Modern Engineering Thermodynamics

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3.7 Phase Diagrams 65 WHO WAS EMMY NOETHER? PART 2 Emmy Noether never became a language teacher; instead she decided to attend the University of Erlangen to study mathematics. Unfortunately, at that time, women were not allowed to enroll because the faculty felt that allowing female students would “overthrow all academic order.” She could only audit classes with the permission of each professor whose lectures she wished to attend. Nonetheless, on July 14, 1903, she passed the graduation exam. During the winter of 1903–1904, she studied at the University of Göttingen, attending lectures by astronomer Karl Schwarzschild and mathematicians Hermann Minkowski, Otto Blumenthal, Felix Klein, and David Hilbert. By then, restrictions on women’s rights in Erlangen were rescinded and she returned there. She officially reentered the university on October 24, 1904, and declared her intention to focus solely on mathematics. In 1907, she received a doctorate in mathematics. Other thermodynamic properties, such as entropy and availability, are introduced later in this text when they are needed. It must be remembered, however, that not all thermodynamic properties are directly measurable. A pressure gauge and a thermometer give us numerical values for p and T, but there are no instruments that give us values of u and h directly. It takes much more sophisticated measurements to allow us to calculate accurate values for u and h. More complex mathematical relations between thermodynamic properties are developed after the reader is thoroughly familiar with the concept of entropy discussed in Chapter 7. 3.7 PHASE DIAGRAMS A pure substance is composed of a single chemical compound, which may itself be composed of a variety of chemical elements. Water (H 2 O), ammonia (NH 3 ), and carbon dioxide (CO 2 ) are all pure substances, but air is not because it is a mixture of N 2 ,O 2 ,H 2 O, CO 2 , and so forth. All substances can exist in one or more of the gaseous (or vapor), liquid, or solid physical states, and some solids can have a variety of molecular structures. In 1875, the American physicist Josiah Willard Gibbs (1839–1903) introduced the term phase to describe the different forms in which a pure substance can exist. We now speak of the gaseous, liquid, and solid phases of a pure substance, and we recognize that a pure substance may have a number of different solid phases. 2 Multiple solid phases are called allotropic, a term that comes from the Greek words allos, meaning“related to,” and trope meaning “forms of the same substance.” For example, graphite and diamond are allotropic forms of carbon. A substance made up of only one physical phase is called homogeneous; if it is composed of two or more phases it is called heterogeneous. Coexistent phases are separated by an interface, called the phase boundary, of finite thickness across which the property values change uniformly. A system in which two phases coexist in equilibrium is called saturated. The number of degrees of freedom within a heterogeneous mixture of pure substances is given by Gibbs’s phaseruleas f = C − P + 2 where f is the number of degrees of freedom, C is the number of components (pure substances) in the mixture, and P is the number of phases. Also, f can be interpreted to be the number of intensive properties of the individual phases required to fix the state of the individual phases. For example, a homogeneous (P = 1) pure substance (C =1) requires f =1− 1+2=2intensivepropertiestofixitsstate.Similarly,ahomogeneous(P = 1) mixture of two pure substances (C = 2) requires f =2− 1+2=3intensive properties to fix its state, and so forth. The case of a two-phase (P = 2) pure substance (C = 1), however, is misleading, because f =1− 2+2=1,butthissimplymeansthateach SATURATED WITH WHAT? The term saturated comes from the 18th century, when heat was thought to be a fluid. At that time, it was thought that a substance could be saturated with heat, just like water can become saturated with salt or sugar. Today we recognize that heat is not a fluid, and therefore the use of the word saturation in reference to a thermodynamic phase change is really a misnomer. However, this term is now completely entrenched in modern thermodynamic literature and cannot be changed. 2 Actually, matter can exist in a bewildering variety of phases beyond the common solid, liquid, and vapor forms. Ferromagnetic, antiferromagnetic, ferroelectric, superconducting, superfluid, nematic, smectic, and so on are all valid phases.
