Modern Engineering Thermodynamics

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15.4 Fuel Modeling 599 Hydrocarbon fuels refined from petroleum normally contain a mixture of many organic components. Gasoline, for example, is a mixture of over 30 compounds. It is, however, convenient to model these fuels as a single average hydrocarbon compound of the form C n H m , as discussed in the following section. 15.4 FUEL MODELING It is fairly easy to obtain accurate composition analysis of combustion products with modern gas chromatography or mass spectroscopy techniques. With an accurate combustion analysis of a fuel that is in reality a complex mixture of hydrocarbons, an equivalent or average hydrocarbon model of the form C n H m can be determined from a chemical element balance. For example, if the combustion products contain only CO 2 ,CO,O 2 ,H 2 O, and N 2 , then Eqs. (15.3a–c) could be used to determine the composition parameters n and m when the stoichiometric coefficients of the products are measured. Since the fuel model formula C n H m represents an average of all the different hydrocarbon compounds present in the fuel mixture, n and m usually do not turn out to be integers and the resulting model does not represent any real hydrocarbon (except possibly when n and m are rounded to integers). EXAMPLE 15.2 A new hydrocarbon fuel is being developed that consists of 1.00 kgmole of methane (CH 4 )mixedwith3.00kgmolesof propane (C 3 H 8 ). Determine the hydrocarbon fuel model for this mixture. Solution This mixture is assumed to produce 1.00 kgmole of the fuel model C n H m ,so An element balance for this equation gives 1CH 4 + 1C 3 H 8 = 1C n H m Carbon balance: 1 + 3ð3Þ = 10 = n Consequently, the hydrocarbon fuel model is C 10 H 28 . Hydrogen balance: 4 + 3ð8Þ = 28 = m Exercises 4. Determine the hydrocarbon fuel model in Example 15.2 if only 2.00 kgmoles of propane are used in the mixture. Answer: Hydrocarbon fuel model = C 7 H 20 . 5. Determine the hydrocarbon fuel model in Example 15.2 if ethane (C 2 H 6 ) is used in place of the methane. Answer: Hydrocarbon fuel model = C 11 H 30 . 6. 1.00 lbmole each of methane (CH 4 ), propane (C 3 H 8 ), and butane (C 4 H 10 ) are mixed to form 1.00 lbmole of a new super fuel. Determine the hydrocarbon fuel model for this mixture. Answer: Hydrocarbon fuel model = C 8 H 22 . Often, you do not know the exact hydrocarbon composition of a fuel. However, you can analyze the products of the fuel’s combustion and deduce the fuel model. Several modern instruments produce an accurate exhaust gas analysis. For example, gas chromatography and mass spectrometry are commonly used in exhaust gas analysis today. But perhaps the quickest, simplest, and most inexpensive method of obtaining an approximate combustion analysis is with an Orsat analyzer. This gas analyzer uses a chemical absorption technique to determine the volume fractions (which are equivalent to the mole fractions) of CO 2 ,CO,andO 2 in the exhaust gas (see Figure 15.4). Since it cannot measure the H 2 O content, the exhaust gas sample is always cooled to room temperature, or below the dew point of any water vapor present, so that most of the water in the combustion products condenses out. Therefore, the Orsat technique is said to produce a dry products analysis. Also, the Orsat technique cannot detect unburned hydrocarbons (typically CH 4 ) and free hydrogen (H 2 ) in the exhaust gas. These are usually small and can normally be neglected. However, studies have shown that the mole fractions of methane and hydrogen in the combustion products of a hydrocarbon can be approximated as χ CH4 ≈ 0:0022 and χ H2 ≈ 0:5ðx CO Þ, and these relations can be used with an Orsat analysis if necessary.
