Word of Caution

A significant problem has been overlooked in many of the mixture correlations presented above. Many of the mixture correlations require the pure component property at the temperature and pressure of interest. For example, the specific volume of a liquid mixture can be calculated using the following equation, which was presented earlier  

How do we apply this equation if all of the substances are not liquids For example, consider a mixture containing 10% carbon dioxide and 90% hydrogen sulfide at 50°C and 7 MPa. At these conditions, the mixture is a liquid as is H2S, but pure C02 is not. At this temperature, carbon dioxide is supercritical and behaves like a gas regardless of the pressure. What value should be used for the specific 

A similar problem can arise in any of the correlations that relate the properties of a mixture to the pure component properties at the temperature and pressure of the mixture. In this module these included the viscosity and thermal conductivity of both liquids and gases. 

Answer At these conditions, assume that the mixture is a liquid (the pressure is greater than the vapor pressure of either pure component). In the next chapter, methods will be presented for determining which phases are present for a given condition. Further assume that the properties of the liquid are independent of the pressure. The pure component properties are taken from the tables presented earlier in this chapter. 

Density In order to estimate the density, they must be converted to molar volumes, since they are more fundamental than densities. 

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As a word of caution, the Bom-Oppenlieimer assumption is not universally valid. There are many reactions in which. 

The theoretical steam rate (sometimes referred to as the water rate) for stream turbines can be determined from Keenan and Keyes or Mollier charts following a constant entropy path. The theoretical steam rate is given as Ib/hr/kw which is easily converted to Ib/hr/hp. One word of caution—in using Keenan and Keyes, steam pressures are given in PSIG. Sea level is the basis. For low steam pressures at high altitudes appropriate coirections must be made. See the section on Pressure Drop Air-Cooled Air Side Heat Exchangers, in this handbook, for the equation to correct atmospheric pressure for altitude. 

Total interpenetration of chains (X approaches Rg) is not necessary to achieve complete strength when M > M and x < 7). However, a word of caution while complete strength may be obtained in terms of critical fracture measures such as G c and A lc, the durability, measured in sub-critical fracture terms, such as the fatigue crack propagation rate da/AN, may be very far from its fully healed state at r. We have shown that while the weld toughness A lc increases linearly with interdiffusion depth X as K f. X, the fatigue crack propagation behavior of partially healed welds behaves as [1]... 

A word of caution before we start. A rigorous approach to many of the derivations requires keeping track of several different indices and validating why certain transformations are possible. The derivations will be performed less rigorously, trying to illustrate the flow of arguments, rather than focus on mathematical details. 

There are three main methods for calculating electron correlation Configuration Interaction (Cl), Many Body Perturbation Theory (MBPT) and Coupled Cluster (CC). A word of caution before we describe these methods in more details. The Slater determinants are composed of spin-MOs, but since the Hamilton operator is independent of spin, the spin dependence can be factored out. Furthermore, to facilitate notation, it is often assumed that the HF determinant is of the RHF type. Finally, many of the expressions below involve double summations over identical sets of functions. To ensure only the unique terms are included, one of the summation indices must be restricted. Alternatively, both indices can be allowed to run over all values, and the overcounting corrected by a factor of 1/2. Various combinations of these assumptions result in final expressions which differ by factors of 1 /2, 1/4 etc. from those given here. In the present book the MOs are always spin-MOs, and conversion of a restricted summation to an unrestricted is always noted explicitly. 

A word of caution Any publication that claims major advantages for a particular breed of suspension or propulsion should be viewed with skepticism. 

The constant matrix in Group III is conveniently defined as all the sample except the elements being determined, but a word of caution is necessary. If these elements are present at appreciable concentration, then absorption and enhancement effects to which they give rise must of course be considered for, as was pointed out in Section 7.3, these effects do not reside in the matrix alone. 

A word of caution is in order at this point. There is an unrealistic tendency on the part of some to think that once the mathematical solution of a problem has been found the task of the scientist is completed, and that the effort of interpreting and applying the solution is an easy one. We must emphasize the fact that the difficulty of solving an operational problem is really encountered after the mathematical solution has been obtained i.e., in the effective application of the theoretical solution to a specific, physical problem. 

A word of caution should be added with regard to the calculation of the burn-out flux for a pressure intermediate to the main pressure groups that have been correlated this calculation must not be done by taking intermediate y values from Table II. The recommended procedure is to estimate the burn-out flux for the required conditions for the main pressure groups above and below the required pressure, and then to interpolate linearly. It must be also emphasized that while the above correlations can be used with confidence within the experimental ranges of the data, extrapolation outside these ranges should not be taken very far without allowing for a possible reduction in the accuracy obtained. 

A word of caution different authors use different conventions for Zemike notation and normalization. We are using the convention of Bom and Wolf (1999). 

