Modern Engineering Thermodynamics

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18.6 Equipartition of Energy 739 We can therefore conclude that the total energy of a system of N molecules with F degrees of freedom per molecule is given by U = F 2 NkT = F 2 m TRT and that its specific internal energy is u = U/m T = FRT/2: From the definition of constant volume specific heat introduced in Chapter 3, we have c v = ∂u = ∂ F ∂T v ∂T 2 RT = FR (18.27) v 2 and, since c p − c v = R for an ideal gas, c p = R + c v = 1 + F R (18.28) 2 finally the specific heat ratio k becomes k = c p c v = F + 2 F (18.29) For a molecule containing b atoms, there are F = 3b degrees of freedom. If b = 1, then F = 3andthethree degrees of freedom are all translational. If b = 2, then F = 6 and there are three degrees of freedom in translation, two in rotation and one in vibration. If b > 2, then F = 3b and there are three degrees of freedom in translation, three in rotation and 3b − 6 in vibration. In the case of monatomic (single-atom) molecules like He, Ne, Ar,Kr,orXe,thereareonlythreedegreesoffreedom(alltranslational).ThenEqs.(18.27),(18.28),and (18.29) give 9 c v = 1:5R >= c p = 2:5R Monatomic gases >; k = 1:67 For diatomic (two-atom) molecules, such as H 2 ,O 2 , CO, or NO, we have b = 2 and consequently F = 3(2) = 6. Then, we have 9 c v = 3R >= c p = 4R Diatomic gases >; k = 1:33 Similarly for triatomic gases, such as CO 2 ,H 2 O, NO 2 ,orSO 2 , we have b = 3 and F = 9. Then, 9 c v = 4:5R >= c p = 5:5R Triatomic gases >; k = 1:22 A comparison of these values with the measured specific heats of some real gases, given in Table 18.3, reveals that, for simple molecules (e.g., monatomic gases), the kinetic theory works quite well. For complex molecules, however, kinetic theory predictions are much less accurate. In summary, the thermodynamic properties of an ideal gas as predicted by Maxwell’s kinetic theory are where pV = mRT u 2 − u 1 = c v ðT 2 − T 1 Þ h 2 − h 1 = c p ðT 2 − T 1 Þ s 2 − s 1 = c p ln ðT 2 /T 1 Þ− R ln ðp 2 /p 1 Þ = c v ln ðT 2 /T 1 Þ+ R ln ðv 2 /v 1 Þ c p − c v = R c v = FR/2 c p = ð1 + F/2ÞR F = 3b b = number of atoms in the molecule
740 CHAPTER 18: Introduction to Statistical <strong>Thermodynamics</strong> Table 18.3 Measured Values of the Specific Heats of Various Gases at 20.0ºC Gas c v /R c p /R k = c p /c v Monatomic He 1.50 2.50 1.67 Ne 1.50 2.50 1.67 Ar 1.51 2.52 1.67 Kr 1.00 1.68 1.68 Xe 1.52 2.51 1.65 Diatomic CO 2.51 3.51 1.40 NO 2.51 3.51 1.40 H 2 2.44 3.42 1.40 O 2 2.53 3.53 1.40 N 2 2.50 3.50 1.40 Triatomic CO 2 3.48 4.48 1.29 SO 2 3.97 4.97 1.25 H 2 O 3.05 4.05 1.33 EXAMPLE 18.4 Estimate the heat transfer rate required to heat low-pressure gaseous carbon tetrachloride (CCl 4 ) from 500. to 1200. K in a steady state, steady flow, single-inlet, single-outlet, aergonic (i.e., zero work) process at a flow rate of 1.00 kg/min. Solution The system here is just the gas in the heating zone. Neglecting the flow stream kinetic and potential energies, the energy rate balance for this system reduces to so that Q : + m : ðh in − h out Þ = 0 Q : = m : ðh out − h in Þ = m : c p ðT out − T in Þ For CC1 4 , b = 5; consequently, F = 3b = 15. Then, Eq. (18.28) gives Now, the molecular mass of carbon tetrachloride is and its gas constant is so Therefore, R = R M c p = ð1 + 15=2ÞR = 8:5 × R M = 12:0 + 4ð35:5Þ = 154 kg=kgmole = 8:3143 kJ/ðkgmole ⋅ KÞ 154 kg/kgmole = 0:0540 kJ/ðkg ⋅ KÞ c p = 8:5½0:0540 kJ/ðkg⋅KÞŠ = 0:459 kJ/ðkg.KÞ _Q = ð1:00 kg/minÞ½0:459 kJ/ðkg⋅KÞŠð1200: − 500:KÞ = 321 kJ/min Exercises 10. If the mass flow rate of gaseous carbon tetrachloride in Example 18.4 is suddenly increased from 1.00 to 3.50 kg/min, determine the new heat transfer rate, assuming all the other variables remain unchanged. Answer: _Q = 1120 kJ/min: 11. The exit temperature of the gaseous carbon tetrachloride in Example 18.4 is increased from 1200. K to 2000. K. Determine the heat transfer rate, assuming all the other variables remain unchanged. Answer: _Q = 688 kJ/min: 12. The gas in Example 18.4 is changed from carbon tetrachloride to gaseous dichlorodifluoromethane (CCl 2 F 2 ). Estimate the heat transfer rate for this gas, assuming all the other variables in Example 18.4 remain unchanged. Answer: _Q = 409 kJ/min:
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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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Problems 589 under these conditions
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CHAPTER 15 Chemical Thermodynamics
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15.2 Stoichiometric Equations 593 1
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15.2 Stoichiometric Equations 595 C
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15.3 Organic Fuels 597 ANSWERS SOME