66 CHAPTER 3: Thermodynamic Properties phase requires one intensive property to fix its state. Hence, two independent properties are required to fix the state of the complete two-phase system. To find the state of a mixture of two phases, we need to know how much of each phase is present, that is, the composition of the mixture. The phase composition in a liquid-vapor mixture is given by a new thermodynamic property called the quality of the mixture, which is defined shortly. A phase diagram is made by plotting thermodynamic properties as coordinates. Figure 3.4 illustrates typical p-T and p-v phase diagrams for a substance that expands on freezing (such as water or antimony). When the p-T and p-v diagrams are combined to form a three-dimensional p-v-T surface, thermodynamic surfaces arise, as shown in Figure 3.5. Figures 3.6 and 3.7 show the similar plots for a substance that contracts on freezing (such as carbon dioxide and most other substances). The expansion or contraction behavior of a substance on solidification can be deduced either from the increase or decrease in specific volume as the substance goes from a liquid to a solid, or from the slope of the fusion line on the p-T diagram. If the p-T fusion line has a negative slope, then the substance contracts on melting; if it has a positive slope, then it expands on melting. Thepuresubstancep-T phase diagram shown in Figures 3.4 and 3.5 is composed of three unique curves. The fusion line represents the region of two-phase solid-liquid equilibrium, the vaporization line represents the region S L Liquid Liquid Solid Pressure S Solid V Triple point L Vapor V Critical point Gas Pressure Critical point Gas Liquid− vapor Triple line Solid−vapor Vapor Temperature Volume FIGURE 3.4 Pressure-temperature and pressure-volume diagrams for a substance that expands on freezing (for example, water). Liquid Pressure Solid Liquid− vapor Critical point Triple line Gas Vapor Solid− vapor Volume Temperature FIGURE 3.5 The p-v-T surface for a substance that expands on freezing (for example, water).
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Modern Engineering Thermodynamics
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Modern Engineering Thermodynamics R
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Dedication WHAT IS AN ENGINEER AND
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Contents PREFACE . . . . . . . . .
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Contents ix 7.6 Heat Engines Runnin
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Contents xi 14.13 Air Standard Gas
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Preface TEXT OBJECTIVES This textbo
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Preface xv Step 5. Write down the b
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Acknowledgments I wish to acknowled
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Resources That Accompany This Book
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List of Symbols A a B COP CR c c p
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Prologue PARIS FRANCE, 10:35 AM, AU
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CHAPTER 1 The Beginning CONTENTS 1.
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1.2 Why Is Thermodynamics Important
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1.3 Getting Answers: A Basic Proble
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1.5 How Do We Measure Things? 7 bei
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1.6 Temperature Units 9 THE DEVELOP
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1.7 Classical Mechanical and Electr
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1.7 Classical Mechanical and Electr
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Page 42 and 43: 1.10 Significant Figures 17 CRITICA
Page 44 and 45: 1.10 Significant Figures 19 WHAT AB
Page 46 and 47: 1.11 Potential and Kinetic Energies
Page 48 and 49: 1.11 Potential and Kinetic Energies
Page 50 and 51: Summary 25 FIGURE 1.19 Case study 1
Page 52 and 53: Problems 27 Problems (* indicates p
Page 54 and 55: Problems 29 14. Determine the mass
Page 56 and 57: Problems 31 49. Using the CGS units
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Page 60 and 61: 2.3 Phases of Matter 35 System boun
Page 62 and 63: 2.4 System States and Thermodynamic
Page 64 and 65: 2.6 Thermodynamic Processes 39 WHAT
Page 66 and 67: 2.7 Pressure and Temperature Scales
Page 68 and 69: 2.9 The Continuum Hypothesis 43 Sur
Page 70 and 71: 2.10 The Balance Concept 45 Solutio
Page 72 and 73: 2.11 The Conservation Concept 47 or
Page 74 and 75: 2.11 The Conservation Concept 49 Th
Page 76 and 77: Summary 51 change in the mass of X
Page 78 and 79: Problems 53 Problems (* indicates p
Page 80 and 81: Problems 55 and Death rate = α 2 +
Page 82 and 83: CHAPTER 3 Thermodynamic Properties
Page 84 and 85: 3.3 Fun with Mathematics 59 CRITICA
Page 86 and 87: 3.4 Some Exciting New Thermodynamic
Page 88 and 89: 3.6 Enthalpy 63 WHO WAS AMALIE EMMY
Page 92 and 93: Pressure Vapor 3.7 Phase Diagrams 6
Page 94 and 95: 3.7 Phase Diagrams 69 WHAT IS A “
Page 96 and 97: 3.7 Phase Diagrams 71 considerable
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Page 100 and 101: 3.8 Quality 75 Although Eq. (3.26)
Page 102 and 103: 3.9 Thermodynamic Equations of Stat
Page 110 and 111: 3.10 Thermodynamic Tables 85 Critic
Page 112 and 113: 3.12 Thermodynamic Charts 87 vð100
Page 114 and 115: 3.13 Thermodynamic Property Softwar
Page 116 and 117: Summary 91 and e = E/m = u + V2 2g
Page 118 and 119: Problems 93 c. For a saturated mixt
Page 120 and 121: Problems 95 specific enthalpy of sa
Page 122 and 123: Problems 97 Table 3.23 Problem 65 M
Page 124 and 125: CHAPTER 4 The First Law of Thermody
Page 126 and 127: 4.3 The First Law of Thermodynamics
Page 128 and 129: 4.3 The First Law of Thermodynamics
Page 130 and 131: 4.4 Energy Transport Mechanisms 105
Page 132 and 133: 4.5 Point and Path Functions 107 4.
