Practice Problem

Give a reason for the following practices well known to wine connoisseurs  

Mass Transfer and Separation Processes Principles and Applications 

5 The Hypsometric Formula Greenhouse Gases in the Upper Atmosphere 

Equation 1.7b, known as the barometric or hypsometric formula, gives a good description of the pressure distribution in the troposphere (i.e., up to a height of 11 km), provided the local temperature is used in tiie formula. That temperature is given by the empirical relation T(K) = 288.15 - 6.5 x IQ- (K/m)h. 

In a typical uranium enrichment cascade operating at steady state, the feed coming into a centrifuge is exactly balanced by equal amounts of gas withdrawn from the periphery and the center. The peripheral stream is sent backward to a parallel array of cenfrifuges for further stripping, while the central portion moves forward into a similar succession of units for further enrichment. 

Consult Appendices IV and VII for K, and pK values. Answers to the Practice Problems are given on pages 421-423. 

Starting with 150 ml of a 40% saturated ammonium sulfate solution at OX calculate (a) the weight of solid ammonium sulfate that must be added to bring the solution to 60% saturation, and (b) the volume of saturated solution that must be added to attain 60% saturation. The specific volume of ammonium sulfate is 0.565 m /g. 

What is the molarity of pure ethanol— that is, how many moles are present in 1 liter of pure ethanol The density of ethanol is 0.789 g/ml. The MW of ethanol is 46.07. 

How many milliliters of 0.12 M HsSO are required to neutralize exactly half of ihe OH Ions present in 540 ml of 0.18 N NaOH  

How many grams of solid Na COs are required to neutralize exactly 2 liters of an HCl solution of pH 2.0  

1) Describe what is meant by the terms monocrystalline, polycrystalline, quasicrystalline, semi-crystalline, amorphous, and glassy. 

2) Write the transformation matrix for each type of point symmetry operation. 

3) What is the difference between a crystallographic general position and special position  

4) Consider a pure metal with the cubic-closed packed (CCP) structure (space group Fm 3 m). In this structure, there is an atom at each corner of a cube and an atom at the center of each of the cube s six faces. How many atoms are there in the unit cell Which point could be chosen as the origin What are the point-coordinates of all the atoms, relative to the origin Is the origin on a special position What is the multiplicity of the origin  

Flint The CCP structure just described is face-centered cubic (FCC) and the atomic sites coincide with the lattice points, as in Example 1.3. 

More about Driving Forces and Transport Coefficients 

Show that the bulk-flow component of the diffusing 

Conversion Factors for Mass Transfer Coefficients Prove the relation  

Derive the concentration profile C = jF(r) in a spherical shell, which arises when a solute with uniform internal concentration Q diffuses through the shell to an external medium held at a fixed concentration C. 

State under what conditions the Ohmian resistance, usually taken to be a constant, might become a variable for a conductor of fixed length. 

Derive a model for heat flux and temperature profile at steady conditions. Assume constant temperature To at the outer surface. 

The cross-sectional area A and circumference P vary with distance from the wall according to = A(x) and P = P(x). 

In the Liseberg Amusement Park in Gothenburg, there is a fountain where a water film flows along the outside of a vertical pipe. Derive a model for the velocity profile in the film  

The inner surface of the outer shell is kept at temperature T and the outer surface of the inner shell is to be maintained at a lower temperature Dry air 

Develop, using a shell balance, an expression for the temperature at steady conditions. In addition, give an expression for the rate of heat removal from the inner sphere. Assume steady laminar flow. 

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Since we did not know that we were in NDT we were unaware of others in the field and felt it to be a rather new field, we felt like explorers For us it was new and we carried on for some time blissfully unaware that Prof. Hughes had demonstrated the effect almost 100 years before and Foerster had solved most of the practical problems more than a decade earlier. We only gradually became aware that we were not alone. 

It is necessary to sum over these pemuitations in a path integral simulation. (The same sum is needed for bosons, without the sign factor.) For femiions, odd pemuitations contribute with negative weight. Near-cancelling positive and negative pemuitations constitute a major practical problem [196]. 

Isoparametric mapping removes tlie geometrical inflexibility of rectangular elements and therefore they can be used to solve many types of practical problems. For example, the isoparametric C continuous rectangular Hermite element provides useful discretizations in the solution of viscoelastic flow problems. 

Despite the simplicity of the outlined weighted residual method, its application to the solution of practical problems is not straightforward. The main difficulty arises from the lack of any systematic procedure that can be used to select appropriate basis and weight functions in a problem. The combination of finite element approximation procedures with weighted residual methods resolves this problem. This is explained briefly in the forthcoming section. 

These equations apply when an entire population is available for measurement. The most common situation in practical problems is one in which the number of measurements is smaller than the entire population. A group of selected measurements smaller than the population is called a sample. Sample statistics are slightly different from population statistics but, for large samples, the equations of sample statistics approach those of population statistics. 

This section provides an overview and review of quantum mechanics calculations. The information can help you use Hyper-Chem to solve practical problems. For quantitative details of quantum mechanics calculations and how HyperChem implements them, see the second part of this book. Theory and Methods. 

Each example problem includes a detailed solution that helps students in applying the chapter s material to practical problems. 

