Calculation Exercise

Appendix G contains answers to tiie review and dosage calculation exercises appearing at the end of tiie chapters. 

Appendix G contains answers to die review and dos calculation exercises ipearing at the end of die ch iters. 

These exercises are intended to probe your understanding of key concepts rather than your ability to utilize formulas and perform calculations. Exercises with red exercise numbers have answers in the back of the book. 

As far as the WAC group is concerned, the benchmark exerdse about BN-8(X) in its nearly-zero void reactivity version focused on severe transient accident conditions of the ULOF type. At their yearly review meeting of May 94, the IWGFR of IAEA had agreed to support this new BN-800 calculational exercise proposed by IPPE. Participation includes Germany, France, UK, Italy and Russia as the traditional partners of the WAC comparative exercises, as well as USA, Japan and India as additional "IAEA" parmers. 

The oil formation volume factor at initial reservoir conditions (B., rb/stb) is used to convert the volumes of oil calculated from the mapping and volumetries exercises to... 

While the result should not have very exact physical meaning, as an exercise, calculating the f potential of lithium ion, knowing that its equivalent conductivity is 39 cm /(eq)(ohm) in water at 25°C. 

If we go back and calculate the slope and intercept for the data set in Exercise 3-2 without the constraint that the line must pass through the origin, we get the solution vector 0.95, 0.09 for a line parallel to the line in Exercise 3-3 and 2.0 units distant from it, as expected. 

Select several values for p of the data set in Exercise 3-1 and calculate xi — p) for each of them. Plot the curve of xi — p) as a function of the selected parameter p and locate the minimum visually. Compare with Solution 3-1. 

Calculate the integrals H -j. H-f. and tiff that go with the integral calculated in Exercise 8-1. 

How many iterations does it take to achieve self-consistency for the helium problem treated (partially) in Exercises 8-3 and 8-4 What is the % discrepancy between the calculated value of the first ionization potential and the experimental value of 0.904 hartiees when the solution has been brought to self-consistency ... 

There is considerable variation in the values assigned to the election repulsion integrals in Exercise 8.9.1. Salem (1966) points out that calculation using Slater orbitals leads to... 

Note that agreement with Pariser and Parr s empirical value is better for Y13 than for Yn ) Use Salem s values to calculate election densities on the three carbon atoms of the allyl anion for one iteration beyond the initial Huckel values, as was done in Exercise 8.9.1. Comment on the results you get, as to the qualitative picture of the anion, the influence of election repulsion on the charge densities, and agreement or lack of agreement with the results already obtained with the Pariser and Parr parameters. 

Procedure. Cany out the STO-3G single point calculations on H2 in a way similar to that of Exercise 10-9 at interatomic distances of 0.4 to 1.2 A at intervals of 0.1 A. This is best done in the z-mahix format, for example. 

The Huckel method and is one of the earliest and simplest semiempirical methods. A Huckel calculation models only the 7t valence electrons in a planar conjugated hydrocarbon. A parameter is used to describe the interaction between bonded atoms. There are no second atom affects. Huckel calculations do reflect orbital symmetry and qualitatively predict orbital coefficients. Huckel calculations can give crude quantitative information or qualitative insight into conjugated compounds, but are seldom used today. The primary use of Huckel calculations now is as a class exercise because it is a calculation that can be done by hand. 

Atextbook describing the theory associated with calculations of the electronic structure of molecular systems. While the book focuses on ab initio calculations, much of the information is also relevant to semi-empirical methods. The sections on the Hartree-Fock and Configuration Interactions methods, in particular, apply to HyperChem. The self-paced exercises are useful for the beginning computational chemist. 

In this problem you will collect and analyze data in a simulation of the sampling process. Obtain a pack of M M s or other similar candy. Obtain a sample of five candies, and count the number that are red. Report the result of your analysis as % red. Return the candies to the bag, mix thoroughly, and repeat the analysis for a total of 20 determinations. Calculate the mean and standard deviation for your data. Remove all candies, and determine the true % red for the population. Sampling in this exercise should follow binomial statistics. Calculate the expected mean value and expected standard deviation, and compare to your experimental results. 

The calculation of the remaining vertices is left as an exercise. The progress of the completed optimization is shown in Table 14.3 and in Figure 14.10. The optimum response of (3, 7) first appears in the twenty-fourth simplex, but a total of 29 steps is needed to verify that the optimum has been found. 

Cell geometry, such as tab/terminal positioning and battery configuration, strongly influence primary current distribution. The monopolar constmction is most common. Several electrodes of the same polarity may be connected in parallel to increase capacity. The current production concentrates near the tab connections unless special care is exercised in designing the current collector. Bipolar constmction, wherein the terminal or collector of one cell serves as the anode and cathode of the next cell in pile formation, leads to gready improved uniformity of current distribution. Several representations are available to calculate the current distribution across the geometric electrode surface (46—50). 

Diffiusion Coefficient. The method of Reference 237 has been recommended for many low pressure binary gases (238). Other methods use solvent and solute parachors to calculate diffusion coefficients of dissolved organic gases in Hquid solvents (239,240). Molar volume and viscosity are also required and may be estimated by the methods previously discussed. Caution should be exercised because errors are multiphcative by these methods. 

Problems can also arise when allocating overheads on the basis of direct labor cost. Let us consider a company that evaluates overheads at 125 percent of direct labor cost. A process plant employs seven operators, each with a direct cost of 10,000 per budget period. As a result of a works-study exercise, it is found that the plant can operate satisfactorily with six operators. The ac tual cost saving is hkely to oe far nearer to the direct labor savings of 10,000 per period than to the calculated saving of 10,000 -t- 10,000(125/100) = 22,500 per period. The 22,500 calculated saving is the direct labor cost plus overheads taken as 125 percent of the direct labor cost. 

To make the necessary thermodynamic calculations, plausible reaction equations are written and balanced for production of the stated molar flows of all reactor products. Given the heat of reaction for each applicable reaction, the overall heat of reaction can be determined and compared to that claimed. However, often the individual heats of reaction are not all readily available. Those that are not available can be determined from heats of combustion by combining combustion equations in such a way as to obtain the desired reaction equations by difference. It is a worthwhile exercise to verify this basic part of the process. 

For relatively uniform elevated terrain, or as a "first cut" conservative estimate of terrain effects, the user should input the maximum terrain elevation (above stack base) within 50 km of the source, and exercise the automated distance array option out to 50 km. For isolated terrain features a separate calculation... 

An estimate of the linear velocity of air through ductwork is a common exercise for process engineers. The calculation requires information on the static pressure drop and volumetric flowrate at any given temperature and pressure. 

Quite a few years ago, Dr. Azbel and I analyzed the operational requirements for these machines and developed some design formulae. You can find this analysis on pages 646 through 665 in Fluid Mechanics and Unit Operations, David S. Azbel and Nicholas P. Cheremisinoff, Ann Arbor Science Publishers, 1983. There are some sample calculations and sizing criteria that you can follow for some practical exercises in this publication. 

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