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4.6 Mechanical Work Modes of Energy
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4.7 Nonmechanical Work Modes of Ene
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4.9 Work Efficiency 125 In the case
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4.12 Heat Modes of Energy Transport
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4.13 Heat Transfer Modes 129 Table
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4.14 A Thermodynamic Problem Solvin
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4.14 A Thermodynamic Problem Solvin
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4.15 How to Write a Thermodynamics
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4.15 How to Write a Thermodynamics
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Summary 139 The general open system
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Problems 141 11.* Determine the hea
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Problems 143 where K = 0.810 lbf. D
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Problems 145 Table 4.12 Problem 67
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CHAPTER 5 First Law Closed System A
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5.2 Sealed, Rigid Containers 149 In
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5.4 Power Plants 151 Step 7. Calcul
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5.5 Incompressible Liquids 153 The
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1Q 2 − 1 W 2 = mðu 2 − u 1 Þ
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5.8 Closed System Unsteady State Pr
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5.9 The Explosive Energy of Pressur
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Problems 161 Problems (* indicates
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Problems 163 31. A thermoelectric g
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Problems 165 where v, T, and r are
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CHAPTER 6 First Law Open System App
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6.2 Mass Flow Energy Transport 169
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6.3 Conservation of Energy and Cons
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6.4 Flow Stream Specific Kinetic an
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6.5 Nozzles and Diffusers 175 m (a)
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6.5 Nozzles and Diffusers 177 We ar
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6.6 Throttling Devices 179 These as
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6.6 Throttling Devices 181 For an i
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6.7 Throttling Calorimeter 183 The
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6.8 Heat Exchangers 185 Convective
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6.9 Shaft Work Machines 187 6.9 SHA
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6.9 Shaft Work Machines 189 1 Basem
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6.10 Open System Unsteady State Pro
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Problems 197 we have _m R / _m D =
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Problems 201 32.* A commercial slid
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Summary 203 59. Incompressible liqu
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CHAPTER 7 Second Law of Thermodynam
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7.3 The Second Law of Thermodynamic
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7.4 Carnot’s Heat Engine and the
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7.4 Carnot’s Heat Engine and the
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7.5 The Absolute Temperature Scale
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7.5 The Absolute Temperature Scale
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7.6 Heat Engines Running Backward 2
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7.7 Clausius’s Definition of Entr
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7.8 Numerical Values for Entropy 22
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7.10 Differential Entropy Balance 2
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7.11 Heat Transport of Entropy 229
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7.13 Entropy Production Mechanisms
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7.14 Heat Transfer Production of En
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7.15 Work Mode Production of Entrop
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7.15 Work Mode Production of Entrop
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7.16 Phase Change Entropy Productio
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Summary 241 ■ Indirect method inv
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Problems 243 amount of work W irr i
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Problems 245 a. If the heat pump is
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Problems 247 51. Develop a program
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CHAPTER 8 Second Law Closed System
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8.2 Systems Undergoing Reversible P
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8.3 Systems Undergoing Irreversible
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8.4 Diffusional Mixing 271 Exercise
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Summary 273 Note that this example
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Problems 275 15. A 20.0 ft 3 tank c
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Problems 277 46. a. Determine a for
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CHAPTER 9 Second Law Open System Ap
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9.4 Open System Entropy Balance Equ