Generally, the attainable resolving power of a TOE instrument is limited, particularly at higher mass, for two major reasons one inherent in the technique, the other a practical problem. First, the flight times are proportional to the square root of m/z. The difference in the flight times (t and t ,+i) for two ions separated by unit mass is given by Equation 26.5. 

Of course, some substances are sufficiently volatile that a heated inlet line can be used to get them into a mass spectrometer. Even here, there are practical problems. Suppose a liquid or solid is sufficiently volatile, that heating it to 50°C is enough to get the vapor into the mass spectrometer through a heated inlet line. If the mass spectrometer analyzer is at 30°C, there is a significant possibility that some of the sample will condense onto the inner walls of the spectrometer and slowly vaporize from there. If the vacuum pumps cannot remove this vapor quickly, then the mass... 

Into the late 1940s, Nobel Laureate Robert S. Mulliken, a physical chemist at the University of Chicago, maintained a skeptical view regarding the future of applying the theories of physics to solving practical problems in chemistry (4,5). Subsequentiy, Mulliken (5) related that... 

The practical problems He ia the separatioa of the chlorine from the hydrogea chloride and nitrous gases. The dilute nitric acid must be reconcentrated and corrosion problems are severe. Suggested improvements iaclude oxidation of concentrated solutions of chlorides, eg, LiCl, by nitrates, followed by separation of chlorine from nitrosyl chloride by distillation at 135°C, or oxidation by a mixture of nitric and sulfuric acids, separating the... 

In some cases particles have been added to electrical systems to improve heat removal, for example with an SF -fluidized particulate bed to be used in transformers (47). This process appears feasible, using polytetrafluoroethylene (PTFE) particles of low dielectric constant. For a successful appHcation, practical problems such as fluidizing narrow gaps must be solved. 

Of the water-soluble vitamins, intakes of nicotinic acid [59-67-6] on the order of 10 to 30 times the recommended daily allowance (RE)A) have been shown to cause flushing, headache, nausea, and moderate lowering of semm cholesterol with concurrent increases in semm glucose. Toxic levels of foHc acid [59-30-3] are ca 20 mg/d in infants, and probably approach 400 mg/d in adults. The body seems able to tolerate very large intakes of ascorbic acid [50-81-7] (vitamin C) without iH effect, but levels in excess of 9 g/d have been reported to cause increases in urinary oxaHc acid excretion. Urinary and blood uric acid also rise as a result of high intakes of ascorbic acid, and these factors may increase the tendency for formation of kidney or bladder stones. AH other water-soluble vitamins possess an even wider margin of safety and present no practical problem (82). 

Polymerization Processes. Free-radical polymerization is carried out in a variety of ways. One of the practical problems that must be dealt with is mnaway reactions which can result from auto acceleration, an increase in rate of polymerization caused by diffusion-limited termination (reduced... 

The chemical potential, plays a vital role in both phase and chemical reaction equiUbria. However, the chemical potential exhibits certain unfortunate characteristics which discourage its use in the solution of practical problems. The Gibbs energy, and hence is defined in relation to the internal energy and entropy, both primitive quantities for which absolute values are unknown. Moreover, p approaches negative infinity when either P or x approaches 2ero. While these characteristics do not preclude the use of chemical potentials, the appHcation of equiUbrium criteria is faciUtated by the introduction of a new quantity to take the place of p but which does not exhibit its less desirable characteristics. 

Preferably, high pressure Hquid chromatography (hplc) is used to separate the active pre- and cis-isomers of vitamin D from other isomers and allows their analysis by comparison with the chromatograph of a sample of pure reference i j -vitainin D, which is equiUbrated to a mixture of pre- and cis-isomers (82,84,85). This method is more sensitive and provides information on isomer distribution as well as the active pre- and cis-isomer content of a vitamin D sample. It is appHcable to most forms of vitamin D, including the more dilute formulations, ie, multivitamin preparations containing at least 1 lU/g (AOAC Methods 979.24 980.26 981.17 982.29 985.27) (82). The practical problem of isolation of the vitamin material from interfering and extraneous components is the limiting factor in the assay of low level formulations. 

Generation of Heat in Electric Fields. One of the practical problems encountered in electrophoresis is the generation of heat from resistive dissipation of energy in the electrophoretic medium. The generation of heat (foule heating) is given by... 

These are the criteria of phase equilibrium apphed in the solution of practical problems. 

When temperatures of materials are a function of both time and space variables, more complicated equations result. Equation (5-2) is the three-dimensional unsteady-state conduction equation. It involves the rate of change of temperature with respect to time 3t/30. Solutions to most practical problems must be obtained through the use of digital computers. Numerous articles have been published on a wide variety of transient conduction problems involving various geometrical shapes and boundaiy conditions. 

Formulation of the Objective Function The formulation of objective functions is one of the crucial steps in the application of optimization to a practical problem. You must be able to translate the desired objective into mathematical terms. In the chemical process industries, the obective function often is expressed in units of currency (e.g., U.S. dollars) because the normal industrial goal is to minimize costs or maximize profits subject to a variety of constraints. 

This is an important practical problem area, as piping vibration can cause consider le downtime or even pipe failure. 

The lone remaining aspect of this topic that requires additional discussion is the fact that the mechanical threshold stress evolution is path-dependent. The fact that (df/dy)o in (7.41) is a function of y means that computations of material behavior must follow the actual high-rate deformational path to obtain the material strength f. This becomes a practical problem only in dealing with shock-wave compression. 

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