600 CHAPTER 15: Chemical <strong>Thermodynamics</strong> Sample Valve C B A D Measuring chamber E CuCl CO Absorbed C 6H 6O3 O 2 Absorbed KOH CO 2 Absorbed Leveling bottle (a) FIGURE 15.4 A typical Orsat analyzer. (a) Schematic: Vessel A contains a potassium hydroxide (KOH) solution that absorbs CO 2 . Vessel B contains a pyrogallic acid (1,2,3-trihydroxybenzene, C 6 H 6 O 3 ) solution that absorbs O 2 . Vessel C contains a cuprous chloride (CuCl) solution that absorbs CO. The remaining gas is assumed to be N 2 . Vessel D is the measuring chamber, and vessel E is the leveling bottle. (b) Photograph of a typical Orsat analyzer. (b) EXAMPLE 15.3 The exhaust gas of a gasoline-fueled automobile engine is cooled to 20.0°C and subjected to an Orsat analysis. The results (on a volume or mole basis) are Determine CO 2 = 7:10% CO = 0:800% O 2 = 9:90% N 2 = 82:2% Total = 100:% a. The hydrocarbon model (C n H m ) of the fuel. b. The composition of the fuel on a molar and a mass basis. c. The air-fuel ratio on a molar and a mass basis. d. The % of theoretical air used in the combustion process. Solution a. Since the Orsat analysis is carried out at 20.0°C, we assume that virtually all the water of combustion has condensed out and therefore the composition given is on a dry basis. However, the water term must be left in the chemical reaction
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Modern Engineering Thermodynamics
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Modern Engineering Thermodynamics R
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Dedication WHAT IS AN ENGINEER AND
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Contents PREFACE . . . . . . . . .
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Contents ix 7.6 Heat Engines Runnin
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Contents xi 14.13 Air Standard Gas
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Preface TEXT OBJECTIVES This textbo
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Preface xv Step 5. Write down the b
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Acknowledgments I wish to acknowled
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Resources That Accompany This Book
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List of Symbols A a B COP CR c c p
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Prologue PARIS FRANCE, 10:35 AM, AU
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CHAPTER 1 The Beginning CONTENTS 1.
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1.2 Why Is Thermodynamics Important
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1.3 Getting Answers: A Basic Proble
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1.5 How Do We Measure Things? 7 bei
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1.6 Temperature Units 9 THE DEVELOP
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1.7 Classical Mechanical and Electr
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1.7 Classical Mechanical and Electr
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1.9 Modern Units Systems 15 where M
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1.10 Significant Figures 17 CRITICA
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1.10 Significant Figures 19 WHAT AB
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1.11 Potential and Kinetic Energies
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1.11 Potential and Kinetic Energies
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Summary 25 FIGURE 1.19 Case study 1
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Problems 27 Problems (* indicates p
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Problems 29 14. Determine the mass
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Problems 31 49. Using the CGS units
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CHAPTER 2 Thermodynamic Concepts CO
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2.3 Phases of Matter 35 System boun
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2.4 System States and Thermodynamic
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2.6 Thermodynamic Processes 39 WHAT
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2.7 Pressure and Temperature Scales
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2.9 The Continuum Hypothesis 43 Sur
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2.10 The Balance Concept 45 Solutio
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2.11 The Conservation Concept 47 or
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2.11 The Conservation Concept 49 Th
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Summary 51 change in the mass of X
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Problems 53 Problems (* indicates p
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Problems 55 and Death rate = α 2 +
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CHAPTER 3 Thermodynamic Properties
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3.3 Fun with Mathematics 59 CRITICA
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3.4 Some Exciting New Thermodynamic
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3.6 Enthalpy 63 WHO WAS AMALIE EMMY
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3.7 Phase Diagrams 65 WHO WAS EMMY
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Pressure Vapor 3.7 Phase Diagrams 6
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3.7 Phase Diagrams 69 WHAT IS A “
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3.7 Phase Diagrams 71 considerable
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3.8 Quality 73 10 5 300 C Critical
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3.8 Quality 75 Although Eq. (3.26)
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3.9 Thermodynamic Equations of Stat
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3.10 Thermodynamic Tables 85 Critic
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3.12 Thermodynamic Charts 87 vð100
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3.13 Thermodynamic Property Softwar
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Summary 91 and e = E/m = u + V2 2g
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Problems 93 c. For a saturated mixt
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Problems 95 specific enthalpy of sa
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Problems 97 Table 3.23 Problem 65 M
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CHAPTER 4 The First Law of Thermody
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4.3 The First Law of Thermodynamics
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4.3 The First Law of Thermodynamics
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4.4 Energy Transport Mechanisms 105
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4.5 Point and Path Functions 107 4.
