-dependent theory, such as END, offer the capabilities to obtain information about the details of the transition from initial-to-final states in reactive processes. The assumptions of time-dependent perturbation theory coupled with Fermi s Golden Rule, namely, that there are well-defined (unperturbed) initial and final states and that these are occupied for times, which are long compared to the transition time, no longer necessarily apply. Therefore, truly dynamical methods become very appealing and the results from such theoretical methods can be shown as movies or time lapse photography. 

The golden rule is a reasonable prediction of state-crossing transition rates when those rates are slow. Crossings with fast rates are predicted poorly due to the breakdown of the perturbation theory assumption of a small interaction. 

Most of the assumptions are based on idealized models, indicating the limitations of the mathematical methods employed and the quantity and type of experimental data available. For example, the details of the combinatorial entropy of a binary mixture may be well understood, but modeling requires, in large measure, uniformity so the statistical relationships can be determined. This uniformity is manifested in mixing rules and a minimum number of adjustable parameters so as to avoid problems related to the mathematics, eg, local minima and multiple solutions. 

Rules may represent either guidelines based on experience, or compact descriptions of events, processes, and behaviors with the details and assumptions omitted. In either case, there is a degree of uncertainty associated with the appHcation of the rule to a given situation. Rule-based systems allow for expHcit ways of representing and dealing with uncertainty. This includes the representation of the uncertainty of individual rules, as weU as the computation of the uncertainty of a final conclusion based on the uncertainty of individual rules, and uncertainty in the data. There are numerous approaches to uncertainty within the rule-based paradigm (2,35,36). One of these approaches is based on what are called certainty factors. In this approach, a certainty factor (CF) can be associated with variable—value pairs, and with individual rules. The certainty of conclusions is then computed based on the CF of the preconditions and the CF for the rule. For example, consider the foUowing example. 

For a sequenee of reaetion steps two more eoneepts will be used in kinetics, besides the previous rules for single reaetions. One is the steady-state approximation and the seeond is the rate limiting step eoneept. These two are in strict sense incompatible, yet assumption of both causes little error. Both were explained on Figure 6.1.1 Boudart (1968) credits Kenzi Tamaru with the graphical representation of reaction sequences. Here this will be used quantitatively on a logarithmic scale. 

At the same time it is not surprising that polymer melts are non-Newtonian and do not obey such simple rules. Fortunately, if we make certain assumptions, it is possible to analyse flow in certain viscometer geometries to provide measurements of both shear stress (t) and shear rate (7) so that curves relating the two (flow curves) may be drawn. 

While HiickeTs 4n + 2 rule applies only to monocyclic systems, HMO flieory is applicable to many other systems. HMO calculations of fused-ring systems are carried out in much the same way as for monocyclic species and provide energy levels and atomic coefficients for the systems. The incorporation of heteroatoms is also possible. Because of the underlying assumption of orthogonality of the a and n systems of electrons, HMO dieory is restricted to planar molecules. 

A useful rule of thumb is that the turbine work in a STIC plant is increased by a factor of about (1 + 25), since the specific heat of the steam is about double that of the specific heat of the dry gas. This is in agreement with the example given above and with the earlier detailed calculations by Fraize and Kinney [3]. (Their work was based on the assumption that the mixture of air and steam in the turbine behaved as a semi-perfect gas, with specific heats being determined simply by mass averaging of the values for the two components.)... 

The foregoing are but examples of the types of mechanics of materials approaches that can be used. Other assumptions of physical behavior lead to different expressions for the four elastic moduli for a unidirectionally reinforced lamina. For example, Ekvall [3-2] obtained a modification of the rule-of-mixtures expression for and of the expression for E2 in which the triaxial stress state in the matrix due to fiber restraint is accounted for ... 

The model is intrinsically irreversible. It is assumed that both dissociation of the dimer and reaction between a pair of adjacent species of different type are instantaneous. The ZGB model basically retains the adsorption-desorption selectivity rules of the Langmuir-Hinshelwood mechanism, it has no energy parameters, and the only independent parameter is Fa. Obviously, these crude assumptions imply that, for example, diffusion of adsorbed species is neglected, desorption of the reactants is not considered, lateral interactions are ignored, adsorbate-induced reconstructions of the surface are not considered, etc. Efforts to overcome these shortcomings will be briefly discussed below. 

In order to cope with a complex environment, people make extensive use of rules or assumptions. This rule based mode of operation is normally very efficient. However, errors will arise when the underlying assumptions required by the rules are not fulfilled. Chapter 2 discusses the causes of these rule based errors in detail. 

Many of these applications require tasks or parts of a task to be categorized according to the SRK scheme. Although this is difficult in some cases, a simple flowchart may assist in this process. This is given in Figure 2.8. This assumes that the tasks will be performed by a worker of average competence. This assumption is necessary, since the actual mode that the task will be performed in (skill, rule, or knowledge) obviously depends on the characteristics of the individual (how well trained, how capable) as well as the task. 

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