Modern Engineering Thermodynamics

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15.8 Adiabatic Flame Temperature 613 Table 15.4 Explosion Limits and Ignition Temperatures for Common Fuel–Air Mixtures Substance LEL (%) UEL (%) Ignition Temp. (°F) Carbon monoxide (CO) 12.5 74.0 1128 Hydrogen (H 2 ) 4.00 75.0 968 Methane (CH 4 ) 5.00 15.0 1301 Acetylene (C 2 H 2 ) 2.50 81.0 763–824 Ethylene (C 2 H 4 ) 2.75 28.6 914 Ethane (C 2 H 6 ) 3.00 12.5 968–1166 Propylene (C 3 H 6 ) 2.00 11.1 856 Propane (C 3 H 8 ) 2.10 10.1 871 n-Butane (C 4 H 10 ) 1.86 8.4 761 Gasoline 1.12 6.75 495 15.8 ADIABATIC FLAME TEMPERATURE The maximum possible combustion temperature occurs when combustion takes place inside an adiabatic (i.e., insulated) system. This temperature is called the adiabatic combustion temperature or the adiabatic flame temperature. In practice, though, the combustion temperature can never reach this temperature, because 1. No system can be made truly adiabatic. 2. The combustion reaction is always somewhat incomplete. 3. The combustion products ionize at high temperatures and thus lower the reaction temperature. Nonetheless, the adiabatic flame temperature provides a useful upper bound on combustion temperatures and can be used to estimate the thermal effects of combustion on material physical properties and exhaust gas states. There are actually two types of adiabatic flame temperature, depending on whether the combustion process is carried out under constant volume or constant pressure. The constant volume adiabatic flame temperature is the temperature resulting from a complete combustion process that occurs inside of a closed, rigid vessel with no work, heat transfer, or changes in kinetic or potential energy. The constant pressure adiabatic flame temperature is the temperature that results from a complete combustion process that occurs at a constant pressure (like an open flame) with no heat transfer or change in kinetic or potential energy. The constant pressure adiabatic flame temperature is lower than the constant volume adiabatic flame temperature, because some of the combustion energy is used to change the volume of the reactants and thus generates work. For an open, constant pressure, adiabatic system, q r = 0 and Eq. (15.9) reduces to h R = h P , then, ∑ R ðn i /n fuel Þ½h°+hðTÞ f − hðT°ÞŠ i = ∑ ðn i /n fuel Þ½h°+hðT f A Þ − hðT°ÞŠ i where T A is the adiabatic flame temperature and T is the temperature of the reactants. If the reactants are all at the standard reference state and the products can all be treated as ideal gases with constant specific heats over the temperature range from T° to T A , then the previous equation reduces to ∑ R ðn i /n fuel Þ h° f i = ∑ P P ðn i /n fuel Þ h°+c f p ðT A − T° Þ i Now, let us suppose that all of the reactants except the fuel are elements; then, their h f ° values are all zero. This equation can now be solved for T A as Open system, constant pressure, adiabatic, flame temperature when the reactants are at the SRS: T A = T°+ open system h f ° fuel −∑ P ∑ P ðn i /n fuel Þ h° f i ðn i /n fuel Þ c pi avg (15.17) Equation (15.17) represents the only method for calculating the adiabatic flame temperature directly. It requires ideal gas behavior, which is usually reasonable, and it requires constant specific heats over the range T° =25.0°C
614 CHAPTER 15: Chemical <strong>Thermodynamics</strong> Table 15.5 Molar Specific Heats Averaged over the Temperature Range from 25 to 3000°C (77 to 5400°F) Substance ðc p Þ avg ðc v Þ avg kJ/(kgmole ·K) Btu/(lbmole·R) kJ/(kgmole·K) Btu/(lbmole ·R) CO 2 (g) 58.18 13.90 49.87 11.91 H 2 O (g) 42.50 10.15 34.19 8.17 O 2 (g) 32.99 7.88 24.68 5.89 N 2 (g) 31.18 7.45 22.87 5.46 to T A , which is not so reasonable unless average values are used (as noted in the equation). Average molar specific heats for typical combustion products in the range 25 to 3000°C are given in Table 15.5. This range covers most adiabatic flame temperatures. In the case of a constant volume adiabatic closed system (Table 15.6), Eq. (15.7) tells us that u P = u R , and if the reactants are at the SRS and the products can again be treated as ideal gases with constant (or average) specific heats, it is easy to show that the adiabatic flame temperature in this system is given by Closed system constant volume adiabatic flame temperature when the reactants at the SRS: T A = T°+ closed system u f ° fuel −∑ R ðn i /n fuel Þh° f − RT° ∑ R ∑ P ðn i /n fuel ðn i /n fuel Þ−∑ P ðn i /n fuel Þ Þðc vi Þ avg (15.18) where we again assume that the reactants contain only the fuel and its combustion elements. Also, we use the definition of enthalpy to find u° f = h° f − ðpvÞ°=h° f − RT° for the ideal gas products and the nonfuel reactants, where T° is the standard reference state absolute temperature (298 K or 537 R). Further, for most liquids and solids at the standard reference state, we can use the approximation u f ° fuel ≈ h f ° fuel : Table 15.6 Constant Volume Adiabatic Flame Temperatures of Common Hydrocarbon Fuels when the Reactants Enter the Combustion Process at 25°C (77°F) and 1 Atm Pressure and the Products Leave the Process at 1 Atm Pressure. The Combustion Is Stoichiometric with No Excess Air Fuel Oxidizer T ad (°C) T ad (°F) Acetylene (C 2 H 2 ) Air 2500 4532 O 2 3480 6296 Butane (C 4 H 10 ) Air 1970 3578 O 2 3100 5612 Hydrogen (H 2 ) Air 2210 4010 O 2 3200 5792 Methane (CH 4 ) Air 1950 3542 O 2 2810 5090 Propane (C 3 H 8 ) Air 1980 3596 O 2 2526 4579 MAPP gas (C 3 H 4 ) Air 2010 3650 O 2 2927 5301 Wood Air 1980 3596
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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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1.9 Modern Units Systems 15 where M
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1.10 Significant Figures 17 CRITICA
