Modern Engineering Thermodynamics

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15.8 Adiabatic Flame Temperature 617 For example, the reaction for the combustion of liquid octane with Y % theoretical air is C 8 H 18 + ðY/100Þ12:5 O 2 + 3:76ðN 2 Þ ! 8CO ð 2 Þ+ 9H ð 2 OÞ+ ðY/100 − 1ÞO 2 + 47ðY/100ÞðN 2 Þ To simplify matters, assume that, before the combustion, the reactants are at the SRS. Then, hðT R Þ = hðT°Þ and hðT R Þ − hðT°Þ = 0 for all the reactants. The heat produced by this reaction when the combustion products are at temperature T P is q r = ∑ R ðn i /n fuel Þðh f °Þ i −∑ P ðn i /n fuel Þ½h° f + hðT P Þ − hðT°ÞŠ i = ðh f °Þ C8H 18 − 8½h f ° + hðT P Þ − hðT°ÞŠ CO2 − 9½h f ° + hðT P Þ − hðT°ÞŠ H2O − ðY/100 − 1Þ½h f ° + hðT P Þ − hðT°ÞŠ O2 − 47ðY/100 − 1Þ½h f ° + hðT P Þ − hðT°ÞŠ N2 The molar specific heat equations in kJ/(kgmole·K), accurate to at least 0.43% over the range of 300 to 3500 K, can be found in Table C.14b in Thermodynamic Tables to accompany Modern Engineering Thermodynamics as Carbon dioxide: ðc p Þ CO2 = −3:7357 + 30:529θ 0:5 − 4:1034θ + 0:024198θ 2 Water: ðc p Þ H2 O = 143:05 − 183:54θ0:25 + 82:751θ 0:5 − 3:6989θ Oxygen: ðc p Þ O2 = 37:432 + 0:020102θ 1:5 − 178:57θ −1:5 + 236:88θ −2 Nitrogen: ðc p Þ N2 = 39:060 − 512:79θ −1:5 + 1072:7θ −2 − 820:40θ −3 where θ° =T°/100 = 298/100 = 2:98, and θ P = T p /100. Integrating these equations from the SRS (θ°) tothe temperature of the combustion products (θ P ) gives ½hðT P Þ − hðT°ÞŠ CO2 = 100 × Z θP θ° ðc p Þ CO2 dθ = −373:57ðθ P − θ° Þ+ 2035:3 ðθ P Þ 1:5 − ðθ° Þ 1:5 − 205:17 ðθ P Þ 2 − ðθ°Þ 2 + 0:8066 ðθ P Þ 3 − ðθ°Þ 3 ½hðT P Þ − hðT°ÞŠ H2 O Z θP = 100 × ðc p Þ H2 O dθ θ° = 14,305: ðθ P − θ° Þ− 14,683:2 ðθ P Þ 1:25 − ðθ° Þ 1:25 + 5516:7 ðθ P Þ 1:5 − ðθ°Þ 1:5 − 184:95 ðθ P Þ 2 − ðθ°Þ 2 ½hðT P Þ − hðT°ÞŠ O2 = 100 × Z θP θ° ðc p Þ O2 dθ = 3743:2ðθ P − θ° Þ+ 0:80408 ðθ P Þ 2:5 − ðθ° Þ 2:5 + 35:714: ðθ P Þ −0:5 − ðθ°Þ −0:5 − 23,688 ðθ P Þ −1 − ðθ°Þ −1 ½hðT P Þ − hðT°ÞŠ N2 = 100 × Z θP θ° ðc p Þ N2 dθ To simplify the algebra, we define the following terms: = 3906:0ðθ P − θ° Þ+ 102,558 ðθ P Þ −1/2 − ðθ° − 107,270: ðθ P Þ −1 − ðθ°Þ −1 + 41,020 ðθ P Þ −2 − ðθ°Þ −2 Þ −1/2 A = θ P − θ° B = ðθ P Þ 1:25 − ðθ°Þ 1:25 C = ðθ P Þ 1:5 − ðθ°Þ 1:5 D = ðθ P Þ 2 − ðθ°Þ 2 E = ðθ P Þ 2:5 − ðθ°Þ 2:5 F = ðθ P Þ 3 − ðθ°Þ 3 G = ðθ P Þ −1/2 − ðθ°Þ −1/2 H = ðθ P Þ −1 − ðθ°Þ −1 I = ðθ P Þ −2 − ðθ°Þ −2
618 CHAPTER 15: Chemical Thermodynamics Then, the heat of the combustion reaction becomes q r = ∑ R ðn i /n fuel Þðh°Þ f i −∑ ðn i /n fuel Þ½h°+hðT f P Þ − hðT°ÞŠ i P = ðh f °Þ C8H 18 − 8½h f ° − 373:57A + 2035:3C − 205:17D + 0:8066FŠ CO2 − 9½h f °+14,305:A − 14,683:2B + 5516:7C − 184:95DŠ H2O − ðY/100 − 1Þ½3743:2A + 0:80408E + 35,714:G − 23,688HŠ O2 − 47ðY/100 − 1Þ½3906:0A + 102,558G − 107270:H + 41,020IŠ N2 From Table 15.1, we find h° f C = −249:952 MJ/kgmole, h° 8H 18ðlÞ f CO 2 = −393:522 MJ/kgmole, h f ° H 2 OðgÞ = −241:827 MJ/kgmole, and h f ° N 2 = h f ° O 2 = 0 because they are elements: While these equations are difficult to handle using a hand calculator, they are easily solved using an equation solver or a spreadsheet. The spreadsheet in Figure 15.7 illustrates the process for the combustion of liquid octane with 200% theoretical air. Typing control + tilde (Ctrl and Shift + ~) reveals the details, shown in Figure 15.8. FIGURE 15.7 Solving the equations with a spreadsheet.
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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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14.11 Commercial and Household Refr
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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 630 and 631: 15.6 Heat of Formation 605 and H 2
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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 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 668 and 669: ðn i /n fuel Þðc pi Þ E system
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Page 684 and 685: 16.4 The Mach Number 659 Since for
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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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