Elements of Chemical Reaction 5th Edition Part 1

Preface The man who has ceased to learn ought not to be allowed to wander around loose in these dangerous days. M. M. Coady A. Who Is the Intended Audience? This book and interactive Web site is intended for use as both an undergraduate-level and a graduate-level text in chemical reaction engineering. The level will depend on the choice of chapters, the Professional Reference Shelf (PRS) material (from the companion Web site) to be covered, and the type and degree of difficulty of problems assigned. It was written with today’s students in mind. It provides instantaneous access to information; does not waste time on extraneous details; cuts right to the point; uses more bullets to make information easier to access; and includes new, novel problems on chemical reaction engineering (e.g., solar energy). It gives more emphasis to chemical reactor safety (Chapters 12 and 13) and alternative energy sources—solar (Chapters 3, 8, and 10) and biofuel production (Chapter 9). The graduate material on topics such as effectiveness factors, non-ideal reactors, and residence time distribution is in Chapters 14–18 and now includes the software solutions for maximum mixedness and segregation models. A draft version of this book was class tested at the University of Michigan and other leading universities; then the text was further revised, taking into account the suggestions of more than 100 students. Much of the material was revised and reworked based on that feedback. B. What Are the Goals of This Book? B.1 To Have Fun Learning Chemical Reaction Engineering (CRE) Chemical reaction engineering (CRE) is one of two core courses that is unique to chemical engineering and that separates the chemical engineer from other xvii xviii Preface engineers. CRE is a great subject that is fun to learn and is the heart of chemical engineering. I have tried to provide a little Michigan humor as we go. Take a look at the humorous YouTube videos (e.g., “Black Widow” or “Chemical Engineering Gone Wrong”) that illustrate certain principles in the text. These videos were made by chemical engineering students at the universities of Alabama and Michigan. In addition, I have found that students very much enjoy the Interactive Computer Games (ICGs) that, along with the videos, are linked from the CRE homepage (http://www.umich.edu/~elements/5e). B.2 To Develop a Fundamental Understanding of Reaction Engineering The second goal of this book is to help the reader clearly understand the fundamentals of CRE. This goal is achieved by presenting a structure that allows the reader to solve reaction engineering problems through reasoning rather than through memorization and recall of numerous equations and the restrictions and conditions under which each equation applies. The algorithms presented in the text for reactor design provide this framework, and the homework problems give the reader practice using the algorithms described in Figures P-1 and P-2, shown in Section C. The conventional homework problems at the end of each chapter are designed to reinforce the principles in the chapter. These problems are about equally divided between those that can be solved with a calculator and those that require a personal computer with a numerical software package, such as Polymath, AspenTech, or COMSOL. To give a reference point as to the level of understanding of CRE required in the profession, a number of reaction engineering problems from the California Board of Registration for Civil and Professional Engineers—Chemical Engineering Examinations (PECEE) are included in the text.1 Typically, these problems should each require approximately 30 minutes to solve. Finally, the companion Web site should greatly facilitate learning the fundamentals of CRE because it includes Summary Notes of the material in each chapter, PowerPoint slides of class lecture notes, additional examples, expanded derivations, and self-tests. A complete description of these learning resources is in Appendix I. B.3. To Enhance Thinking Skills A third goal of this text is to enhance critical thinking skills and creative thinking skills. How does the book help enhance your critical and creative thinking skills? We discuss ways to achieve this enhancement in Section I of the Preface. 