Modern Engineering Thermodynamics

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12.9 Mixtures of Real Gases 431 When p, v, T, andc v data on the gas mixture of interest are not available, engineering approximations can be obtained by combining either Dalton’s orAmagat’s law with the simplified compressibility factor equation of state pV = ZmRT. For example, using Dalton’s law, p m = ∑ N where p Di is the Dalton compressibility factor partial pressure, defined by i=1 p Di = Z Dm m m R m T m /Vm (12.35) p Di = Z Di m i R i T m /V m and Z Di and Z Dm are the Dalton species i and mixture compressibility factors, respectively. Substituting the latter equation into the former and solving for Z Dm gives Dalton compressibility factor Z Dm = ∑ N i=1 w i M m Z di = ∑ N M i i=1 χ i Z Di (12.36) For each gas i, the Dalton Z Di compressibility factor is determined from the compressibility charts (Figures 7.5, 7.6, and 7.9 in Chapter 7) by using the reduced temperature T Ri and reduced pseudospecific volume v′ Ri for gas i at the temperature and volume of the mixture, or T Ri = T m /T ci v′ Ri = v Di p ci /ðR i T ci Þ = ðV m /m i Þðm m /m m Þðp ci Þ/ðR i T ci Þ = ðv m /w i Þ½p ci /ðR i T ci ÞŠ = ðV m /n i Þðn m /n m Þðp ci Þ/ðRT ci Þ = ðv m /x i Þ½p ci /ðRT ci ÞŠ where v Di = V m /m i = v m /w i is the Dalton specific volume of gas i, and v m = V m /m m and v m = V m /n m are the mixture mass and molar specific volumes, respectively. Notethatwecannotusethereducedpressurep Ri = p Di /p ci in this case because p Di = Z Di m i R i T m /V m , and Z Di is not usually known in advance. EXAMPLE 12.14 A new type of fuel for the camping stove shown in Figure 12.12 is made by mixing 3.00 lbm of methane (CH 4 ) with 4.00 lbm of propane (C 3 H 8 ) and compressing the mixture into a 1.00 ft 3 portable storage tank. Use the Dalton compressibility factor to determine the total pressure in the tank when it is exposed to the hot summer sun and its internal temperature reaches 240.°F. Solution The unknown is the total pressure in the tank. Here, we use Eq. (12.35) to determine the mixture pressure as p m = Z Dmm m R m T m V m where Z Dm is the Dalton compressibility factor, determined from Eq. (12.36) as Z Dm = ∑ N i=1 w i M m M i First, we find the mixture composition and molecular mass. The mass of the entire mixture is m m = m methane + m propane = 3.00 + 4.00 = 7.00 lbm. The mass fractions are Z Di w methane = 3:00=7:00 = 0:429 w propane = 4:00=7:00 = 0:571 FIGURE 12.12 Example 12.14. (Continued )
432 CHAPTER 12: Mixtures of Gases and Vapors EXAMPLE 12.14 (Continued ) The molecular masses of the components are found in Table C.12a in Thermodynamic Tables to accompany Modern Engineering Thermodynamics as then, Eq (12.12) gives the molecular mass of the mixture as M m = 1 ∑ 2 w i i=1 M i = M methane = 16:043 lbm=lbmole M propane = 44:097 lbm=lbmole 1 w methane + w = propane M methane M propane 1 0:429 16:043 + 0:571 44:097 = 25:2 lbm lbmole The Dalton compressibility factors for the components, Z Di ,arefoundfromthereducedtemperatureT Ri and the reduced pseudospecific volume v′ Ri for each component. From Tables C.12a and C.13a, we find that The specific volume of the mixture is ðp c Þ methane = 673 psia, (T c Þ methane = 343:9 R, and R methane = 96:3ft.lbf=ðlbm.RÞ ðp c Þ propane = 617 psia, (T c Þ propane = 665:9 R, and R propane = 35:0ft.lbf=ðlbm.RÞ v m = V m 1:00 ft3 = m m 7:00 lbm = 0:143 ft3 /lbm then, the reduced temperature and reduced pseudospecific volume for methane are ðT R Þ methane = T m 240: + 459:67 R = = 2:03 ðT c Þ methane 343:9R and For propane, they are ðv′ R Þmethane = = v m w methane ðp c R methane T c Þ methane ð Þ methane 0:143 ft 3 =lbm mixture 0:429 lbm methane=lbm mixture = 0:975 × ð673 lbf=in 2 Þð144 in 2 =ft 2 Þ ð96:3ft.lbf=lbm.RÞð343:9RÞ and v ðv′ R Þpropane = m w propane = ðT R Þ propane = T m 240: + 459:67 R = = 1:05 ðT c Þ propane 665:9R ! ðp c Þ propane ð Þ propane R propane T c 0:143 ft 3 =lbm mixture 0:571 lbm methane=lbm mixture = 0:955 × ð617 lbf=in 2 Þð144 in 2 =ft 2 Þ ð35:0ft.lbf=lbm.RÞð665:9RÞ Using Figure 7.6 with T R = 2.03 and v′ R = 0:975, we find that the Dalton compressibility factor for methane is (Z D ) methane = 0.975; and using T R = 1.05 and v′ R = 0:95, we find that the Dalton compressibility factor for propane is (Z D ) propane = 0.720. Then, Eq. (12.36) gives the mixture Dalton compressibility factor as Z Dm = ∑ 2 w i M m Z Di = i=1 M i = ð0:429Þð25:2Þ 16:043 w methaneM m M methane ð0:975Þ + The mixture gas constant can be easily calculated from ðZ D Þ methane + ð0:571Þð25:2Þ 44:097 w propaneM m M propane ð0:720Þ = 0:892 ðZ D Þ propane R m = R M m = 1545:35 ft .lbf/ðlbmole.RÞ 25:2 lbm/lbmole = 61:3 ft .lbf lbm.R
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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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Page 424 and 425: Summary 399 equation, and a series
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Page 428 and 429: Problems 403 Design Problems The fo
Page 430 and 431: CHAPTER 12 Mixtures of Gases and Va
Page 432 and 433: 12.2 Thermodynamic Properties of Ga
Page 438 and 439: 12.3 Mixtures of Ideal Gases 413 Th
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Page 442 and 443: 12.4 Psychrometrics 417 Finally, th
Page 444 and 445: 12.4 Psychrometrics 419 EXAMPLE 12.
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Page 448 and 449: 12.6 The Sling Psychrometer 423 p w
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Page 452 and 453: 12.8 Psychrometric Enthalpies 427 E
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Page 458 and 459: 12.9 Mixtures of Real Gases 433 and
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Page 464 and 465: Summary 439 Last, we combine Dalton
Page 466 and 467: Problems 441 Problems (* indicates
Page 468 and 469: Problems 443 exhaust gas is an idea
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Page 472 and 473: CHAPTER 13 Vapor and Gas Power Cycl
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Page 488 and 489: 13.5 Operating Efficiencies 463 b.
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Page 502 and 503: 13.9 Rankine Cycle with Reheat 477
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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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