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4.6 Mechanical Work Modes of Energy
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4.7 Nonmechanical Work Modes of Ene
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4.9 Work Efficiency 125 In the case
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4.12 Heat Modes of Energy Transport
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4.13 Heat Transfer Modes 129 Table
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4.14 A Thermodynamic Problem Solvin
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4.14 A Thermodynamic Problem Solvin
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4.15 How to Write a Thermodynamics
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4.15 How to Write a Thermodynamics
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Summary 139 The general open system
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Problems 141 11.* Determine the hea
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Problems 143 where K = 0.810 lbf. D
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Problems 145 Table 4.12 Problem 67
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CHAPTER 5 First Law Closed System A
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5.2 Sealed, Rigid Containers 149 In
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5.4 Power Plants 151 Step 7. Calcul
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5.5 Incompressible Liquids 153 The
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1Q 2 − 1 W 2 = mðu 2 − u 1 Þ
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5.8 Closed System Unsteady State Pr
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5.9 The Explosive Energy of Pressur
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Problems 161 Problems (* indicates
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Problems 163 31. A thermoelectric g
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Problems 165 where v, T, and r are
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CHAPTER 6 First Law Open System App
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6.2 Mass Flow Energy Transport 169
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6.3 Conservation of Energy and Cons
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6.4 Flow Stream Specific Kinetic an
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6.5 Nozzles and Diffusers 175 m (a)
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6.5 Nozzles and Diffusers 177 We ar
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6.6 Throttling Devices 179 These as
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6.6 Throttling Devices 181 For an i
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6.7 Throttling Calorimeter 183 The
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6.8 Heat Exchangers 185 Convective
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6.9 Shaft Work Machines 187 6.9 SHA
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6.9 Shaft Work Machines 189 1 Basem
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6.10 Open System Unsteady State Pro
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Problems 197 we have _m R / _m D =
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Problems 201 32.* A commercial slid
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Summary 203 59. Incompressible liqu
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CHAPTER 7 Second Law of Thermodynam
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7.3 The Second Law of Thermodynamic
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7.4 Carnot’s Heat Engine and the
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7.4 Carnot’s Heat Engine and the
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7.5 The Absolute Temperature Scale
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7.5 The Absolute Temperature Scale
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7.6 Heat Engines Running Backward 2
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7.7 Clausius’s Definition of Entr
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7.8 Numerical Values for Entropy 22
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7.10 Differential Entropy Balance 2
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7.11 Heat Transport of Entropy 229
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7.13 Entropy Production Mechanisms
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7.14 Heat Transfer Production of En
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7.15 Work Mode Production of Entrop
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7.15 Work Mode Production of Entrop
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7.16 Phase Change Entropy Productio
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Summary 241 ■ Indirect method inv
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Problems 243 amount of work W irr i
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Problems 245 a. If the heat pump is
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Problems 247 51. Develop a program
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CHAPTER 8 Second Law Closed System
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8.2 Systems Undergoing Reversible P
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8.3 Systems Undergoing Irreversible
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8.4 Diffusional Mixing 271 Exercise
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Summary 273 Note that this example
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Problems 275 15. A 20.0 ft 3 tank c
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Problems 277 46. a. Determine a for
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CHAPTER 9 Second Law Open System Ap
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9.4 Open System Entropy Balance Equ
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9.4 Open System Entropy Balance Equ
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9.5 Nozzles, Diffusers, and Throttl
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9.5 Nozzles, Diffusers, and Throttl
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9.6 Heat Exchangers 289 Exercises 1
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9.6 Heat Exchangers 291 (T H ) (T H
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9.7 Mixing 293 Now, _m air is given
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9.7 Mixing 295 Critical value of y,
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9.9 Unsteady State Processes in Ope
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Problems 309 Multiplying this equat
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Problems 311 entropy production rat
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Problems 313 heat is added to the b
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Problems 315 55.* Determine the max
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Problems 317 The cavitation process
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CHAPTER 10 Availability Analysis CO
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10.3 What Are Conservative Forces?
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10.6 Availability 323 WHAT IS A SYS
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10.6 Availability 325 and the total
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10.7 Closed System Availability Bal
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10.7 Closed System Availability Bal
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10.8 Flow Availability 331 EXAMPLE
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s − s 0 = c ln T T 0 10.8 Flow Av
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10.10 Modified Availability Rate Ba
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10.10 Modified Availability Rate Ba
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10.11 Energy Efficiency Based on th
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Summary 351 In this problem, we hav
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Summary 353 7. The general open sys
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Problems 355 12.5 Btu/hr·ft ·R. I
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Problems 357 flow rate of 15.0 lbm/
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Problems 359 85. Create a specific
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CHAPTER 11 More Thermodynamic Relat
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11.2 Two New Properties: Helmholtz
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11.2 Two New Properties: Helmholtz
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11.4 Maxwell Equations 367 11.4 MAX
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11.4 Maxwell Equations 369 then,
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11.5 The Clapeyron Equation 371 and
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11.6 Determining u, h, and s from p
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11.7 Constructing Tables and Charts
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11.8 Thermodynamic Charts 381 so th
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11.9 Gas Tables 383 where p r is th
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11.10 Compressibility Factor and Ge
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11.11 Is Steam Ever an Ideal Gas? 3
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Summary 399 equation, and a series
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Problems 401 20.* Estimate h fg for
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Problems 403 Design Problems The fo
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CHAPTER 12 Mixtures of Gases and Va
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12.2 Thermodynamic Properties of Ga
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12.3 Mixtures of Ideal Gases 413 Th
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12.3 Mixtures of Ideal Gases 415 Co
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12.4 Psychrometrics 417 Finally, th
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12.4 Psychrometrics 419 EXAMPLE 12.