1 The permission for use of these problems—which, incidentally, may be obtained from the Documents Section, California Board of Registration for Civil and Professional Engineers—Chemical Engineering, 1004 6th Street, Sacramento, CA 95814, is gratefully acknowledged. (Note: These problems have been copyrighted by the California Board of Registration and may not be reproduced without its permission.) xix Preface C. What Is the Structure of CRE? C.1 What Are the Concepts that Form the Foundation of CRE? The strategy behind the presentation of material is to build continually on a few basic ideas in CRE to solve a wide variety of problems. These ideas, referred to as the Pillars of Chemical Reaction Engineering (Figure P-1), are the foundation on which different applications rest. They represent not only components of chemical reaction analysis, but also the physical phenomena of diffusion and contacting that affect chemical reactor design. Figure P-2 shows the first building blocks of CRE and the primary algorithm that allows us to solve CRE problems through logic rather than memorization. We start with the Mole Balance Building Block (Chapter 1) and then place the other blocks one at a time on top of the others until we reach the Evaluate Block (Chapter 5), by which time we can solve a multitude of isothermal CRE problems. As we study each block we need to make sure we understand everything in that block and don’t leave anything out so we don’t wind up with a cylindrical block. A tower containing cylindrical blocks would be unstable and would fall apart as we study later chapters. See the end of Chapter 1 lecture notes on the CRE Web site to see the tower of CRE fall if you have blocks with rounded edges. MULTIPLE REACTIONS MASS TRANSFER OPERATIONS NONISOTHERMAL OPERATION, MULTIPLE STEADY STATES MODELING REAL REACTORS, RTD, DISPERSION, SEGREGATION ANALYSIS OF RATE DATA, LABORATORY REACTORS, LEAST-SQUARES ANALYSIS DESIGN OF CHEMICAL REACTORS, PFR, CSTR, BATCH, SEMIBATCH, PACKED BEDS M O L E R A T E B A L A N C E S L A W S S T O I C H I O M E T R Y E N E R G Y B A L A N C E S D I F F U S I O N Figure P-1 Pillars of Chemical Reaction Engineering. C O N T A C T I N G Evaluate Combine Stoichiometry Rate Law Mole Balance Figure P-2 Building blocks. From these pillars and building blocks, we construct our CRE algorithm: Mole Balance + Rate Laws + Stoichiometry + Energy Balance + Combine → Solution With a few restrictions, the contents of this book can be studied in virtually any order after students have mastered the first six chapters. A flow diagram showing the possible paths is shown in Figure P-3. The reader will observe that although metric units are used primarily in this text (e.g., kmol/m3, J/mol), English units are also employed (e.g., lbm/ft3, Btu). This choice is intentional! We believe that whereas most papers published today use the metric system, a significant amount of reaction engineering data exists in the older literature in English units. Because engineers will be faced with extracting information and reaction rate data from older literature as well as from the current literature, they should be equally at ease with both English and metric units. xx Preface Ch. 1 Mole Balances Ch. 10 Catalysis and Catalytic Reactors Ch. 14 Mass Transfer Limitations in Reacting Systems Ch. 15 Diffusion and Reaction Ch. 2 Conversion and Reactor Sizing Ch. 3 Rate Laws Ch. 4 Stoichiometry Ch. 9 Reaction Mechanisms, Pathways, Bioreactions, and Bioreactors Ch. 5 Isothermal Reactor Design: Conversion Ch. 7 Collection and Analysis of Rate Data Ch. 8 Multiple Reactions Ch. 11 Nonisothermal Reactor Design─ The Steady-State Energy Balance and Adiabatic PFR Applications Ch. 12 Steady-state Nonisothermal Reactor Design─ Flow Reactors with Heat Exchange Ch. 13 Unsteady-State Nonisothermal Reactor Design Ch. 6 Isothermal Reactor Design: Moles and Molar Flow Rates Ch. 16 Residence Time Distributions of Chemical Reactors Ch. 17 Predicting Conversion Directly from the Residence Time Distribution Ch. 18 Models for Nonideal Reactors Figure P-3 Sequences for study using this text. C.2 What Is the Sequence of Topics in which This Book Can Be Used? Table P-1 shows examples of topics that can be converged in a graduate course and an undergraduate course. In a four-hour undergraduate course at the University of Michigan, approximately thirteen chapters are covered in the following order: Chapters 1 through 7 (Exam 1); Chapters 8, 11, and 12 (Exam 2); and Chapter 13 and parts of Chapters 9 and 10 (Exam 3). There are notes in the margins, which are meant to serve two purposes. First, they act as guides or commentary as one reads through the material. Second, they identify key equations and relationships that are used to solve CRE problems. D. What Are the Components of the CRE Web Site? The companion, interactive Web site material is an updated version of the CRE Web site and is a novel and unique part of this book. The main purposes of the Web site are to serve as an enrichment resource and as a “professional reference shelf.” The home page for the CRE Web site (http://www.umich.edu/~elements/5e/index.html) is shown in Figure P-4. For discussion of how to use the Web site and text interactively, see Appendix I. xxi Preface TABLE P-1 UNDERGRADUATE/GRADUATE COVERAGE Undergraduate Material/Course Mole Balances (Ch. 1) Smog in Los Angeles Basin (PRS Ch. 1) Reactor Staging (Ch. 2) Hippopotamus