Modern Engineering Thermodynamics

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15.4 Fuel Modeling 601 equation, since it results from the oxidation of the hydrogen in the fuel. For convenience, we write the combustion reaction for 100. moles of dry product formed by burning 1.00 mole of the fuel model C n H m . Using the given combustion analysis, we have C n H m + a½O 2 + 3:76ðN 2 ÞŠ ! 7:10ðCO 2 Þ + 0:800ðCOÞ + 9:90ðO 2 Þ + bðH 2 OÞ + 82:2ðN 2 Þ The element balances are Carbon (C) balance: n = 7.10 + 0.800 = 7.90 Hydrogen (H) balance: m = 2b Nitrogen (N 2 ) balance: 3:76a = 82:2, or a = 82:2/3:76 = 21:9 Oxygen (O 2 ) balance: a = 21:9 = 7:10 + 0:800/2 + 9:90 + b/2, or b = 9:00: Then, from the preceding hydrogen balance, m = 2b = 18:0: Consequently, the fuel model is C 7.90 H 18.0 , which is approximately octane, C 8 H 18 . The final reaction equation is C 7:90 H 18:0 + 21:9½O 2 + 3:76ðN 2 ÞŠ ! 7:10ðCO 2 Þ + 0:800ðCOÞ + 9:90ðO 2 Þ + 9:00ðH 2 OÞ + 82:2ðN 2 Þ b. On a molar basis, 1.00 mole of fuel contains 7.90 moles of C and 18.0 moles of H, and on a molar percentage basis, this becomes [7.90/(7.90 + 18.0)](100.) = 31.0% C and [18.0/(7.90 + 18.0)](100) = 69.0% H. The molecular mass of the fuel in this model is and so the fuel’s composition on a mass basis is and M fuel = 7:90ð12Þ + 18:0ð1Þ = 113 kg/kgmole = 113 lbm/lbmole ð7:90 kgmole C/kgmole fuelÞð12:0 kg C/kgmole CÞ/ ð113 kg fuel/kgmole fuelÞ = 0:840 kg C/kg fuel = 0:840 lbm C/lbm fuel ð9:00Þð2:016Þ/113 = 0:161 kg H/kg fuel = 0:161 lbm H/lbm fuel Therefore, the fuel can be said to consist of 31% carbon and 69% hydrogen on a molar basis or 84% carbon and 16% hydrogen on a mass basis. c. Referring to the final combustion equation determined in part a, the air/fuel ratio on a molar basis is ðA/FÞ molar = n air 21:9 × ð1 + 3:76Þ moles of air = = 104 moles air/mole fuel n fuel 1 mole of fuel and on a mass basis it is 28:97 kg air/kgmole air ðA/FÞ mass = ð104 kgmole air/kgmole fuelÞ× 113 kg fuel/kgmole fuel = 26:7 kg air/kg fuel = 26:7 lbm air/lbm fuel d. To determine the percent of theoretical air used, we must first determine the minimum air required for complete combustion. The reaction for 100.% theoretical air has the form C 7:90 H 18:0 + a½O 2 + 3:76ðN 2 ÞŠ ! bðCO 2 Þ + cðH 2 OÞ + dðN 2 Þ The element balances are Carbon (C) balance: 7.90 = b Hydrogen (H) balance: 18.0 = 2c, orc = 11.0 Oxygen (O 2 ) balance: a = b + c/2 = 7:90 + 9:00/2 = 12:4 Nitrogen (N 2 )balance:3:76a = d = 3:76ð12:4Þ = 46:6 Then the theoretical molar air/fuel ratio (for 100% theoretical air) is 12:4ð1 + 3:76Þ ðA/FÞ molar = = 59:0 mole air/mole fuel 1 theoretical finally, the percent of theoretical air used in the actual combustion process is " , # % of theoretical air = ðA/FÞ molar actual ðA/FÞ molar theoretical or 77.0% excess air. = 104/59:0 ð100Þ = 177% × 100 (Continued )
602 CHAPTER 15: Chemical Thermodynamics EXAMPLE 15.3 (Continued) Exercises 7. Determine the hydrocarbon fuel model in Example 15.3 if the CO and O 2 concentrations are both 0.00%, and the CO 2 and N 2 concentrations are 17.0% and 83.0%, respectively, in the Orsat analysis. Answer: Hydrocarbon fuel model = C 17 H 20.3 . 