Sample shelves also become overcrowded quickly, but it is often required to keep samples for extended periods of time. Older samples can be stacked into cardboard cartons, clearly identified by laboratory project references or quality control numbers, and stored at a convenient location away from the laboratory. Periodically they should be inspected and the out of date ones eliminated. One word of caution, however. Under current pollution control rules, laboratory samples may not be indiscriminatly disposed of as garbage. The laboratory operator should call in a waste disposal service when in doubt. 

So much for the advantages. Virtual organs clearly have one major drawback they are models only. While this very nature of in silico technology is the core foundation for the benefits listed above, it also calls for a word of caution. It is imperative for in silico tools to be seen in the context of a whole range of scientific and research tools, and to never neglect that theoretical considerations will continue to need experimental validation. 

However, before we accept this conclusion as the definitive one, a word of caution is necessary. Due to the CO-CO interactions the heats of adsorption depend on the coverage 0. Shek et al (17) compared Pt and alloys at a constant dosage and this could mean that the coverage of Pt was (at the same dosage) lower on Pt than on alloys, and consequently - the heat of adsorption higher. Shek et al report the above mentioned data for the (111) faces of Pt and alloys. They studied also the (110) faces, but there the effect of alloying is masked by the reconstruction of the surface upon CO-adsorption (18). 

A word of caution is appropriate. The reactions that are used for illustration are very seldom specihc for a single taxon—or even close relatives, and it is not generally possible to establish the range of organisms that will be able to carry ont the reaction. 

A word of caution Metals, materials in general, chemicals used to study metals in the laboratory, chemicals used for corrosion protection, and essentially any chemicals should be (1) used in compliance with all applicable codes, laws, and regulations (2) handled by trained and experienced individuals in keeping with workmanlike environmental and safety standards and (3) disposed only using allowable methods and in allowable quantities. 

One word of caution For gas mixtures or air, be sure to include the contained water. It can be a healthy percentage for a Gulf Coast air compressor. 

Albertus, Frater], Words of caution. Alchem Lab Bulls, no. 17 (Q4 1963). rhttp //www.spagyria.com/alb.zip1. 

Even Geigy s New York representative, Victor Froehlicher, urged caution until tests feeding DDT to animals were completed. Attempts have been made to determine the fate of DDT after absorption by the animal body but no positive results have been obtained as yet.. .. A word of caution might well be in order. This is a new product and as such would require years of research under normal conditions. ... 

After all this fancy mathematics, we need a word of caution. It is extremely dangerous to apply the state estimate as presented in this chapter. Why The first hint is in Eq. (9-32). We have assumed perfect knowledge of the plant matrices. Of course, we rarely do. Furthermore, we have omitted actual terms for disturbances, noises, and errors in measurements. Despite these drawbacks, material in this chapter provides the groundwork to attack serious problems in modem control. 

A variety of mechanisms have since been suggested to explain the physical basis for the observed transition between flow patterns (Ishii, 1975 Taitel and Dukler, 1976b Taitel et al., 1980 Barnea, 1987 Taitel and Barnea, 1990). Dukler and Taitel (1991b) summarized the various mechanisms to explain such flow pattern transitions (Table 3.1), where the letters in Table 3.1 identify the theoretical curves shown in the accompanied graphs (Fig. 3.7) for different flow directions. A word of caution was given in the reference ... 

On the subject of comparing iterative methods a word of caution is in order. Clearly in any quantitative comparison, the termination criteria should be comparable and the benchmark problems should be run on the same computer. Yet even for simple problems and methods, these two requirements prove to be difficult to enforce and insufficient to ensure meaningful comparisons. To allow for the fact that different methods do not terminate at exactly the same point even when the same termination criterion is used, Broyden (B13) introduced a mean convergence rate, R, which is... 

Ablin, AJ. 2005. Lycopene A word of caution. Am J Health Syst Pharm 62 899. 

A final word of caution on aromatic systems - the electron donating groups (notably those in which oxygen is the shielding entity) can cause problems, because their ortho- and para- effects are so similar. Consider the following example - you are presented with a sample known to be one of the two isomers shown in Structure 5.3 ... 

A word of caution should be made here the assumption in both Bennett s original calculation [21] and in the maximum-likelihood formalism [22] is that all work values are statistically independent. This may not be the case, for instance, if consecutive initial configurations are close in time along an equilibrium trajectory. If results... 

A word of caution should be made with respect to estimating tenability for human exposures. Experimental LC values are determined using rat lethality as the bioassay. Judgement should be exercised for human tenability, with limits set considerably lower than FED summation at unity. An FED limit of, perhaps, 0.3 may be more appropriate for assessment of the potential escape of humans. 

Despite this word of caution, one should not lose site of the fact that there are many industrial reactor systems that can be accurately simulated with existing SGS models ... 

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