Real problems

We have now completed our survey of the thermodynamic principles required to model natural systems. It only remains to gain practice in formulating problems involving natural systems in thermodynamic terms. Quite often, that is the hardest part. Once the problem is set up in terms of relevant reactions and components, the equations can be solved by anyone who has absorbed the previous chapters. However, choosing the appropriate components and setting up the relevant balanced reactions only comes from experience. In this chapter we explore a few situations that have been investigated by thermodynamic methods. 

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Having to readjust the capital/energy tradeoff after every process change would be a real problem if it were not for the existence of the total cost targeting procedures discussed in Chap. 7. 

Where function characterizing the flat optical element Without giving details of technology, we can say it is possible to create flat computer element if the function (, 77) is known. In real problems of synthesis, we know only the absolute... 

If X, y and h are functions with Fourier transforms X, Y and H (real problem), we can write equation (9) in the frequency domain ... 

This formula is exact for a quadratic function, but for real problems a line search may be desirable. This line search is performed along the vector — x. . It may not be necessary to locate the minimum in the direction of the line search very accurately, at the expense of a few more steps of the quasi-Newton algorithm. For quantum mechanics calculations the additional energy evaluations required by the line search may prove more expensive than using the more approximate approach. An effective compromise is to fit a function to the energy and gradient at the current point x/t and at the point X/ +i and determine the minimum in the fitted function. 

Because of its severe approximations, in using the Huckel method (1932) one ignores most of the real problems of molecular orbital theory. This is not because Huckel, a first-rate mathematician, did not see them clearly they were simply beyond the power of primitive mechanical calculators of his day. Huckel theory provided the foundation and stimulus for a generation s research, most notably in organic chemistry. Then, about 1960, digital computers became widely available to the scientific community. 

Problems with several published solutions This section gives you some real problems which have akesdy been solved by several different routes. You can check your answer against these published routes. 

As an exercise, let s adapt this model of the analytical approach to a real problem. For our example, we will use the determination of the sources of airborne pollutant particles. A description of the problem can be found in the following article ... 

GaUium prices, stable up to 1991, fluctuated in 1992 because of gallium from China and Eastern European Bloc countries. The market destablized owing to spot offers and dumping. The reHabUity of these products was a real problem, however, and the consequence of market variations was dramatic for small manufacturers. 

Practical Processes. With acid leveling dyes no real problems exist because the dyes show good migration, electrolyte is added from the beginning, and rather like Class A direct dyes level dyeing is achieved by prolonging the times at the boil. 

The accident at the Three Mile Island nuclear plant clearly demonstrated that an alarm system can be counterprociuc tive. An excessive number of alarms can distract the operator s attention from the real problem that needs to be addressed. Alarms that merely tell the operator something that is already known do the same. In fac t, a very good definition of a nuisance alarm is one that informs the operator of a situation of which the operator is already aware. The only problem with applying this definition is determining what the operator already knows. 

Another serious distraction to a process operator is the multiple alarm event, where a single event within the process results in iTuuti-ple alarms. When the operator must individually acknowledge each alarm, considerable time can be lost in silencing the obnoxious annunciator before the real problem is addressed. Air-handling systems are especially vulnerable to this, where any fluctuation in pressure (for example, resulting from a blower trip) can cause a number of pressure alarms to occur. Point alarms (high alarms, low alarms, status alarms, etc.) are especially vulnerable to the multiple alarm event. This can be addressed in one of two ways ... 

Figure 9-2 is a chart showing the residual unbalance and the resulting force in pounds. It can be generated from Equation 9.1 using the unbalance in inch-ounces at several different speeds. The real problem is that there has not been any practical method of relating unbalance to rotor... 

The change management process should also ensure that a root cause analysis has been conducted to make sure the real problem has been identified and corrected. For example, if a pump seal fails it could simply be replaced with an identical seal. However, it may have failed because it was left in service beyond its natural life and the real failure was in the preventative maintenance program that should have replaced it earlier. 