Stomach (PRS Ch. 2) Rate Laws (Ch. 3) Stoichiometry (Ch. 4) Reactors (Ch. 5): Batch, PFR, CSTR, PBR Reactors (Ch. 6): Semibatch, Membrane Data Analysis: Regression (Ch. 7) Multiple Reactions (Ch. 8) Bioreaction Engineering (Ch. 9) Adiabatic Reactor (Ch. 11) Steady-State Heat Effects (Ch. 12): PFR and CSTR with and without a Heat Exchanger Multiple Steady States Unsteady-State Heat Effects (Ch. 13) Reactor Safety Catalysis (Ch. 10) OF CRE Graduate Material/Course Short Review (Ch. 1–8, 11–12) Collision Theory (PRS Ch. 3) Transition State Theory (PRS Ch. 3) Molecular Dynamics (PRS Ch. 3) Aerosol Reactors (PRS Ch. 4) Multiple Reactions (Ch. 8): Fed Membrane Reactors Bioreactions and Reactors (Ch. 9, PRS 9.3–9.5) Polymerization (PRS Ch. 9) Co- and Countercurrent Heat Exchange (Ch. 12) Radial and Axial Gradients in a PFR COMSOL (Ch. 12) Reactor Stability and Safety (Ch. 12, 13, PRS 12.3) Runaway Reactions (PRS, Ch. 12) Catalyst Deactivation (Ch. 10) Residence Time Distribution (Ch. 16, 17) Models of Real Reactors (Ch. 18) Applications (PRS): Multiphase Reactors, CVD Reactors, Bioreactors Figure P-4 Screen shot of the book’s companion Web site (http://www.umich.edu/~elements/ 5e/index.html). The objectives of the Web site are fourfold: (1) To facilitate the learning of CRE by using the companion Web site to actively address the Felder/Solomon Inventory of Learning Styles 7 discussed in Web Appendix I (2) To provide additional technical material xxii Preface (3) To provide tutorial information and self-assessment exercises (4) To make the learning of CRE fun through the use of interactive games The following sections (D.1 through D.4) are listed at the end of most chapters and can be accessed from each chapter in the companion Web site.2 D.1 Expanded Material The expanded material consists of material that was removed from the printed text and moved to the Web site to reduce the size and weight of the physical textbook. Reducing the weight makes it easier for the students to carry the book with them at all times, such as while on the campus shuttle or while eating at the cafeteria or the student union. The expanded material includes derivations, examples, and novel applications of CRE principles. D.2 Learning Resources The Learning Resources give an overview of the material in each chapter and provide extra explanations, examples, and applications to reinforce the basic concepts of CRE; the Learning Resources are described in Appendix I. The CRE Web site includes the following additional resources: 1. Summary Notes and PowerPoint Slides The Summary Notes give an overview of each chapter and provide on-demand additional examples, derivations, and audio comments, as well as self-tests to assess each reader’s understanding of the material. Copies of the PowerPoint slides are available from this course taught at the University of Michigan as well as those from Professor Mary Kraft’s class at the University of Illinois. 2. What Entertainment Is on the Web Site? 2.A. YouTube Videos We have included links to humorous YouTube Videos made by students in Professor Alan Lane’s 2008 chemical reaction engineering class at the University of Alabama, as well as videos from the University of Michigan 2011 class. Specifically, check out “The Black Widow Murder Mystery” (Chapter 3), “CRF Reactor,” and “Diet Coke and Mentos” (Chapter 4); learn a new dance and song (“CSTR” to the tune of “YMCA”); hear a rap song (“Find Your Rhythm,” an “Ice Ice Baby” remix (Chapter 5)); and watch University of Michigan videos, including the ever-popular chemical engineering classic, “Reaction Engineering Gone Wrong.” 2.B. Interactive Computer Games (ICGs) Students have found the Interactive Computer Games to be both fun and extremely useful to review the important chapter concepts and then apply them to real problems in a unique and 2 http://www.ncsu.edu/felder-public/ILSdir/styles.htm xxiii Preface entertaining fashion. The following ICGs are available on the Web site: • • • • • • Quiz Show I (Ch. 1) Reactor Staging (Ch. 2) Quiz Show II (Ch. 4) Murder Mystery (Ch. 5) Tic Tac (Ch. 5) Ecology (Ch. 7) • • • • • The Great Race (Ch. 8) Enzyme Man (Ch. 9) Catalysis (Ch. 10) Heat Effects I (Ch. 12) Heat Effects II (Ch. 12) As you play these interactive games, you will be asked a number of questions related to the corresponding material in the textbook. The ICG keeps track of all the correct answers and at the end of the game displays a coded performance number that reflects how well you mastered the material in the text. Instructors have a manual to decode the performance number. 2.C. Web Modules The Web Modules are a number of examples that apply key CRE concepts to both standard and nonstandard reaction engineering problems (e.g., glow sticks, the use of wetlands to degrade toxic chemicals, and pharmacokinetics of death from a cobra bite). The Web Modules can be loaded directly from the CRE Web site (http://www.umich.edu/~elements/5e/web_mod/ index.html). 