Extrapolability Subject

The sohd line in Figure 3 represents the potential vs the measured (or the appHed) current density. Measured or appHed current is the current actually measured in an external circuit ie, the amount of external current that must be appHed to the electrode in order to move the potential to each desired point. The corrosion potential and corrosion current density can also be deterrnined from the potential vs measured current behavior, which is referred to as polarization curve rather than an Evans diagram, by extrapolation of either or both the anodic or cathodic portion of the curve. This latter procedure does not require specific knowledge of the equiHbrium potentials, exchange current densities, and Tafel slope values of the specific reactions involved. Thus Evans diagrams, constmcted from information contained in the Hterature, and polarization curves, generated by experimentation, can be used to predict and analyze uniform and other forms of corrosion. Further treatment of these subjects can be found elsewhere (1—3,6,18). 

In this example it has been assumed that the service temperature is 20 °C. If this is not the case, then curves for the appropriate temperature should be used. If these are not available then a linear extrapolation between temperatures which are available is usually sufficiently accurate for most purposes. If the beam in the above example had been built-in at both ends at 20 °C, and subjected to service conditions at some other temperature, then allowance would need to be made for the thermal strains set up in the beam. These could be obtained from a knowledge of the coefficient of thermal expansion of the beam material. This type of situation is illustrated later. 

Extrapolations are always subject to error, but fortunately the contribution to the entropy resulting from the extrapolation is a small part of the total. In glucose, for example, S g = 219.2 0.4 J-K -moF1, but the entropy contribution at 10 K obtained from the Debye extrapolation is only 0.28 J-K 1-mol 1. Well-designed cryogenic calorimeters are able to produce Cp measurements of high accuracy hence, the Third Law entropy obtained from the Cp measurements can also be of high accuracy. 

More recently, the curvature at air/solution interfaces has been accounted for by Nikitas and Pappa-Louisi98 in terms of a specific molecular model that predicts a linear dependence of (lM/ ) on (1/0). The same model also reproduces the behavior at metal/solution interfaces, specifically Hg electrodes, for which most of the experimental data exist. Nikitas treatment provides a method for an unambiguous extrapolation of the adsorption potential shift to 0= 1. However, the interpretation of the results is subject to the difficulties outlined above. Nikitas approach does provide... 

The statistical interpretations are there is a 5% chance that the extrapolation is below 90% at f = 26 and there is a 5% chance that a further measurement at / = 26 months will yield a result below y 89% of nominal. Every batch in the stability program is subjected to this procedure the batch that yields the shortest shelf-life sets the expiration date. Possible solutions are as follows ... 

The physical nature of the ZEKE states has been the subject of intense experimental and theoretical investigation in the past several years. In the well-studied case of NO,14,21 we know from the 3 cm-1 red shift of the ZEKE-PFI threshold band relative to the true adiabatic ionization potential (extrapolated from highly accurate measurements of Rydberg series) that the ZEKE states have principal quantum number n 200 and lifetime of 2 (is or longer. Recent work has found ZEKE states with lifetimes as long as 20 ps.22... 

As developed in the 1850s, positivism came to be understood as a philosophical belief which held that the methods of natural science offer the only viable way of thinking correctly about human affairs. Accordingly, empirical experience - processed with a self-conscious fear of subjective contamination - served as the basis of all knowledge. Facts, the products of sensory experience, and, by extrapolation, the data derived from machines and instruments built as extensions of that faculty, were first ascertained, and then classified. 

Are the equilibrium constants for the important reactions in the thermodynamic dataset sufficiently accurate The collection of thermodynamic data is subject to error in the experiment, chemical analysis, and interpretation of the experimental results. Error margins, however, are seldom reported and never seem to appear in data compilations. Compiled data, furthermore, have generally been extrapolated from the temperature of measurement to that of interest (e.g., Helgeson, 1969). The stabilities of many aqueous species have been determined only at room temperature, for example, and mineral solubilities many times are measured at high temperatures where reactions approach equilibrium most rapidly. Evaluating the stabilities and sometimes even the stoichiometries of complex species is especially difficult and prone to inaccuracy. 

No studies have been conducted with silver and avian or mammalian wildlife, and it is unreasonable to extrapolate the results of limited testing with domestic poultry and livestock to wildlife to establish criteria or administratively enforced standards. Research on silver and avian and terrestrial wildlife merits the highest priority in this subject area. No silver criteria are available for the protection of avian and mammalian health, and all criteria now proposed are predicated on human health (Table 7.8). As judged by the results of controlled studies with poultry and small laboratory mammals, safe concentrations of silver ion were less than 250 pg/L in drinking water of mammals, less than 100 mg/L in drinking water of poultry, less than 6 mg/kg in diets of mammals, less than 10 mg/kg in copper-deficient diets of poultry, less than 200 mg/kg in copper-adequate diets of poultry, and less than 1.8 mg/kg in chicken eggs. The proposed short-term (10-day) allowable limit of 1142 pg Ag/L in drinking water for human health protection (Table 7.8) should... 

From the measurements published in the paper it cannot be inferred that the concentration-time curves can safely be extrapolated to zero time. The authors do not communicate details as to how well the beginning of the reaction could be defined. It should be pointed out that reaction kinetics derived by these means are subject to the uncertainties inherent in the extrapolation method. This holds particularly for a rapidly accelerated reaction. Furthermore, the possibility that the decomposition was initiated heterogeneously could not be excluded with certainty. These objections have to be considered when regarding the following kinetic results. 

Efficacy. A relative concept referring to the ability of a medicine to elicit a beneficial clinical effect. This may be measured or evaluated using objective or subjective parameters, and in terms ranging form global impressions to highly precise measurements. Efficacy is assessed at one or more levels of organization (e.g., subcellular, cellular, tissue, organ, whole body) and may be extrapolated to other levels. 

Estimates of service life are usually made either by natural or simulated trials or, most commonly, by accelerated tests with extrapolation to predict performance at longer times under less severe conditions. An alternative approach is to subject the product to environmental exposures which equate to the whole design life, and then to assess performance by real or simulated service tests (the end performance assessment). The exposures usually have to involve accelerated procedures and can be composed of several environmental agents applied simultaneously or sequentially. 

Reproducibility is important and a parameter with distinct advantages in other ways may have to be rejected if it is poor in this respect. When time scales may extend over months and the results are subject to extrapolation, poor reproducibility will result in uncertainty levels which render the conclusions meaningless. This is particularly important when logarithmic time scales are applied, in which a modest level of scatter converts to errors in time stretching from minutes to centuries. 

When extrapolation of measured data is carried out all the uncertainties become magnified, increasing as the degree of extrapolation is increased. Inevitably, extrapolations from accelerated tests to normal ambient conditions will be subject to enormous uncertainties, which is why the general advice for temperature is to extrapolate to 30-40 °C beyond the last data point at the very most. Additional to this, but generally not quantifiable, is the uncertainty of the validity of the extrapolation model. 

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