Accuracy graphical method

A model-free method for the analysis of lattice distortions is readily established from Eq. (8.13). It is an extension of Stokes [27] method for deconvolution and has been devised by Warren and Averbach [28,29] (textbooks Warren [97], Sect. 13.4 Guinier [6], p. 241-249 Alexander [7], Chap. 7). For the application to common soft matter it is of moderate value only, because the required accuracy of beam profile measurement is rarely achievable. On the other hand, for application to advanced polymeric materials its applicability has been demonstrated [109], although the classical graphical method suffers from extensive approximations that reduce its value for the typical polymer with small crystal sizes and stronger distortions. 

This graphical method is generally a good means of obtaining values of K to an accuracy of about 5-10%. The accuracy is maximized if each value of i/2 is obtained by using the Heyrovsky-Ilkovic procedure (via equation (6.6) as seen earlier). Furthermore, the values of 1/2 (both complexed and free) are more accurate if well separated. 

A prime application of graphical methods in modern distillation technology is for analyzing the results of computer simulations. Several of the graphical construction rules can be bent in order to benefit from computer accuracy and to reduce effort. Johnson and Morgan (28) described several key considerations their work is expanded here using the author s experience. 

Another useful electroanalytical procedure is the standard addition method successive quantities of a standard solution are added to the unknown solution, the concentration of species in the unknown solution being determined from the intercept of the plot of response vs. quantity added. Note that the use of graphical methods without comparison with theoretical equations and known systems does not prove the accuracy of the experiments, but only their precision. 

Refinements in the Schmidt graphical method are discussed by Jakob [5], particularly the techniques for improving accuracy at the boundary for either convection or other boundary conditions. The accuracy of the method is improved when smaller Ax increments are taken, but this requires a larger number of time increments to obtain a temperature distribution after a given time. 

If you had a mixture of two liquids, how many plates would be needed to separate them This is important, because if you do not use enough plates, the mixture will not be adequately separated, and if you use too many, you are wasting time and energy, both of which are expensive. In this section, several equations will be reproduced that have been developed by others to determine the number of plates for a system at total reflux, for a system at partial reflux, and for a graphical method to do it quicker and with reasonable accuracy. The equations developed below were from the following original papers ... 

The accuracy of determination of small values of the geometric factor at the initial part of the response is usually very low. It becomes specially noticeable in the case of a nonuniform medium, for example, when the borehole is much more conductive than the formation. For these conditions the focusing abilities of a probe, chosen by the graphical method, can be insufficient in order to eliminate the influence of the borehole or the invasion zone especially, if the latter is more conductive than the formation. For this reason focusing features of a multi-coil induction probe, chosen by the graphical method, manifests themselves as a rule only for relatively small ratios p jP -... 

Considering the accuracy of the graphical methods and the use of arithmetic mean values for G and ys, this is reasonable agreement. 

A graphical method proposed by Novikova and Natradze [56] is based on a three-dimensional co-ordinate system, in which the variation of the parameters is represented by a straight line. The abscissa corresponds to the azeotropic composition in moiyo) ike ordinate to the reciprocal of the boiling point and the applicate (third axis) to the logarithm of the pressure. If the azeotropic data are known at two pressures it is possible to determine with accuracy for binary mixtures ... 

This procedure involves making measurements on each sample between measurements on two calibration standards prepared such that their ion abundances fall just above and below the ion abundances of the sample. Analyte concentration is calculated by linear interpolation between bracketing standards and good precision and accuracy can be achieved using this procedure. This is a specialised version of the graphical method and, again, is mostly used for organic IDMS. 

However, since accuracy is limited by the equilibrium data, the conputer calculations assuming CMO are not more accurate than the graphical method. 

The results of thermochemical calculations on a computer give values P(t2) = 74.4 psia (0.51 MPa), T(t2> = 240rR (1334 K). The difference between the results (summarized in Table 4A-1) gives an indication of the accuracy to be expected from the simple graphical methods. 

In hen of careful independent checks of predictive accuracy, the results of the comprehensive theoretical work will not be presented here. Simpler, more easily understood predictive methods, for certain important limiting cases, will be presented. As a check on the accuracy of these simpler methods, it will perhaps be prudent to calculate the bubble diameter from the graphical representation by Mersmann (loc. cit.) of the resiJts of Kumar et al. (loc. cit.). 

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