3. Solved Problems A number of solved problems are presented along with problem-solving heuristics. Problem-solving strategies and additional worked example problems are available in the Problem Solving section of the CRE Web site. D.3 Professional Reference Shelf This section of the CRE Web site contains 1. Material from the fifth edition of Elements of Chemical Reaction Engineering that is not included in the printed textbook. 2. Material that is important to the practicing engineer, such as details of the industrial reactor design for the oxidation of SO2 and design of spherical reactors and other material that is typically not included in the majority of chemical reaction engineering courses but is included here. E. Why Do We Assign Homework Problems? The working of homework problems facilitates a true understanding of CRE. After reading a chapter the student may feel they have an understanding of the material. However, when attempting a new or slightly different application of CRE in a homework problem, students sometimes need to go back and re-read xxiv Preface different parts of the chapter to get the level of understanding needed to eventually solve the homework problem. The end-of-chapter problems numbered “2” (e.g., P3-2A, P11-2B) ask questions about the example problems in that chapter. These example problems are a key resource. These number-2-level problems should be worked before tackling the more challenging homework problems in a given chapter. The subscript letter (A, B, C, or D) after each problem number denotes the difficulty of the problem (i.e., A = easy; D = difficult). F. What Is a Living Example Problem (LEP)? The example problems that use an Ordinary Differential Equation (ODE) solver (e.g., Polymath) are referred to as “Living Example Problems” or “LEPs” because students can load the Polymath program directly onto their own computers in order to study the problem. Students are encouraged to change parameter values and to “play with” the key variables and assumptions. Using the LEPs to explore the problem and asking “what if…?” questions provide students with the opportunity to practice critical and creative thinking skills. G. What Software Is Available to Solve the LEPs? Polymath. Polymath was developed by Professors Michael Cutlip and Mordechai Shacham. The Polymath software includes an ordinary differential equation (ODE) solver, a nonlinear equation solver, and nonlinear regression. As with previous editions of this book, Polymath is used to explore the example problems and to solve the homework problems. Polymath tutorials with screen shots are given on the CRE Web site Summary Notes in Chapter 1 and can also be accessed from the Home Page by going to Living Example Problems (LEPs) and then clicking on Polymath. Most chemical engineering departments in the United States have site licenses for Polymath. If your department does not have a site license and would like one, have your instructor e-mail the CACHE Corporation at cache@uts.cc.utexas.edu to learn how to obtain one. The LEPs need to be copied from the CRE Web site and pasted into the Polymath software. The Polymath software used in the examples in the text is available in most department computer labs in the United States. If you want to have Polymath on your personal laptop computer, you will need to purchase the program. An educational version of the software has been made available by Professors Cutlip and Shacham to students for $20 for a 4-month license, $30 for a 12-month license, or for $39 for a perpetual-use license. Polymath 6.1 is compatible with Windows XP, Windows Vista, Windows 7, and Windows 8. See the Polymath Web site (http://www.polymath-software.com) to obtain the laptop version. A special Polymath Web site (http://www.polymath-software.com/fogler) has been set up for this book by Polymath authors Professors Cutlip and Shacham. AspenTech. AspenTech is a process flow sheet simulator used in most senior chemical engineering design courses. It is now routinely introduced in earlier chemical engineering courses, such as thermodynamics, separations, and now in CRE. See the AspenTech Web site (http://www.aspentech.com) for more xxv Preface information. Like Polymath, AspenTech site licenses are available in most chemical engineering departments in the United States. Four AspenTech simulation examples specific to CRE are provided on the CRE Web site with step-by-step tutorial screen shots. As with Polymath programs, the input parameters in AspenTech can be varied to learn how they change the temperature and concentration profiles. Further details are given in Appendix D. COMSOL Multiphysics. The COMSOL Multiphysics software is a partial differential equation solver that is used with Chapters 12 and 18 