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12.6 The Sling Psychrometer 421 The
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12.6 The Sling Psychrometer 423 p w
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12.7 Air Conditioning 425 WHAT ENVI
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12.8 Psychrometric Enthalpies 427 E
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12.8 Psychrometric Enthalpies 429 o
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12.9 Mixtures of Real Gases 431 Whe
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12.9 Mixtures of Real Gases 433 and
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12.9 Mixtures of Real Gases 435 The
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12.9 Mixtures of Real Gases 437 Sol
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Summary 439 Last, we combine Dalton
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Problems 443 exhaust gas is an idea
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Problems 445 57.* Cooling towers ar
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CHAPTER 13 Vapor and Gas Power Cycl
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13.2 Part I. Engines and Vapor Powe
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13.4 Rankine Cycle 457 A B Reversib
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13.5 Operating Efficiencies 459 For
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13.5 Operating Efficiencies 461 13.
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13.5 Operating Efficiencies 463 b.
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13.5 Operating Efficiencies 465 Sta
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13.6 Rankine Cycle with Superheat 4
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13.7 Rankine Cycle with Regeneratio
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13.8 The Development of the Steam T
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13.9 Rankine Cycle with Reheat 477
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13.9 Rankine Cycle with Reheat 479
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13.10 Modern Steam Power Plants 481
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13.12 Air Standard Power Cycles 487
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13.13 Stirling Cycle 489 Q H 4 1 4
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13.14 Ericsson Cycle 491 Q H 4 1 3
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13.15 Lenoir Cycle 493 Exercises 28
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13.16 Brayton Cycle 495 Solution Us
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13.16 Brayton Cycle 497 Equation (7
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13.17 Aircraft Gas Turbine Engines
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13.17 Aircraft Gas Turbine Engines
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13.18 Otto Cycle 503 T Q H 1 1 1 v
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13.18 Otto Cycle 505 Exercises 40.
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13.18 Otto Cycle 507 and, since the
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13.20 Miller Cycle 509 13.19.1 Mode
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13.20 Miller Cycle 511 Then, from F
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13.21 Diesel Cycle 513 to stroll on
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13.21 Diesel Cycle 515 Solution a.
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13.22 Modern Prime Mover Developmen
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13.23 Second Law Analysis of Vapor
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Summary 525 Fill port 160 mm End of
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Problems 527 7. The thermal efficie
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efficiency increase if the condense
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Problems 531 horsepower hour. Assum
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Problems 533 72. Determine the valu
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CHAPTER 14 Vapor and Gas Refrigerat
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14.3 Carnot Refrigeration Cycle 537
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14.4 In the Beginning There Was Ice
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14.4 In the Beginning There Was Ice
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14.5 Vapor-Compression Refrigeratio
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14.5 Vapor-Compression Refrigeratio
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14.6 Refrigerants 547 T 3 2s 2 p 3
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Page 604 and 605: 14.18 Second Law Analysis of Refrig
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Page 610 and 611: Problems 585 13.* A refrigeration u
Page 612 and 613: Problems 587 Loop B Station 1B Stat
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Page 616 and 617: CHAPTER 15 Chemical Thermodynamics
Page 618 and 619: 15.2 Stoichiometric Equations 593 1
Page 620 and 621: 15.2 Stoichiometric Equations 595 C
Page 622 and 623: 15.3 Organic Fuels 597 ANSWERS SOME
Page 626 and 627: 15.4 Fuel Modeling 601 equation, si
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Page 630 and 631: 15.6 Heat of Formation 605 and H 2
Page 632 and 633: 15.7 Heat of Reaction 607 EXAMPLE 1
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Page 636 and 637: 15.7 Heat of Reaction 611 Then, h P
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Page 650 and 651: 15.11 Entropy of Formation and Gibb
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Page 668 and 669: ðn i /n fuel Þðc pi Þ E system
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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
Page 820 and 821:
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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