Homework Problems

Unlike most engineering homework, the following homework problans benefit greatly from an Internet search. 

Open the plastic housing of a household appliance. Examples are vacuum cleaners, blenders, mixers, humidifiers, and so on. Desaibe the differences between modern-day appliance housing and (me from the 1950s. What is the weight difference What is the price difference in today s dollars based on current costs of materials Discuss any differences in speed of manufactuie. 

Consider the evolution of the Chevrolet Corvette s body. What has been the evolution Where there any other cars that either preceded or were concurrent with the Corvette body development  

What was the first composite pedestrian bridge designed for high volumes of foot traffic (i.e., in a city) What were the design considerations  

Consider a nematic liquid crystal. The molecule can be regarded as a cylinder with the length of 2 nm and diameter of 0.5 nm. The molecule has a permanent dipole moment of 10 m - C at the center of the molecule. The interaction between the molecules comes from the interactions between the permanent dipoles. Calculate the interaction between two molecules in the following cases (1) one molecule is on top of the other molecule and the dipoles are parallel, (2) one molecule is on top of the other molecule and the dipoles are anti-parallel, (3) the molecules are side by side and the dipoles are parallel, and (4) the molecules are side by side and the dipoles are anti-paraUel. 

Maier-Saupe theory. Use Equation (1.50) to numerically calculate all the possible order parameters as a function of the normalized temperature t = fcgT/v, and use Equation (1.54) 

Consider a nematic Uquid crystal cell with the thickness of 10 pm. On the bottom surface the liquid crystal is ahgned parallel to the cell surface, and on top of the top surface the liquid crystal is ahgned perpendicular to the cell surface. Assume the tilt angle of the Uquid crystal director changes linearly with the coordinate z, which is in the cell normal direction. Calculate the total elastic energy per unit area. The elastic constants of the Uquid crystal are = 6 x 10 N, K22 = 3 x 10 N and ATn = 10 x 10 N. 

R of the hemisphere and the ring number n. Pg and for small r only twist elastic energy has to be considered. Hint, vs. n is a straight line with a slope dependent on Pg and R. 

Consider a sphere of radius R. The polarization inside the sphere is P. Calculate the electric field at the center of the sphere produced by the polarization. Hint, the polarization 

Using resources at a local library, write a one-paragraph summary of an invention, material, or process used in current microelectronic technology. 

What is the lowest doping density in units of cm that can be obtained in the 1 nm X 1 nm device if the thickness of the device is 4 atomic layers (1 nm) as 

Assume that electronic grade Pt can be purchased for 3000 g and given that the atomic weight of Pt is 195 g moT and its density is 21.4 g cm . Estimate the cost of a 30 nm layer of Pt used in a 1 cm microprocessor assuming that it coats the entire area of the device. 

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Homework problems are also handled differently. At the end of each chapter are short, mostly derivation type, problems which we call Review Problems. Hints or solutions are provided for these exercises. To enhance the skill of problem solving, we take the extreme approach, more so than... 

We have given up the pretense that we can cover controller design and still have time to do all the plots manually. We rely on MATLAB to construct the plots. For example, we take a unique approach to root locus plots. We do not ignore it like some texts do, but we also do not go into the hand sketching details. The same can be said with frequency response analysis. On the whole, we use root locus and Bode plots as computational and pedagogical tools in ways that can help to understand the choice of different controller designs. Exercises that may help such thinking are in the MATLAB tutorials and homework problems. 

While our analyses use deviation variables and not the real variables, examples and homework problems can keep bouncing back and forth. The reason is that when we do an experiment, we measure the actual variable, not the deviation variable. You may find this really confusing. All we can do is to be extra careful when we solve a problem. 

This section is a review of the properties of a first order differential equation model. Our Chapter 2 examples of mixed vessels, stined-tank heater, and homework problems of isothermal stirred-tank chemical reactors all fall into this category. Furthermore, the differential equation may represent either a process or a control system. What we cover here applies to any problem or situation as long as it can be described by a linear first order differential equation. 

We do not need to carry the algebra further. The points that we want to make are clear. First, even the first vessel has a second order transfer function it arises from the interaction with the second tank. Second, if we expand Eq. (3-46), we should see that the interaction introduces an extra term in the characteristic polynomial, but the poles should remain real and negative.1 That is, the tank responses remain overdamped. Finally, we may be afraid( ) that the algebra might become hopelessly tangled with more complex models. Indeed, we d prefer to use state space representation based on Eqs. (3-41) and (3-42). After Chapters 4 and 9, you can try this problem in Homework Problem 11.39. 

In homework problems, by and large, the variables are stated. Things will be different when we are on the job. Here are some simple ideas on how we may make the decision ... 