to view both axial and radial temperature and concentration profiles. For users of this text, COMSOL has provided a special Web site that includes a step-by-step tutorial, along with examples. See http://www.comsol.com/ecre. Further details are given in Appendix D. Further details of these three software packages can be found in Appendix D. H. Are There Other Web Site Resources? FAQs. The Frequently Asked Questions (FAQs) page on the CRE Web site contains a compilation of questions collected over the years from undergraduate students taking reaction engineering. Visual Encyclopedia of Equipment (http://encyclopedia.che.engin.umich.edu). This section was developed by Dr. Susan Montgomery at the University of Michigan. Here, a wealth of photographs and descriptions of real and ideal reactors are given. Students with visual, active, sensing, and intuitive learning styles of the Felder/Solomon Index will particularly benefit from this section. Reactor Lab (http://www.ReactorLab.net). Developed by Professor Richard Herz at the University of California at San Diego, this interactive tool will allow students not only to test their comprehension of the CRE material, but also to explore different situations and combinations of reaction orders and types of reactions. CRE Web Site. The CRE Web site (http://www.umich.edu/~elements/5e/ index.html) will be used to update the text and identify typographical and other errors in the first and later printings of this text—available under Updates and FAQs on the CRE Web site home page. Additional material may also be added to include more solved problems, as well as additional Web Modules, which will also be found under Updates and FAQs. xxvi Preface I. How Can Critical Thinking and Creative Thinking Skills Be Enhanced? I.1. Enhance Critical Thinking Skills A third goal of this book is to enhance critical thinking skills. How does one enhance their critical thinking skills? Answer by learning how to ask the critical thinking questions in Table P-2 and carry out the actions in Table P-3. A number of homework problems have been included that are designed for this purpose. Socratic questioning is at the heart of critical thinking, and a number of homework problems draw from R. W. Paul’s six types of Socratic questions,3 shown in Table P-2 and given in the expanded material on the Web site. TABLE P-2 SIX TYPES OF SOCRATIC QUESTIONS USED IN CRITICAL THINKING (1) Questions for clarification: Why do you say that? How does this relate to our discussion? “Are you going to include diffusion in your mole balance equations?” (2) Questions that probe assumptions: What could we assume instead? How can you verify or disprove that assumption? “Why are you neglecting radial diffusion and including only axial diffusion?” (3) Questions that probe reasons and evidence: What would be an example? “Do you think that diffusion is responsible for the lower conversion?” (4) Questions about viewpoints and perspectives: What would be an alternative? “With all the bends in the pipe, from an industrial/practical perspective, do you think diffusion and dispersion will be large enough to affect the conversion?” (5) Questions that probe implications and consequences: What generalizations can you make? What are the consequences of that assumption? “How would the results be affected if you neglected diffusion?” (6) Questions about the question: What was the point of this question? Why do you think I asked this question? “Why do you think diffusion is important?” It is important to know these six types and be able to apply them when investigating a problem such as “Is there a chance the reactor will run away and explode?” or “Why did the reactor explode?” Critical thinking skills are like any skill, they must be practiced. Scheffer and Rubenfeld4,5 describe how to practice critical thinking skills using the activities, statements, and questions shown in Table P-3. The reader should try to practice using some or all of these actions every day, as well as asking the critical thinking questions in Table P-1 and on the Web site. R. W. Paul, Critical Thinking (Santa Rosa, CA: Foundation for Critical Thinking, 1992). 4 Courtesy of B. K. Scheffer and M. G. Rubenfeld, “A Consensus Statement on Critical Thinking in Nursing,” Journal of Nursing Education, 39, 352–359 (2000). 5 Courtesy of B. K. Scheffer and M. G. Rubenfeld, “Critical Thinking: What Is It and How Do We Teach It?” Current Issues in Nursing (2001). 