Modern Engineering Thermodynamics

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12.2 Thermodynamic Properties of Gas Mixtures 411 EXAMPLE 12.2 The molar composition of air that is normally used to determine the thermodynamic properties of air at standard temperature and pressure is Component Molar % Nitrogen 78.09 Oxygen 20.95 Argon 0.930 CO 2 and trace gases 0.0300 Total 100.00% Determine (a) the equivalent molecular mass, (b) the gas constant for this mixture, and (c) the composition of air on a mass (or weight) basis. Solution a. Since we are given the molar composition for air, we can find its equivalent molecular weight from Eq. (12.11). Assuming that argon and carbon dioxide are the only minor components present, Table C.13 provides the necessary molecular masses as Then, Eq. (12.11) gives M air = ∑ 4 b. Equation (12.15) gives the gas constant of this mixture as i=1 M nitrogen = 28:02 kg=kgmole M oxygen = 32:00 kg=kgmole M argon = 39:94 kg=kgmole M carbon dioxide = 44:01 kg=kgmole χ i M i = χ N2 M N2 + χ O2 M O2 + χ Ar M Ar + χ CO2 M CO2 = 0:7809ð28:02 kg=kgmoleÞ + 0:2095ð32:00 kg=kgmoleÞ + 0:00930ð39:94 kg=kgmoleÞ + 0:000300ð44:10 kg=kgmoleÞ = 28:97 kg=kgmole R air = R = 8:3143 kJ=ðkgmole .KÞ = 0:287 kJ M air 28:97 kg=kgmole kg .K which agrees with the values given in Table C.13b in Thermodynamic Tables to accompany Modern Engineering Thermodynamics. c. Equation (12.13) can be used to determine the corresponding mass or weight fraction composition as w N2 = χ N2 M N2 M air w O2 = χ O2 M O2 M air = 0:7809 = 0:2095 28:02 kg=kgmole 28:97 kg=kgmole 32:00 kg=kgmole 28:97 kg=kgmole = 0:7553 = 75:53% by mass = 0:2314 = 23:14% by mass M w Ar = χ Ar 39:94 kg=kgmole Ar = 0:00930 = 0:0128 = 1:28% by mass M air 28:97 kg=kgmole M CO2 44:01 kg=kgmole w CO2 = χ CO2 = 0:000300 = 0:00046 = 0:0456% by mass M air 28:97 kg=kgmole Note the difference between the mass and mole fraction composition values. Exercises 1. Research has suddenly discovered that the composition given in Example 12.1 was wrong. It should have been 30.0% propane and 70.0% air on a mass basis. Determine the proper molar basis composition for this new mixture. Answer: χ propane = 0.220 and χ air = 0.780. (Continued )
412 CHAPTER 12: Mixtures of Gases and Vapors EXAMPLE 12.2 (Continued ) 2. Oops, Research discovered still another error; it turns out that the composition given in Example 12.1 was correct except that it is 50.0% propane and 50.0% air on a molar basis. Now , Research wants you to determine the corresponding mass based composition. Answer: w propane = 0.603 and w air = 0.397. 3. A more detailed composition for air than that given in Example 12.2 is Component Molar % (Answer: Mass %) Nitrogen (N 2 ) 78.084 75.519 Oxygen (O 2 ) 20.948 23.143 Argon (Ar) 0.934 1.288 Carbon dioxide (CO 2 ) 0.0314 0.0477 Neon (Ne) 0.00182 0.00127 Helium (He) 0.000520 0.0000720 Methane (CH 4 ) 0.000200 0.000110 Krypton (Kr) 0.000110 0.000320 Hydrogen (H 2 ) 0.0000500 0.00000350 Dinitrogen monoxide (N 2 O) 0.0000500 0.0000620 Xenon (Xe) 0.00000800 0.0000360 Total = 100.000% 100.000% Determine the equivalent molecular mass and the corresponding composition on a mass (or weight) basis. Answer: M m = 28.97 kg/kgmole = 28.97 lbm/lbmole, and see the table. 12.3 MIXTURES OF IDEAL GASES A mixture of ideal gases behaves as a unique ideal gas with an equivalent molecular mass M m and gas constant R m given by Eqs. (12.11) or (12.12) and (12.15). Ideal gas mixtures obey all of the ideal gas equations of state: p m V m = m m R m T m u m2 − u m1 = Z Tm2 T m1 c vm dT m and h m2 − h m1 = Z Tm2 T m1 c pm dT m s m2 − s m1 = = Z Tm2 T m1 Z Tm2 T m1 ðc vm /T m Þ dT m + R m lnðv m2 /v m1 Þ c pm /T m dTm − R m lnðp m2 /p m1 Þ where p m and T m are the mixture pressure and temperature, respectively. If the mixture can be considered to have constant specific heats, then these equations reduce to u m2 − u m1 = c vm ðT m2 − T m1 Þ h m2 − h m1 = c pm ðT m2 − T m1 Þ s m2 − s m1 = c vm lnðT m2 /T m1 = c pm lnðT m2 /T m1 i=1 Þ+ R m lnðv m2 /v m1 Þ Þ− R m lnðp m2 /p m1 Þ From p m V m = m m R m T m and Eqs. (12.3), (12.12), and (12.15), we find that, for a mixture of ideal gases, V m = m mR m T m = m R T m m p m M m p m = m m R ∑ N ! w i T m = RT N m M i p m p ∑ m i m M i i=1
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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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Page 392 and 393: 11.4 Maxwell Equations 367 11.4 MAX
Page 394 and 395: 11.4 Maxwell Equations 369 then,
Page 396 and 397: 11.5 The Clapeyron Equation 371 and
Page 398 and 399: 11.6 Determining u, h, and s from p
Page 404 and 405: 11.7 Constructing Tables and Charts
Page 406 and 407: 11.8 Thermodynamic Charts 381 so th
Page 408 and 409: 11.9 Gas Tables 383 where p r is th
Page 410 and 411: 11.10 Compressibility Factor and Ge
Page 422 and 423: 11.11 Is Steam Ever an Ideal Gas? 3
Page 424 and 425: Summary 399 equation, and a series
Page 426 and 427: Problems 401 20.* Estimate h fg for
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
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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.
Page 446 and 447: 12.6 The Sling Psychrometer 421 The
Page 448 and 449: 12.6 The Sling Psychrometer 423 p w
Page 450 and 451: 12.7 Air Conditioning 425 WHAT ENVI
Page 452 and 453: 12.8 Psychrometric Enthalpies 427 E
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Page 456 and 457: 12.9 Mixtures of Real Gases 431 Whe
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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
Page 470 and 471: Problems 445 57.* Cooling towers ar
Page 472 and 473: CHAPTER 13 Vapor and Gas Power Cycl
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Page 484 and 485: 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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