Modern Engineering Thermodynamics

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13.23 Second Law Analysis of Vapor and Gas Power Cycles 523 where _Q fuel is the rate of heat produced by the burning fuel. For turbojet engines, this is ðη thrust Þ turbojet = _m aðV exhaust − V aircraft ÞV aircraft _Q fuel and, for turbofan and turboprop engines, this it ðη thrust Þ turbofan = _m aðV exhaust − V aircraft ÞV aircraft _Q or turboprop fuel We can now maximize the thrust efficiency by differentiating it with respect to the aircraft’s velocityV while holding all the other variables constant, then setting the result equal to zero to find the optimum aircraft velocity as V optimum = V exhaust 2 turbojet = V exhaust 2 turbofan or turboprop Inserting this result into the turbojet, turbofan, and turboprop propulsion efficiency equations produces a common optimum propulsion efficiency for all three engines of ðη propulsion Þ optimum = 2 = 0:667 = 66:7% 3 The GE90 engine development In early 1990, the Aircraft Engines Division of General Electric launched the design of the GE90, a high-thrust, turbofan, gas turbine engine (Figure 13.64) designed to meet the needs of the emerging superjumbo wide-body passenger aircraft market. It was clear at that time that there would be increasing air traffic occurring over longer distances as world markets continued to evolve in the Pacific Rim, Eastern Europe, and South America. More passengers traveling longer distances meant more air congestion or larger planes. Also, in the 1990s, the aging fleet of over 3000 Boeing 747s could be replaced with new wide-body, twin-engine passenger aircraft capable of carrying 300 passengers over 6000 miles. Such an aircraft would have a wingspan of about 200 ft and a gross weight of about 500,000 lbf. This meant that each engine required a takeoff thrust of about 100,000 lbf. The resulting GE90 engine specifications were Bypass ratio ð _m aC / _m aH Þ = 10:0to1 Compressor compression ratio p 2s /p 1 = PR = 50:0to1 Engine thrust = T = 100,000 lbf Fan diameter = D fan = 123 in: = 10:25 ft _m a =2150 lbm/s For a static (takeoff) thrust of 100,000 lbf, the average exit velocity must be V exhaust = Tg c _m a = ð100,000 lbfÞð32:174 lbm . ft/lbf . s 2 Þ 2150 lbm/s = 1500 ft/s and for a cruising speed of 500. mph = 733 ft/s, this exhaust velocity yields a propulsion efficiency of η propulsion = 2 1 + 1500: = 0:657 = 65:7% 733 Note that, since V aircraft ≈ V exhaust /2here,thisisveryclosetothe optimum propulsion efficiency (66.7%) for this engine. The GE-IA: The first U.S. turbojet engine In January 1941, the U.S. National Academy of Sciences reported that gas turbine engines were impractical for aircraft propulsion because their power to weight ratio was too low. However, on August 24, 1939, Germany flew its first turbojet-powered aircraft (the Heinkel-178), and by June 1944, German combat jet aircraft (Messerschmitt ME-262 Swallow, powered by two Junkers Juno turbojet engines with an air speed of 540 mph at 20,000 ft) had entered World War II. Also, on May 15, 1941, the British first flew aGlosterMeteor jet aircraft powered by a single Whittle W-1X turbojet engine as part of their war research and development program. These events prompted the U.S. government to issue a contract to General Electric in September 1941 to build and test 15 gas turbojet engines based on the designs of the British aircraft engineer Frank Whittle. On March 18, 1942, the first GE type I-A (pronounced “eye-A”) turbojet engine was completed and tested at GE’s River Works facility in Lynn, Massachusetts. It produced about 1250lbfofstaticthrustat15,000rpm.OnOctober1,1942,the first U.S. turbojet-powered aircraft (the Bell XP-59A Aircomet) was flown at Muroc Dry Lake (now called Edwards Air Force Base) in California. It had an air speed of 400 mph, 140 mph less than the German ME-262. The tests with the Bell XP-59A did not result in U.S. combat aircraft during World War II, but it did play a key role in the later development of the XP-80 Shooting Star, usedintheKoreanWarinthe early 1950s. If the air mass flow rate into the GE-IA engine is 18.0 lbm/s and it produces 1,250 lbf of static thrust, then we can compute the jet exit velocity from the relation given in the GE90 case study as V exhaust = T × g c _m a = ð1250 lbfÞ½32:174 lbm . ft/ðlbf . s 2 ÞŠ 18:0 lbm/s = 2230 ft/s Then, at a flight speed of 400. mph = 587 ft/s, the propulsion efficiency is η propulsion = 1 + 2 2230 ft/s 587 ft/s = 0:417 = 41:7% FIGURE 13.64 Cross-section of the GE90 engine. Case study 13.4. Model Stirling engine projects Though the mechanism and thermodynamic cycle of a Stirling engine are not easy to understand, you can make a working Stirling engine at home. Numerous model Stirling engine designs are available (for example, see Making Stirling Engines, by Andy Ross, (Continued )
