Modern Engineering Thermodynamics

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15.15 Fuel Cells 639 The maximum power _W max and maximum reaction efficiency ðη r Þ max occur when the device is completely reversible or _S P = 0: Then, ðη r Þ max = ∑ in ∑ in _m i g i −∑ out _m i h i −∑ out _m i g i _m i h i = ∑ in ∑ in _n i g i −∑ _n i g i out (15.42) _n i h i −∑ _n i h i out Utilizing Eq. (15.33), the molar forms of Eqs. (15.40), (15.41), and (15.42) are _W = ∑ R _n i g • i −∑ P _n i g • i − T b _S P + RT ln ∏ R ðp i /p° Þ _ni /∏ ðp i /p° P Þ _ni (15.43) and η r = ∑ R _n i g • i −∑ P _n i g • i − T b _S P + RT ln ∏ R ∑ R _n i h i −∑ P ðp i /p° Þ _ni /∏ ðp i /p° P Þ _ni _n i h i (15.44) ðη r Þ maximum fuel cell efficiency = ∑ R ðn i /n fuel Þg • i −∑ P ðn i /n fuel ∑ R Þg • i + RT ln ∏ R ðn i /n fuel Þh i −∑ P ðp i /p° ð Þ ni/n fuel Þ /∏ P ðp i /p° ð Þ ni/n fuelÞ ðn i /n fuel Þh i (15.45) If the reactants or products are unmixed and the pressure of each species (or component) in the reaction is 0.1 MPa, then p i = p° and ∏ P ðp i /p° Þ ni = ∏ R ðp i /p° Þ ni = 1:0 in these three equations. Otherwise, if the reactants are premixed or the product gases are mixed (as they normally are) at a total pressure p m , then the partial pressure of each component gas must be determined. Further, if all the gases present are ideal gases that obey the Gibbs- Dalton ideal gas mixture law, then the partial pressures can be expressed in terms of the mole fractions as p i /p° = ðχ i p m Þ/p°, where x i is the mole fraction of gas i and p°=0.1 MPa. Then, h i ln ∏ðp i /p° Þ ni = ln ∏ðχ i p m /p° Þ ni in Eqs. (15.43), (15.44), and (15.45). In the case of a fuel cell, the output power appears as an electrical current I flowing through a potential (voltage) difference ϕ, and using Ohm’s law we can calculate the actual power output of the cell as _W = ϕI = I 2 R e where ϕ is the cell voltage, I is its current flow, and R e is the external resistance (recall that work output must be positive with our sign convention). Combining this equation with Eq. (15.40) gives the entropy production rate of the fuel cell as ð _S P Þ fuel cell = ∑ P _n i g i −∑ R Also, it can be shown that the electrical current I produced by a fuel cell is given by I = ð_n fuel ÞjF ! _n i g + ϕI /T b ≥ 0 (15.46) where I is in amperes when _n fuel is in kgmole/s. In this equation j is the total valence of the fuel ions in kgmole of electrons per kgmole of fuel, and F is Faraday’s constant, defined as F = ð6:023 × 10 26 electrons/kgmole electronsÞð1:602 × 10 −19 coulombs/electronÞ = 96:487 kilocoulombs/kgmole electrons but since 1 coulomb = 1 joule/volt = 1 J/V, this can be written as F = 96,487 kJ/ðV . kgmole electronsÞ
640 CHAPTER 15: Chemical <strong>Thermodynamics</strong> WHAT IS j ? The letter j represents the number of electrons involved in the cell reaction per kgmole of fuel consumed. For example, for any hydrocarbon fuel, C n H m , j = nð4Þ + mð1Þ = 4n + m kgmole of electrons per kgmole of C n H m . When there is no electron flow in the external circuit, there are no losses within the fuel cell and we can write the maximum (or reversible) power output of a fuel cell as approximately 5 _W max ≈ ϕ o I = ϕ o ð _n fuel Þ jF (15.47) where ϕ o is the open circuit voltage. Then, the maximum reaction efficiency of the fuel cell becomes ðη r Þ max = fuel cell ∑ R ðϕ o jFÞ ðn i /n fuel Þh i −∑ ðn i /n fuel Þh i P EXAMPLE 15.18 Determine the maximum theoretical reaction efficiency, open circuit voltage, and maximum theoretical work output per mole of hydrogen consumed for the hydrogen–oxygen fuel cell operating at 25.0°C and 0.100 MPa, shown in Figure 15.15. R e Electrical load Voltmeter Electrolyte 25.0 ° C H 2 (g) O 2 (g) 25.0 ° C 0.100 MPa 2H + 0.100 MPa Porous anode Porous cathode H 2 O( ) FIGURE 15.15 Example 15.18. The anode reaction is H 2 ðgÞ !2ðH + Þ + 2ðe − Þ: The cathode reaction is 0:5½O 2 ðgÞŠ + 2ðH + Þ + 2ðe − Þ!H 2 OðlÞ: The overall reaction is H 2 ðgÞ + 0:5½O 2 ðgÞŠ ! H 2 OðlÞ: Also, ðp i /p° Þ H2 = ðp i /p° Þ O2 = 1:0: Solution Equation (15.45) can be used to calculate the maximum energy conversion reaction efficiency as ðη r Þ max = g• H2ðÞ g + ð0:5Þðg• O2ðÞ g Þ − g• H2OðÞ l + RT ln 1:0 h H2 ðÞ+ g ð0:5Þ h O2 ðÞ g − hH2OðÞ l where the g • i are determined from Eq. (15.34), and the h i are determined from Eq. (15.14). Since the pressure and temperature given in this problem statement are the standard reference state values, Eqs. (15.14) and (15.34) reduce to h i = h° f i and g • i = g° f : Then, the maximum theoretical reaction efficiency equation becomes i ðη r Þ max = ðg°Þ f H2ðÞ g + ð0:5Þðg°Þ f O2ðÞ g − ðg°Þ f H2OðÞ l + RT ln 1:0 h° f H2ðÞ g + ð0:5Þ h° f O2ðÞ g − h° f H2OðÞ l 5 A small amount of internal irreversibility is generated in producing ϕ o ,soϕ o is slightly less than ϕ rev = ϕ max .
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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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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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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 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 684 and 685: 16.4 The Mach Number 659 Since for
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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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