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15.4 Fuel Modeling 599 Hydrocarbon
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15.4 Fuel Modeling 601 equation, si
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15.5 Standard Reference State 603 I
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15.6 Heat of Formation 605 and H 2
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15.7 Heat of Reaction 607 EXAMPLE 1
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15.7 Heat of Reaction 609 CRITICAL
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15.7 Heat of Reaction 611 Then, h P
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15.8 Adiabatic Flame Temperature 61
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15.9 Maximum Explosion Pressure 619
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15.10 Entropy Production in Chemica
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15.10 Entropy Production in Chemica
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15.11 Entropy of Formation and Gibb
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15.12 Chemical Equilibrium and Diss
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H 2 O !ð1 − yÞH 2 O + yðv H2
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15.14 The van’t Hoff Equation 635
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15.15 Fuel Cells 637 Anode Electrol
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15.15 Fuel Cells 639 The maximum po
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15.16 Chemical Availability 641 and
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ðn i /n fuel Þðc pi Þ E system
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Problems 645 where j = 4n + m kgmol
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Problems 647 c. The percent excess
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Problems 649 77. Determine the mola
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CHAPTER 16 Compressible Fluid Flow
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16.3 Isentropic Stagnation Properti
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16.4 The Mach Number 655 Note that
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16.4 The Mach Number 657 Table 16.1
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16.4 The Mach Number 659 Since for
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16.5 Converging-Diverging Flows 661
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16.5 Converging-Diverging Flows 663
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16.6 Choked Flow 665 T a a p a = co
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16.6 Choked Flow 667 Exercises 16.
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16.7 Reynolds Transport Theorem 669
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16.7 Reynolds Transport Theorem 671
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16.8 Linear Momentum Rate Balance 6
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16.9 Shock Waves 675 16.9 SHOCK WAV
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16.9 Shock Waves 677 and, for an id
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16.9 Shock Waves 679 6 5 4 S P /(m
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16.10 Nozzle and Diffuser Efficienc
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16.10 Nozzle and Diffuser Efficienc
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Summary 685 Since for a diffuser, M
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Page 782 and 783: 18.13 Polyatomic Maxwell-Boltzmann
Page 784 and 785: Summary 759 In this chapter, we sum
Page 786 and 787: Problems 761 4. Find the temperatur
Page 788 and 789: CHAPTER 19 Introduction to Coupled
Page 790 and 791: 19.3 Linear Phenomenological Equati
Page 792 and 793: 19.4 Thermoelectric Coupling 767 Eq
Page 794 and 795: 19.4 Thermoelectric Coupling 769 Th
Page 796 and 797: 19.4 Thermoelectric Coupling 771 wh
Page 798 and 799: 19.4 Thermoelectric Coupling 773 Th
Page 800 and 801: 19.4 Thermoelectric Coupling 775 b.
Page 802 and 803: 19.5 Thermomechanical Coupling 777
Page 808 and 809: water), it seems reasonable that li
Page 810 and 811: Problems 785 b. For a Knudson gas,
Page 812 and 813: Appendix A: Physical Constants and
Page 814 and 815:
Appendix B: Greek and Latin Origins
Page 816 and 817:
Appendix B 791 Table B.4 Plural End
Page 818 and 819:
Index Page numbers followed by f in
Page 820 and 821:
Index 795 E e (specific energy), 10
Page 822 and 823:
Index 797 Isobaric coefficient of v
Page 824 and 825:
Index 799 Ranque, Georges Joseph, 3
Page 826 and 827:
Index 801 William III, King of Engl
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Modern Engineering Thermodynamics

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