3 xxvii Preface TABLE P-3 CRITICAL THINKING ACTIONS6 Analyzing: separating or breaking a whole into parts to discover their nature, function, and relationships “I studied it piece by piece.” “I sorted things out.” Applying Standards: judging according to established personal, professional, or social rules or criteria “I judged it according to….” Discriminating: recognizing differences and similarities among things or situations and distinguishing carefully as to category or rank “I rank ordered the various….” “I grouped things together.” Information Seeking: searching for evidence, facts, or knowledge by identifying relevant sources and gathering objective, subjective, historical, and current data from those sources “I knew I needed to look up/study….” “I kept searching for data.” Logical Reasoning: drawing inferences or conclusions that are supported in or justified by evidence “I deduced from the information that….” “My rationale for the conclusion was….” Predicting: envisioning a plan and its consequences “I envisioned the outcome would be….” “I was prepared for….” Transforming Knowledge: changing or converting the condition, nature, form, or function of concepts among contexts “I improved on the basics by….” “I wondered if that would fit the situation of ….” I have found that the best way to develop and practice critical thinking skills is to use Tables P-2 and P-3 to help students write a question on any assigned homework problem and then to explain why the question involves critical thinking.6 More information on critical thinking can be found on the CRE Web site in the section on Problem Solving (http://www.umich.edu/~elements/5e/probsolv/index.htm). I.2 Enhance Creative Thinking Skills The fourth goal of this book is to help enhance creative thinking skills. This goal is achieved by using a number of problems that are open-ended to various degrees. With these, students can practice their creative skills by exploring the example problems, as outlined at the beginning of the home problems of each chapter, and by making up and solving an original problem. Problem P5-1 in the text gives some guidelines for developing original problems. A number of techniques that can aid students in practicing and enhancing their creativity 6 R. W. Paul, Critical Thinking (Santa Rosa, CA: Foundation for Critical Thinking, 1992); B. K. Scheffer and M. G. Rubenfeld, “A Consensus Statement on Critical Thinking in Nursing,” Journal of Nursing Education, 39, 352–359 (2000). xxviii Preface can be found in Fogler, LeBlanc, and Rizzo7 (and its companion Web site), Strategies for Creative Problem Solving, Third Edition. The Web site for that book can be accessed from the CRE Web site home page. We use these techniques, such as Osborn’s checklist and de Bono’s lateral thinking (which involves considering other people’s views and responding to random stimulation) to answer add-on questions such as those in Table P-4. TABLE P-4 PRACTICING CREATIVE THINKING (1) Brainstorm ideas to ask another question or suggest another calculation that can be made for this homework problem. (2) Brainstorm ways you could work this homework problem incorrectly. (3) Brainstorm ways to make this problem easier or more difficult or more exciting. (4) Brainstorm a list of things you learned from working this homework problem and what you think the point of the problem is. (5) Brainstorm the reasons why your calculations overpredicted the conversion that was measured when the reactor was put on stream. Assume you made no numerical errors in your calculations. (6) “What if…” questions: The “What if…” questions are particularly effective when used with the Living Example Problems, where one varies the parameters to explore the problem and to carry out a sensitivity analysis. For example, what if someone suggested that you should double the catalyst particle diameter, what would you say? One of the major goals at the undergraduate level is to bring students to the point where they can solve complex reaction problems, such as multiple reactions with heat effects, and then ask “What if . . . ?” questions and look for optimum operating conditions and unsafe operating conditions. The solution to one problem exemplifies this goal: the Manufacture of Styrene (Chapter 12, Problem P12-26C). This problem is particularly interesting because two reactions are endothermic and one is exothermic. (1) Ethylbenzene → Styrene + Hydrogen: Endothermic (2) Ethylbenzene → Benzene + Ethylene: Endothermic (3) Ethylbenzene + Hydrogen → Toluene + Methane: Exothermic The student could get further practice in critical and creative thinking skills by adding any of the following exercises (x), (y), and (z) to any of the end-of-chapter homework problems. (x) How could you make this problem easier? More difficult? (y) Critique your answer by writing a critical thinking question. (z) Describe two ways you could work this problem incorrectly. To summarize, it is this author’s experience that both critical and creative thinking skills can be enhanced by using Tables P-2, P-3, and P-4 to extend any of the homework problems at the end of each chapter. 7 H. S. Fogler, S. E. LeBlanc, with B. Rizzo, Strategies for Creative Problem Solving, 3rd Ed. (Upper Saddle River, N.J.: Prentice Hall, 2014).