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9.4 Open System Entropy Balance Equ
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9.5 Nozzles, Diffusers, and Throttl
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9.5 Nozzles, Diffusers, and Throttl
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9.6 Heat Exchangers 289 Exercises 1
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9.6 Heat Exchangers 291 (T H ) (T H
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9.7 Mixing 293 Now, _m air is given
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9.7 Mixing 295 Critical value of y,
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9.9 Unsteady State Processes in Ope
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Problems 309 Multiplying this equat
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Problems 311 entropy production rat
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Problems 313 heat is added to the b
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Problems 315 55.* Determine the max
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Problems 317 The cavitation process
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CHAPTER 10 Availability Analysis CO
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10.3 What Are Conservative Forces?
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10.6 Availability 323 WHAT IS A SYS
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10.6 Availability 325 and the total
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10.7 Closed System Availability Bal
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10.7 Closed System Availability Bal
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10.8 Flow Availability 331 EXAMPLE
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s − s 0 = c ln T T 0 10.8 Flow Av
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10.10 Modified Availability Rate Ba
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10.10 Modified Availability Rate Ba
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10.11 Energy Efficiency Based on th
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Summary 351 In this problem, we hav
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Summary 353 7. The general open sys
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Problems 355 12.5 Btu/hr·ft ·R. I
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Problems 357 flow rate of 15.0 lbm/
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Problems 359 85. Create a specific
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CHAPTER 11 More Thermodynamic Relat
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11.2 Two New Properties: Helmholtz
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11.2 Two New Properties: Helmholtz
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11.4 Maxwell Equations 367 11.4 MAX
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11.4 Maxwell Equations 369 then,
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11.5 The Clapeyron Equation 371 and
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11.6 Determining u, h, and s from p
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11.7 Constructing Tables and Charts
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11.8 Thermodynamic Charts 381 so th
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11.9 Gas Tables 383 where p r is th
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11.10 Compressibility Factor and Ge
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11.11 Is Steam Ever an Ideal Gas? 3
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Summary 399 equation, and a series
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Problems 401 20.* Estimate h fg for
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Problems 403 Design Problems The fo
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CHAPTER 12 Mixtures of Gases and Va
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12.2 Thermodynamic Properties of Ga
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12.3 Mixtures of Ideal Gases 413 Th
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12.3 Mixtures of Ideal Gases 415 Co
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12.4 Psychrometrics 417 Finally, th
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12.4 Psychrometrics 419 EXAMPLE 12.
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12.6 The Sling Psychrometer 421 The
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12.6 The Sling Psychrometer 423 p w
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12.7 Air Conditioning 425 WHAT ENVI
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12.8 Psychrometric Enthalpies 427 E
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12.8 Psychrometric Enthalpies 429 o
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12.9 Mixtures of Real Gases 431 Whe
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12.9 Mixtures of Real Gases 433 and
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12.9 Mixtures of Real Gases 435 The
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12.9 Mixtures of Real Gases 437 Sol
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Summary 439 Last, we combine Dalton
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Problems 443 exhaust gas is an idea
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Problems 445 57.* Cooling towers ar
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CHAPTER 13 Vapor and Gas Power Cycl
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13.2 Part I. Engines and Vapor Powe
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13.4 Rankine Cycle 457 A B Reversib
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13.5 Operating Efficiencies 459 For
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13.5 Operating Efficiencies 461 13.
