Modern Engineering Thermodynamics

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Problems 309 Multiplying this equation through by dt and integrating over time from system state 1 to state 2 gives the open system modified entropy balance (MSB) equation as Z 2 1Q 2 + _m ðs in − s out Þdt + 1 S P Þ T 2 = 0 (9.11) b 1 2. For flow in nozzles, diffusers, or throttles, we have the entropy production rate of an incompressible fluid in an adiabatic nozzle, diffuser, or throttle: _S P adiabatic incompressible fluid = _mc ln T out T in > 0 (9.14) and the entropy production rate of an incompressible fluid in a nozzle, diffuser, or throttle with heat transfer _S P incompressible fluid = _mc ln T out T in 3. For flow in heat exchangers, we have the heat exchanger entropy production rate: − _ Q T b > 0 (9.15) _S P = _m H ðs out − s in Þ H + _m C ðs out − s in Þ C (9.24) See Eqs. (9.25) and (9.26) when the hot and cold fluids are known to be incompressible liquids or ideal gases. 4. When two flow streams, 1 and 2, are combined to form a mixed outlet flow stream, 3, the entropy production rate is _S P mixing = _m 3½ys ð 2 − s 1 Þ+ ðs 3 − s 2 ÞŠ> 0 (9.29) See Eq. (9.32) for the entropy production rate in mixing identical incompressible liquids or identical ideal gases. 5. The entropy production rate for shaft work machines is _S P shaft work machine = _m ðh 1 − T b s 1 Þ− ðh 2 − T b s 2 Þ+ V2 1 − V2 2 + gZ ð 1 − Z 2 Þ − T b 2g c g c _ W actual T b (9.36) 6. The entropy production in adiabatically filling a rigid tank with an incompressible liquid is 1ðS P Þ 2 incomp: liquid ðadiabaticÞ = m 2 c ln T 2 = m 2 c ln 1 + ðpv T in Þ in cT in (9.41) 7. The entropy production in adiabatically filling a rigid tank with an ideal gas is 1ðS P Þ 2 ideal qas ðadiabaticÞ = m 2 c p ln T 2 T in − m 2 R ln p 2 p in = m 2 c p ln k (9.42) 8. The entropy production in isothermally filling a rigid tank with an incompressible liquid is 1ðS P Þ 2 incomp: liquid ðisothermalÞ 9. The entropy production in isothermally filling a rigid tank with an ideal gas is 1ðS P Þ 2 ideal gas ðisothermalÞ = m 2 ðpvÞ in /T (9.45) = m 2 c v ðk − 1Þ = m 2 R = p 2 V/T (9.46)
310 CHAPTER 9: Second Law Open System Applications FINAL COMMENTS ON THE SECOND LAW In Chapter’s 7, 8, and 9, we deal with the fundamentals of the second law of thermodynamics for nonequilibrium systems. This law introduces the new thermodynamic property entropy, which is not conserved in any real engineering process. The second law of thermodynamics states that entropy must always be produced in any irreversible process; however, a positive entropy production does not mean that the net system entropy must necessarily increase, because entropy may be transported out of a system faster than it is produced within the system; therefore, the entropy level of the entire system can either increase or decrease in any real process. In Chapter 8 we investigate closed system applications of the second law of thermodynamics for both reversible and irreversible processes. In so doing, we expand the first law examples given in Chapter 5 to include an entropy balance analysis. Since entropy production is a direct consequence of system losses that lead to diminished operating efficiency, many of the examples in this chapter focus on determining the entropy production or its rate to gain further insight into the causes of system inefficiency. This is done by using either the auxiliary entropy production equations (the direct method) or an appropriate entropy balance equation (the indirect method). In this chapter, we use the second law of thermodynamics in the analysis of open systems. We use the entropy balance to determine the entropy production rates for a variety of common engineering devices (nozzles, diffusers, throttles, heat exchangers, etc.). We also look at how different processes that achieve the same end states affect the amount of entropy produced by the system during those processes. This allows us to choose the process or method of changing the state that is the least dissipative and consequently the most efficient. Determining processes that minimize the entropy production produces economic and productivity rewards to the user. Problems (* indicates problems in SI units) 1. An inventor claims to have a steady state, steady flow system with an isentropic flow stream (i.e., s in = s out ) that requires heat addition. Show whether or not this system violates the second law of thermodynamics. 2. The inventor in Example 9.1 now claims to have a system that generates heat by pumping water through a pipe isothermally (i.e., T in = T out ). Show whether or not this system violates the second law of thermodynamics. 3.* Suppose the inventor in Example 9.1 filed a new patent claim that said the heater was 20.0 kW and the heat transfer boundary temperature was 100ºC. What are the water flow rate and entropy production rate under these conditions? 4.* The inventor in Example 9.1 needs to know the heat transfer rate and entropy production rate required to heat 5.00 kg/s from 15ºC to50ºC. You are the engineer, so what are the answers? 5.* The inventor in Example 9.1 now wants to patent a water cooling system that cools 0.500 kg/s of water from 50ºC to 15ºC by removing heat with a heat transfer boundary temperature of 10.0ºC. What is (a) the heat transfer rate and (b) the entropy production rate for this process. 6. An inventor reports that she has a refrigeration compressor that receives saturated Refrigerant-134a vapor at 0.00°F and delivers it at 150. psia and 120.°F. The compression process is adiabatic. Determine whether or not this process violates the second law of thermodynamics. 7.* A 1.00 MW steam power plant operates on the simple reversible thermodynamic cycle shown Figure 9.23. a. What is its thermal efficiency? b. What is the steam mass flow rate in this system? c. What is its thermal efficiency if it is operated on a Carnot cycle? 8.* A steam turbine is limited to a maximum inlet temperature of 800.°C. The exhaust pressure is 0.0100 MPa, and the moisture in the turbine exhaust is not to exceed 9.00%. T(K) FIGURE 9.23 Problem 7. 700 650 600 550 500 1.0 1.1 1.2 1.3 1.4 s (kJ/kg •K) a. What is the maximum allowable turbine inlet pressure if the flow is adiabatic and reversible? b. What is the maximum power output per unit mass flow rate? 9.* A steam turbine receives steam at 1.00 MPa and 700.°C and exhausts at 0.100 MPa. If the turbine can be considered to operate as a steady flow, reversible, adiabatic machine, what is the work done per pound of steam flowing? Neglect any changes in kinetic or potential energy. 10. Saturated mercury vapor enters a steady flow turbine of a highpressure auxiliary power system at 600. psia and emerges as a mixture of liquid and vapor at a pressure of 1.00 psia. What must be the flow rate if the power output is to be 10.0 kW? Assume the turbine is reversible and adiabatic, and neglect any changes in kinetic or potential energy. 11.* In the year 2138, a law requires certain limits on the production of entropy of any marketable piece of technology. This law is similar in nature to the old air pollution laws of the 20th century. It sets an upper limit of 1.00 × 10 –3 kJ/(kg · K · s) on the
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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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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
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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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Page 356 and 357: 10.8 Flow Availability 331 EXAMPLE
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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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