In reality, the valve characteristic curve is likely nonlinear and we need to look up the technical specification in the manufacturer s catalog. After that, the valve gain can be calculated from the slope of the characteristic curve at the operating point. See Homework Problem 1.33 and the Web... 

We have not included any homework problems in Chapters 11 through 16. As a general suggestion for classroom use, parameters or assumptions in each example can be changed to develop a modified problem. By changing the numerical method employed or the computer code one can achieve a variety of problems. 

Presentation of each optimization technique is followed by examples to illustrate an application. We also have included many practically oriented homework problems. In university courses, this book could be used at the upper-division or the first-year graduate levels, either in a course focused on optimization or on process design. The book contains more than enough material for a 15-week course on optimization. Because of its emphasis on applications and short case studies in Chapters 11-16, it may also serve as one of the supplementary texts in a senior unit operations or design course. 

The AP chemistry exam is coming up Your thorough understanding of months and months of college-level chemistry lectures, tests, quizzes, homework problems, lab write-ups, and notes are to be evaluated in a 3-hour examination. It s just you and the AP exam. In preparing to do the very best job possible, you have four options ... 

There are many computational chemistry software packages available that enable students to make and study the properties of molecules, by quantum mechanics and molecular mechanics methods. These include Gaussian, HyperChem, Spartan, and Biosym. The first four homework problems assume that the student has one of... 

Second, we will attempt to describe the chemical reactors and processes in the chemical industry, not by simply adding homework problems with industrially relevant molecules, but by discussing a number of important industrial reaction processes and the reactors being used to carry them out. 

Listed in Table 1-2 are most of the processes we will be concerned with in this book, both in the text and in homework problems. 

These are aU industrially important reactions that we will discuss throughout this book in the text and in homework problems. The student might want to try to identify the type of reaction represented by each equation and why it is important. 

We will leave for a homework problem the calculation of the equilibrium conversion of methanol versus temperature and pressure. Figure 3-18 is a plot of the equilibrium conversion versus temperature. 

For ki = ki the preceding expressions cannot be used because they become indeterminate (zeros in numerator and denominator). We wiU leave the derivation of the relevant equations as a homework problem. 

Figure 6-11 shows a plot of X versus T for this example for =300 K and z = 1 min. It is seen that for this situation a single low conversion steady state exists for low Caoi a single high conversion steady state exists for high Cao multiple steady states can exist for an intermediate range of We will discuss these further in a homework problem. 

Solutions can be found by plotting the left-hand side and the right-hand side together on a plot of Xi + X2 versus T. In this case Xi -I- X2 versus T may appear as shown in Figure 6-14. For appropriate values of the parameters, these curves give up to five intersections, conesponding to three stable steady states. This situation will be considered in a homework problem. 

Our assumption is that your instmctor will choose specific chapters and sections of chapters and wiU omit or skim large sections. If she or he is an expert in some of these topics, you may see much additional or substituted material and notation that extends and corrects the naive or wrong material in these sections. The material and notation in these chapters are sufficiently simple that you should be able to work many of homework problems without having previous lectures on that chapter. Half of the challenge in chemical reaction engineeiing is recognizing that the previous concepts can be directly applied to these problems. 

The amount of fluid flowing between R and R + dR is 2n R dR, and p t) is foimd by integrating from R = 0 at the center of the tube to R = at the pipe wall. We will leave the derivation of this equation as a homework problem This gives... 

A homework problem considers these equations and their solutions. 

In the simplest version of a surface reaction, the rate of termination of the chain reaction by reaction of R on a surface should be proportional to D, the square of the vessel diameter We will also leave this calculation for a homework problem, but the imphcations are profound for a chain reaction. When the vessel size increases, the rate of a chain reaction can increase drastically, from a slow surface-quenched process in small vessels to very fast process whose only quenching steps are homogeneous reactions. 

Another related process to prepare propylene oxide uses ethyl benzene as the peroxidizable species, and it produces a coproduct that is even more valuable than isobutylene. This process will be left for a homework problem. 

We will leave the derivation of this rate expression for a homework problem. A steady-state balance on C/j yields... 

Table 10-3 Hsts the heats of fonnation of several of these potentially dangerous hydrocarbons. In a homework problem you are asked to calculate the temperatures and pressures of these gases if they suddenly deompose into their elements.

We will not derive this expression here but rather leave it for a homework problem... 

Basically, crystallization occurs either by monomer addition to a growing crystal or by coagulation of smaller crystals unto larger crystals. Monomer addition produces more uniform and regular crystals and a narrower crystal size distribution. Coagulation produces irregularly shaped crystals with a wide range in crystal sizes. These processes are obviously addition crystallization and condensation crystallization, respectively. We will not consider these kinetics in any more detail here, but save them for a homework problem. 

In all computer homework problems you must submit a copy of the program you used with your name and the date appearing on the graph so the graders can be sure you didn t just photocopy someone else s graph. 

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