524 CHAPTER 13: Vapor and Gas Power Cycles CASE STUDIES IN APPLIED THERMODYNAMICS Continued published by Ross Experimental, 1660 W. Henderson Rd., Columbus, Ohio); however, most require machinist skills. The Stirling engine described here can be made from commonly available components and requires minimum manual skill to assemble. Stirling engine 1. A test tube engine This project has been designed for any engineering student with access to simple hand-tools. It was originally developed in 1992 by Wilfried Schlagenhauf in Germany. If you follow the instructions carefully, you can make a simple Stirling cycle engine that runs under its own power. Figure 13.65 shows the eight basic parts. You need a standard test tube (about ¾ inch in diameter and 6 inches long) (1), and five glass marbles (2) that roll freely inside the test tube and function as a free piston displacer. The power cylinder (5) is a 1-inch diameter plastic snap-cap pill bottle with the bottom cut off. Cut the neck off a small balloon (6) and stretch the opening over the uncut end of the pill bottle and snap the cap in place to hold and seal the balloon. Then, cut a small hole in the pill bottle top to insert the air tube and mount it upside down on the base (8). The power piston assembly (4) consists of another plastic bottle cap, small enough to fit inside the power cylinder without jamming when at an angle. A 3 inch long nail is pushed through the center of the bottle cap to provide the piston connecting rod. The test tube support assembly (3) consists of an angle bracket mounted to the base (8), and an adjustable (erector set) member attached to the test tube pivot joint. The air tube (9) is 2 or 3 mm ID pliable plastic or rubber tubing. Finally, counterweights (10) need to be added to the cold end of the test tube to control its motion. The engine is driven by the heat of a single candle (7). A complete engine kit is available from Ginsberg Scientific (ginsbergscientific.com). towards the free end of the test tube, displacing the hot air to the higher, cold end, where it cools, causing the balloon to retract, lowering the piston assembly, and the cycle begins again. When properly adjusted, the engine operates at about one to three cycles per second, and the engine generates enough power to drive a small external device. Heating (a) Heating the air Cooling 1 2 8 7 FIGURE 13.65 A test tube Stirling engine. 6 5 4 Here is how the cycle works (Figure 13.66): (a) When the free end of the test tube is pointing up, the air it contains is heated. The heated air expands and inflates the balloon. (b) The expanding balloon pushes the power piston assembly up, which in turn causes the test tube to pivot its free end downward. Then the marbles roll 3 10 9 FIGURE 13.66 How this engine works. (b) Cooling the air Stirling engine 2. A liquid piston fruit-jar engine A number of easily made liquid piston Stirling cycle engines can be found in the text Liquid Piston Stirling Engines, byC.D.West(New York: Van Nostrand Reinhold, 1983). One of the most intriguing is the fruit-jar engine, shown in Figure 13.67, connected to a water pump. This unit should pump about 5 gallons per hour when properly adjusted. In some cases, the water level in the cylinders and the length of the tuning line inserted into the hot cylinder may require careful adjustment. Some very interesting thermodynamic experiments can be done with this design. For best results, see the details provided in the text by C. D. West.
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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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13.7 Rankine Cycle with Regeneratio
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Page 518 and 519: 13.15 Lenoir Cycle 493 Exercises 28
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Page 550 and 551: Summary 525 Fill port 160 mm End of
Page 552 and 553: Problems 527 7. The thermal efficie
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Page 556 and 557: Problems 531 horsepower hour. Assum
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Page 564 and 565: 14.4 In the Beginning There Was Ice
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Page 568 and 569: 14.5 Vapor-Compression Refrigeratio
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Page 572 and 573: 14.6 Refrigerants 547 T 3 2s 2 p 3
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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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