The review looks for major risk situations. General housekeeping and personnel attitude arc not the objectives, although tliey can be significant indicators of where to look for real problems or places where meaningful improvements are needed. Various hazard evaluation teclmiques, such as checklists (see previous Section), what-if questions (see Section 15.5), and raw materitil evaluations, can be also used during tlie review. 

The number of problems that can be solved exactly in mechanics is not large. Once we have to treat three interacting bodies, life becomes very difficult indeed. This comment applies to classical mechanics just as to quantum mechanics. What we often do is to look for a simple, idealized problem that we can solve exactly, and then treat the real problem in hand as some kind of perturbation on the idealized one. 

In the early days of the industrial revolution, steam engine explosions were a real problem. Metal fatigue... 

Air noise is usually less with multibladed fans (4 or more) than with 2 or 3 blades. In general, noise is not a real problem when associated with other operating machinery and when the frequency level is low and nonpenetrating. When... 

Oil is not a real problem in centrifugal machines, except that its carry-through affects condensation in the condenser. In an ammonia system, the oil will setde out and can be purged from low points of the system, as receiver, evaporator, etc. 

This can be a real problem for baghouses that rely on automatic timers to control cleaning frequency. The use of a timing function to control cleaning frequency is not recommended unless the dust load is known to be consistent. A better approach is to use differential-pressure gages to physically measure the pressure drop across the filter media to trigger the cleaning process based on preset limits. 

The problem now is to find the corresponding Hamiltonian, t Hooft shows that the most obvious construction, obtained by rewriting U(t+l,t) as a product of cyclic elements, unfortunately does not work because at the end of the calculation there is no way to uniquely define the vacuum state. Given a cellular automaton with a local unitary evolution operator U = WgUg and the commutator [Ug, Ug ] 0 if [ af — af j> d for some d > 0, the real problem is therefore to find a Hamiltonian... 

With more than 30 million organic compounds now known and thousands more being created daily, naming them all is a real problem. Part of the problem is due to the sheer complexity of organic structures, but part is also due to the fact that chemical names have more than one purpose. For Chemical Abstracts Service (CAS), which catalogs and indexes the worldwide chemical literature, each compound must have only one correct name. It would be chaos if half the entries for CH3B1 were indexed under "M" for methyl bromide and half under "B" for bromomethane. Furthermore, a CAS name must be strictly systematic so that it can be assigned and interpreted by computers common names are not allowed. 

Abridged Spectrophotometry. It is not always necessary to obtain complete spectrophotometric curves in order to measure physical characteristics related to color. The procedure can often be considerably simplified by some abridged form of spectrophotometry. Measurements may be made only at critical wave lengths or wave-length bands, as has been done to determine chlorophyll degradation (1, 8). In such instances the real problem that faces the investigator is to establish the critical wave lengths. 

Fortunately, there are many different types of plastics that can provide all kinds of properties, including specific dimensional tolerances. It can thus be said that the real problem is not with the different plastics or processes but rather with the designer, who requires knowledge and experience to create products to meet the desired requirements. The designer with no knowledge or experience... 

A price must always be paid for this selection, and the price is generally higher the more rigorous the selection. Additional equipment is always required to accomplish the selection, but this is not the real problem. The most serious cost is reduced intensity, which comes about in two ways. First, the removal of all but one wavelength—more exactly, of... 

F. Moeller If you want to realize a catalyst which can hold some ppm s of sulfur, you should realize that you need not just one catalyst. You need a catalyst which does the job at all temperatures. We know of catalysts that can have some sulfur in the feed gas at relatively high temperature levels. That s no problem. But if you go to the low temperatures that you need to get specification SNG so that you can put your gas into your pipeline, then you have a real problem. So if you look for a sulfur-resistant catalyst, it must be resistant over the whole process sequence. Personally, I cannot foresee a catalyst which will work at lof temperature and be insensitive to sulfur. 

The real problem lies in the middle-sized industrial boilers, where testing still may rely on the use of wet chemistry titrations, and the detection of color change is critical. Under these circumstances, trying to accurately measure chloride, hardness, or alkalinity levels is genuinely difficult. 

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