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13.5 Operating Efficiencies 463 b.
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13.5 Operating Efficiencies 465 Sta
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13.6 Rankine Cycle with Superheat 4
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13.7 Rankine Cycle with Regeneratio
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13.8 The Development of the Steam T
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13.9 Rankine Cycle with Reheat 477
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13.9 Rankine Cycle with Reheat 479
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13.10 Modern Steam Power Plants 481
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13.12 Air Standard Power Cycles 487
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13.13 Stirling Cycle 489 Q H 4 1 4
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13.14 Ericsson Cycle 491 Q H 4 1 3
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13.15 Lenoir Cycle 493 Exercises 28
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13.16 Brayton Cycle 495 Solution Us
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13.16 Brayton Cycle 497 Equation (7
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13.17 Aircraft Gas Turbine Engines
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13.17 Aircraft Gas Turbine Engines
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13.18 Otto Cycle 503 T Q H 1 1 1 v
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13.18 Otto Cycle 505 Exercises 40.
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13.18 Otto Cycle 507 and, since the
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13.20 Miller Cycle 509 13.19.1 Mode
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13.20 Miller Cycle 511 Then, from F
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13.21 Diesel Cycle 513 to stroll on
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13.21 Diesel Cycle 515 Solution a.
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13.22 Modern Prime Mover Developmen
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13.23 Second Law Analysis of Vapor
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Summary 525 Fill port 160 mm End of
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Problems 527 7. The thermal efficie
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efficiency increase if the condense
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Problems 531 horsepower hour. Assum
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Problems 533 72. Determine the valu
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CHAPTER 14 Vapor and Gas Refrigerat
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14.3 Carnot Refrigeration Cycle 537
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14.4 In the Beginning There Was Ice
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14.4 In the Beginning There Was Ice
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14.5 Vapor-Compression Refrigeratio
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14.5 Vapor-Compression Refrigeratio
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14.6 Refrigerants 547 T 3 2s 2 p 3
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14.7 Refrigerant Numbers 549 14.7 R
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14.7 Refrigerant Numbers 551 R-110
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14.8 CFCs and the Ozone Layer 553 H
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14.9 Cascade and Multistage Vapor-C
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14.10 Absorption Refrigeration 561
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14.11 Commercial and Household Refr
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14.14 Reversed Brayton Cycle Refrig
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14.14 Reversed Brayton Cycle Refrig
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14.15 Reversed Stirling Cycle Refri
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14.16 Miscellaneous Refrigeration T
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14.16 Miscellaneous Refrigeration T
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14.18 Second Law Analysis of Refrig
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14.18 Second Law Analysis of Refrig
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2. The coefficient of performance o
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Problems 585 13.* A refrigeration u
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Problems 587 Loop B Station 1B Stat
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Problems 589 under these conditions
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CHAPTER 15 Chemical Thermodynamics
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15.2 Stoichiometric Equations 593 1
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15.2 Stoichiometric Equations 595 C
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15.3 Organic Fuels 597 ANSWERS SOME
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15.4 Fuel Modeling 599 Hydrocarbon
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15.4 Fuel Modeling 601 equation, si
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15.5 Standard Reference State 603 I
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15.6 Heat of Formation 605 and H 2
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15.7 Heat of Reaction 607 EXAMPLE 1
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15.7 Heat of Reaction 609 CRITICAL
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15.7 Heat of Reaction 611 Then, h P
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15.8 Adiabatic Flame Temperature 61
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15.9 Maximum Explosion Pressure 619
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15.10 Entropy Production in Chemica
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15.10 Entropy Production in Chemica
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15.11 Entropy of Formation and Gibb
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15.12 Chemical Equilibrium and Diss
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H 2 O !ð1 − yÞH 2 O + yðv H2
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15.14 The van’t Hoff Equation 635
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15.15 Fuel Cells 637 Anode Electrol
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15.15 Fuel Cells 639 The maximum po
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15.16 Chemical Availability 641 and
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ðn i /n fuel Þðc pi Þ E system
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Problems 645 where j = 4n + m kgmol
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Problems 647 c. The percent excess
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Problems 649 77. Determine the mola
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CHAPTER 16 Compressible Fluid Flow
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16.3 Isentropic Stagnation Properti
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16.4 The Mach Number 655 Note that
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16.4 The Mach Number 657 Table 16.1
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16.4 The Mach Number 659 Since for
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16.5 Converging-Diverging Flows 661
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16.5 Converging-Diverging Flows 663
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16.6 Choked Flow 665 T a a p a = co
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16.6 Choked Flow 667 Exercises 16.
