Modern Engineering Thermodynamics

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9.9 Unsteady State Processes in Open Systems 301 a. From Eq. (9.42) for adiabatic filling, we have ½ 1 ðS P Þ 2 Š adiabatic filling b. From Eq. (9.46) for isothermal filling, we have ½ 1 ðS P Þ 2 Š isothermal filling = ðm 2 Þ adiabatic c p lnðkÞ = ð24:3 lbmÞ½0:219 Btu/ðlbm.RÞŠ ln ð1:39Þ = 1:75 Btu/R filling which is about 20% greater than the entropy produced in part a. = ðm 2 Þ isothermal R = ð33:8 lbmÞ 48:29 ft .lbf/ðlbm.RÞ = 2:10 Btu/R filling 778:16 ft.lbf/Btu Exercises 22. If the volume of the rigid container in Example 9.8 is reduced from 3.00 ft 3 to 2.00 ft 3 , what is the new entropy production for the filling processes described in parts a and b? Keep the values of all the other variables the same as they are in Example 9.8. Answer: (a) [ 1 (S P ) 2 ] adiabatic = 1.17 Btu/R, (b) [ 1 (S P ) 2 ] isothermal = 1.40 Btu/R. 23. The filling pressure in Example 9.8 is to be reduced from 2000. psia to 1500. psia. Determine the new entropy production for the filling processes described in parts a and b. Keep the values of all the other variables the same as they are in Example 9.8. Answer: (a) [ 1 (S P ) 2 ] adiabatic = 1.31 Btu/R, (b) [ 1 (S P ) 2 ] isothermal = 1.57 Btu/R. 24. If the rigid container discussed in Example 9.8 is filled with air instead of oxygen, determine the new entropy production for the filling described in parts a and b. Keep the values of all the other variables the same as they are in Example 9.8. Answer: (a) [ 1 (S P ) 2 ] adiabatic = 1.76 Btu/R, (b) [ 1 (S P ) 2 ] isothermal = 2.10 Btu/R. 25. Determine the amount of entropy produced as 15.7 kg of argon gas is isothermally compressed into a 1.75 m 3 rigid container at 25.0°C. Answer: [ 1 (S P ) 2 ] isothermal = 3.27 kJ/K. Equations (9.42), (9.46), and (9.48) can be combined to give ½ 1 ðS P Þ 2 Š isothermal ½ 1 ðS P Þ 2 Š adiabatic ideal gas = k − 1 ln k which is greater than 1.0 for k > 1.0. This result is shown in Figure 9.17. However, the specific entropy production ratio on a per unit mass of charge basis, that is, as 1 (S P ) 2 /m 2 = 1 (s P ) 2 ,is ½ 1 ðs P Þ 2 Š isothermal ½ 1 ðs P Þ 2 Š adiabatic ideal gas = k − 1 k ln k whichislessthan1.0fork > 1.0, because the two processes do not take on the same total charge of gas (see Eq. (9.48)). 1.5 ( 1 (S P ) 2 ) iso ( 1 (S P ) 2 ) adiab ideal gas 1.4 1.3 1.2 1.1 FIGURE 9.17 Entropy production ratio for an ideal gas. 1.0 1.0 1.2 1.3 1.4 1.5 1.6 1.7 1.8 1.9 2.0 Specific heat ratio, k = c p /c v
302 CHAPTER 9: Second Law Open System Applications CASE STUDIES OF ENTROPY PRODUCTION IN OPEN SYSTEMS The following examples are typical case studies in open system applied engineering thermodynamics. They are included here to provide the student with an exposure to a second law analysis of complex systems typical of 21st century engineering technology. Energy and entropy rate balance equations are used as tools to understand these technologies. Case study 9.1. Temperature magic A vortex tube is a seemingly magical device that separates the temperature of its inlet flow stream into hot and cold outlet flow streams. Remarkably, it contains no moving parts other than the flowing gas itself. The inlet flow enters the vortex tube chamber tangentially, and the resulting swirling motion causes the gaseous core along the chamber centerline to become extremely cold while the gas near the chamber wall becomes very hot. Internal baffles allow the core gas to exit through one tube (cold outlet) while the wall gas exits through the other (hot outlet), thus producing flow stream temperature separation. The illustration in Figure 9.18 shows the operation of this simple device. 3 Hot outlet Cold side outlet 1 Inlet (a) Cold outlet Compressed air inlet Flow control valve (b) FIGURE 9.18 (a) A typical vortex tube. (b) A schematic showing how the off-center inlet causes the flow to form a swirl (vortex) inside the tube. The center of the vortex becomes cold and exits one end of the tube, and the outer part of the vortex becomes hot and exits the other end on the tube. 2 Hot side outlet This remarkable device was discovered by Georges Joseph Ranque and was first described in a French patent in 1931. 