8. Determine the molar and mass air/fuel ratios in Example 15.3 if the CO and O 2 concentrations are both 0.00%, and the CO 2 and N 2 concentrations are 17.0% and 83.0%, respectively, in the Orsat analysis. Answer: A/F = 10.15 kgmole air/ kgmole fuel = 1.31 kg air/kg fuel. 9. If the CO concentration in Example 15.3 is 0.00% and the N 2 concentration is 83.0%, with all the other concentrations unchanged, determine the hydrocarbon fuel model and % of excess air used in the combustion process. Answer: Hydrocarbon fuel model = C 7.1 H 22.28 and % of excess air = 74.2%. In the previous example, we assume that nearly all the water produced by the combustion process condensed out by the time the combustion products cooled to 20.0°C. For this to be a valid assumption, the dew point of the combustion products must be at 20.0°C or higher. The determination of the dew point temperature for this reaction is illustrated in the next example. EXAMPLE 15.4 Determine the dew point temperature of the combustion products given in Example 15.3 if the total pressure of the mixture is 14.7 psia. Solution From Eq. (12.23) of Chapter 12, the volume fractions, mole fractions, and partial pressure ratios are all equal for a mixture of ideal gases. Exhaust products at atmospheric pressure are sufficiently ideal to allow us to determine the water vapor partial pressure at its condensation temperature (i.e., dew point) from this relation. The total number of moles of product, from part a of Example 15.3, is 109 moles. Then, using Eq. (12.23) wherein p m is the total pressure of the mixture gives π H2O = p H2O/p m = ψ H2O = χ H2O = 9:00 109 = 0:0826 where π is the partial pressure ratio, ψ is the volume fraction, and χ is the mole fraction. So, p H2O = 0:0826ð14:7Þ = 1:21 psia The saturation temperature of water vapor at this pressure is defined to be the dew point temperature. By interpolation in Table C.1a in Thermodynamic Tables to accompany Modern Engineering Thermodynamics, we find that T sat ð1:21 psiaÞ = T DP = 108°F = 42:3°C Thus, the exhaust products must be cooled to 108°F ð42:3°CÞ or below to condense the water of combustion and have an essentially dry exhaust gas. Exercises 10. Determine the partial pressure of the water vapor in Example 15.4 if the mixture total pressure is 0.150 MPa. Answer: p H2O= 12.4 kPa. 11. If the dew point temperature in Example 15.4 is 212°F, what is the mixture total pressure? Answer: p m = 178 psia. 12. Determine the partial pressure and dew point temperature of the water vapor present in the 100.% theoretical air combustion process given in part d of Example 15.3. Assume the mixture total pressure is 14.7 psia. Answer: p H2O = 2.08 psia, T DP = 128°F. WHY DO AUTOMOBILE EXHAUST SYSTEMS RUST? Water condenses in an automobile’s exhaust system and drips out the tailpipe until the entire exhaust system has been heated above the dew point temperature by the exhaust gases. This water promotes corrosion and causes the exhaust system to rust out sooner if the vehicle is used for short trips than trips long enough (a half hour or more) to dry out the exhaust system.
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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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Page 616 and 617: CHAPTER 15 Chemical Thermodynamics
Page 618 and 619: 15.2 Stoichiometric Equations 593 1
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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 630 and 631: 15.6 Heat of Formation 605 and H 2
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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,
Page 812 and 813:
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
Page 818 and 819:
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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