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16.7 Reynolds Transport Theorem 669
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16.7 Reynolds Transport Theorem 671
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16.8 Linear Momentum Rate Balance 6
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16.9 Shock Waves 675 16.9 SHOCK WAV
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16.9 Shock Waves 677 and, for an id
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16.9 Shock Waves 679 6 5 4 S P /(m
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16.10 Nozzle and Diffuser Efficienc
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16.10 Nozzle and Diffuser Efficienc
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Summary 685 Since for a diffuser, M
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43. 0.800 lbm/s of air passes throu
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Problems 691 A plot of this functio
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CHAPTER 17 Thermodynamics of Biolog
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17.3 Thermodynamics of Biological C
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17.3 Thermodynamics of Biological C
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17.4 Energy Conversion Efficiency o
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17.4 Energy Conversion Efficiency o
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17.5 Metabolism 703 Table 17.3 Brea
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17.6 Thermodynamics of Nutrition an
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17.7 Limits to Biological Growth 71
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17.7 Limits to Biological Growth 71
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17.8 Locomotion Transport Number 71
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17.9 Thermodynamics of Aging and De
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17.9 Thermodynamics of Aging and De
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1/3 V most efficient = P o ρAC D S
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Problems 723 a. If the monster cons
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Problems 725 the officer asks Paul
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CHAPTER 18 Introduction to Statisti
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18.3 Kinetic Theory of Gases 729 3.
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U trans = 3 2 NkT (Continued ) 18.3
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18.4 Intermolecular Collisions 733
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18.5 Molecular Velocity Distributio
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18.5 Molecular Velocity Distributio
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18.6 Equipartition of Energy 739 We
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18.7 Introduction to Mathematical P
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18.8 Quantum Statistical Thermodyna
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18.9 Three Classical Quantum Statis
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18.11 Monatomic Maxwell-Boltzmann G
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18.12 Diatomic Maxwell-Boltzmann Ga
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18.12 Diatomic Maxwell-Boltzmann Ga
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18.13 Polyatomic Maxwell-Boltzmann
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Summary 759 In this chapter, we sum
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Problems 761 4. Find the temperatur
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CHAPTER 19 Introduction to Coupled
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19.3 Linear Phenomenological Equati
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19.4 Thermoelectric Coupling 767 Eq
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19.4 Thermoelectric Coupling 769 Th
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19.4 Thermoelectric Coupling 771 wh
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19.4 Thermoelectric Coupling 773 Th
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19.4 Thermoelectric Coupling 775 b.
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19.5 Thermomechanical Coupling 777
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water), it seems reasonable that li
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Problems 785 b. For a Knudson gas,
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Appendix A: Physical Constants and
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Appendix B: Greek and Latin Origins
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Appendix B 791 Table B.4 Plural End
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Index Page numbers followed by f in
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Index 795 E e (specific energy), 10
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Index 797 Isobaric coefficient of v
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Index 799 Ranque, Georges Joseph, 3
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Index 801 William III, King of Engl
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Modern Engineering Thermodynamics

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