6 In 1933, Ranque presented a paper to the Societe FrancaisedePhysiqueonthisdevice, and nothing more was heard about it until 1945, when a vortex tube was found by an American and British investigation team at the end of World War II in the laboratory of Rudolph Hilsch at the University of Erlangen, Germany. Hilsch had begun research on the vortex tube in 1944, after reading Ranque’s paper, and he published his results in Germany in 1946 and in the United States in 1947. Since then, interest in the vortex tube has remained high, and it is now frequently used in industry for inexpensive localized cooling applications. Applying the energy rate balance to the adiabatic and aergonic vortex tube shown in Figure 9.18 and assuming ideal gas behavior with constant specific heats yields yT ð 1 − T 2 Þ+ T 2 − T 3 = 0 where y = _m 3 / _m 1 = _m hot / _m cold is the hot-side mass fraction defined by Eq. (9.27). Note that this result is exactly the same as Eq. (9.30), which was developed for the mixing operation. Thus, the first law of thermodynamics is insensitive to whether the fluids are being mixed or separated. It yields the same result in either case. However, application of the entropy rate balance to the same system produces _S P vortex tube = _m 3½ys ð 1 − s 2 Þ+ s 2 − s 3 Š> 0 (9.49) and comparing this with Eq. (9.29) yields the remarkable result that _S P vortex tube = − _S P mixing (9.50) yet both entropy production rates must be positive. This means that these two processes cannot simply be the reverse of each other. They cannot both follow the same thermodynamic path. The vortex tube separation phenomena must occur by a process that is unavailable to the simple mixing process and vice versa; otherwise, one of these devices violates the second law of thermodynamics. To produce temperature separation, the vortex tube must have a significant pressure drop between the inlet and the outlet flow streams. It does not work isobarically. This pressure drop is not necessary in the mixing operation. Mixing is usually nearly isobaric, and emulation of the vortex tube separation operation requires a higher mixer outlet pressure than inlet pressure. This cannot be done without introducing heat or work energy transport into the system, which would alter the basic nature of the simple mixing device. Therefore, it is clear that the vortex tube inlet pressure is the source of the energy needed to produce the observed temperature separation. It is also the source of the entropy generation needed to allow Eq. (9.50) to be valid, as shown in Example 9.9, which follows. Though the vortex tube is not an isobaric device, its two exit pressures are essentially equal (i.e., p 1 ≈ p 2 ). Combining this condition with Eq. (7.37) for ideal gases and substituting the result into Eq. (9.49) gives _S P vortex tube = _m ðT 1 /T 2 Þ y 3 c p ln 1 + yT ð 1 /T 2 − 1Þ + R ln p 3 6 In 1932, he applied for a U.S. patent, which was awarded March 27, 1934 (U.S. patent number 1,952,281). p 2 (9.51)
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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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Page 314 and 315: 9.6 Heat Exchangers 289 Exercises 1
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Page 322 and 323: 9.9 Unsteady State Processes in Ope
Page 334 and 335: Problems 309 Multiplying this equat
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Page 342 and 343: Problems 317 The cavitation process
Page 344 and 345: CHAPTER 10 Availability Analysis CO
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Page 348 and 349: 10.6 Availability 323 WHAT IS A SYS
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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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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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