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1.10 Significant Figures 19 WHAT AB
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1.11 Potential and Kinetic Energies
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1.11 Potential and Kinetic Energies
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Summary 25 FIGURE 1.19 Case study 1
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Problems 27 Problems (* indicates p
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Problems 29 14. Determine the mass
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Problems 31 49. Using the CGS units
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CHAPTER 2 Thermodynamic Concepts CO
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2.3 Phases of Matter 35 System boun
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2.4 System States and Thermodynamic
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2.6 Thermodynamic Processes 39 WHAT
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2.7 Pressure and Temperature Scales
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2.9 The Continuum Hypothesis 43 Sur
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2.10 The Balance Concept 45 Solutio
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2.11 The Conservation Concept 47 or
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2.11 The Conservation Concept 49 Th
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Summary 51 change in the mass of X
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Problems 53 Problems (* indicates p
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Problems 55 and Death rate = α 2 +
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CHAPTER 3 Thermodynamic Properties
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3.3 Fun with Mathematics 59 CRITICA
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3.4 Some Exciting New Thermodynamic
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3.6 Enthalpy 63 WHO WAS AMALIE EMMY
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3.7 Phase Diagrams 65 WHO WAS EMMY
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Pressure Vapor 3.7 Phase Diagrams 6
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3.7 Phase Diagrams 69 WHAT IS A “
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3.7 Phase Diagrams 71 considerable
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3.8 Quality 73 10 5 300 C Critical
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3.8 Quality 75 Although Eq. (3.26)
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3.9 Thermodynamic Equations of Stat
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3.10 Thermodynamic Tables 85 Critic
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3.12 Thermodynamic Charts 87 vð100
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3.13 Thermodynamic Property Softwar
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Summary 91 and e = E/m = u + V2 2g
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Problems 93 c. For a saturated mixt
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Problems 95 specific enthalpy of sa
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Problems 97 Table 3.23 Problem 65 M
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CHAPTER 4 The First Law of Thermody
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4.3 The First Law of Thermodynamics
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4.3 The First Law of Thermodynamics
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4.4 Energy Transport Mechanisms 105
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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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Page 604 and 605: 14.18 Second Law Analysis of Refrig
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Page 610 and 611: Problems 585 13.* A refrigeration u
Page 612 and 613: Problems 587 Loop B Station 1B Stat
Page 614 and 615: Problems 589 under these conditions
Page 616 and 617: CHAPTER 15 Chemical Thermodynamics
Page 618 and 619: 15.2 Stoichiometric Equations 593 1
Page 620 and 621: 15.2 Stoichiometric Equations 595 C
Page 622 and 623: 15.3 Organic Fuels 597 ANSWERS SOME
Page 624 and 625: 15.4 Fuel Modeling 599 Hydrocarbon
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Page 628 and 629: 15.5 Standard Reference State 603 I
Page 630 and 631: 15.6 Heat of Formation 605 and H 2
Page 632 and 633: 15.7 Heat of Reaction 607 EXAMPLE 1
Page 634 and 635: 15.7 Heat of Reaction 609 CRITICAL
Page 636 and 637: 15.7 Heat of Reaction 611 Then, h P
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Page 644 and 645: 15.9 Maximum Explosion Pressure 619
Page 646 and 647: 15.10 Entropy Production in Chemica
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Page 650 and 651: 15.11 Entropy of Formation and Gibb
Page 652 and 653: 15.12 Chemical Equilibrium and Diss
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Page 660 and 661: 15.14 The van’t Hoff Equation 635
Page 662 and 663: 15.15 Fuel Cells 637 Anode Electrol
Page 664 and 665: 15.15 Fuel Cells 639 The maximum po
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Page 668 and 669: ðn i /n fuel Þðc pi Þ E system
Page 670 and 671: Problems 645 where j = 4n + m kgmol
Page 672 and 673: Problems 647 c. The percent excess
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Page 678 and 679: 16.3 Isentropic Stagnation Properti
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Page 682 and 683: 16.4 The Mach Number 657 Table 16.1
Page 684 and 685: 16.4 The Mach Number 659 Since for
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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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