Modern engineering thermodynamics

Modern Engineering

Thermodynamics

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Modern Engineering

Thermodynamics

Robert T. Balmer

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Notices

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Library of Congress Cataloging-in-Publication Data

Balmer, Robert T.

Modern engineering thermodynamics / Robert T. Balmer

p. cm.

ISBN 978-0-12-374996-3

1. Thermodynamics. I. Title.

TJ265.B196 2010

621.402'1–dc22 2010034092

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Dedication

WHAT IS AN ENGINEER AND WHAT DO ENGINEERS DO?

The answer is in the word itself. An er word ending means “the practice of.” For example, a farmer farms, a

baker bakes, a singer sings, a driver drives, and so forth. But what does an engineer do? Do they engine? Yes they

do! The word engine comes from the Latin ingenerare, meaning “to create.“

About 2000 years ago, the Latin word ingenium was used to describe the design of a new machine. Soon after,

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engineer is ingenieur.

So What Is an Engineer?

An engineer is a creative and ingenious person.

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Engineers create ingenious solutions to society’s problems.

This Book Is Dedicated to All the Future Engineers of the World.

v

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Contents

PREFACE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii

ACKNOWLEDGMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xvii

RESOURCES THAT ACCOMPANY THIS BOOK . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xix

LIST OF SYMBOLS. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxi

PROLOGUE . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xxiii

CHAPTER 1 The Beginning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1

1.1 What Is Thermodynamics?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .1

1.2 Why Is Thermodynamics Important Today?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .2

1.3 Getting Answers: A Basic Problem Solving Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .4

1.4 Units and Dimensions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6

1.5 How Do We Measure Things? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .6

1.6 Temperature Units . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .8

1.7 Classical Mechanical and Electrical Units Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

1.8 Chemical Units. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14

1.9 Modern Units Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15

1.10 Significant Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

1.11 Potential and Kinetic Energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25

CHAPTER 2 Thermodynamic Concepts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

2.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33

2.2 The Language of Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34

2.3 Phases of Matter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35

2.4 System States and Thermodynamic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

2.5 Thermodynamic Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38

2.6 Thermodynamic Processes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39

2.7 Pressure and Temperature Scales . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40

2.8 The Zeroth Law of Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42

2.9 The Continuum Hypothesis . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43

2.10 The Balance Concept . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

2.11 The Conservation Concept. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46

2.12 Conservation of Mass. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51

CHAPTER 3 Thermodynamic Properties. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

3.1 The Trees and The Forest . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

3.2 Why are Thermodynamic Property Values Important?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

3.3 Fun with Mathematics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58

3.4 Some Exciting New Thermodynamic Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 60

3.5 System Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62

3.6 Enthalpy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63

3.7 Phase Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65

3.8 Quality . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72

vii

3.9 Thermodynamic Equations of State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76

3.10 Thermodynamic Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84

3.11 How Do You Determine the “Thermodynamic State”?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86

3.12 Thermodynamic Charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

3.13 Thermodynamic Property Software . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

CHAPTER 4 The First Law of Thermodynamics and Energy Transport Mechanisms . . . . . . . . . . . 99

4.1 Introducción (Introduction). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

4.2 Emmy Noether and the Conservation Laws of Physics . . . . . . . . . . . . . . . . . . . . . . . . . . . . 100

4.3 The First Law of Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

4.4 Energy Transport Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 104

4.5 Point and Path Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107

4.6 Mechanical Work Modes of Energy Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108

4.7 Nonmechanical Work Modes of Energy Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 116

4.8 Power Modes of Energy Transport. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

4.9 Work Efficiency . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 124

4.10 The Local Equilibrium Postulate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 126

4.11 The State Postulate . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

4.12 Heat Modes of Energy Transport . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

4.13 Heat Transfer Modes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 128

4.14 A Thermodynamic Problem Solving Technique . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 130

4.15 How to Write a Thermodynamics Problem. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 138

CHAPTER 5 First Law Closed System Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

5.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 147

5.2 Sealed, Rigid Containers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 148

5.3 Electrical Devices. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 150

5.4 Power Plants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 151

5.5 Incompressible Liquids . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 152

5.6 Ideal Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 154

5.7 Piston-Cylinder Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 155

5.8 Closed System Unsteady State Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157

5.9 The Explosive Energy of Pressure Vessels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 159

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 160

CHAPTER 6 First Law Open System Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 167

6.2 Mass Flow Energy Transport. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 168

6.3 Conservation of Energy and Conservation of Mass Equations for Open Systems . . . . . . . . 171

6.4 Flow Stream Specific Kinetic and Potential Energies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 173

6.5 Nozzles and Diffusers. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 174

6.6 Throttling Devices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 179

6.7 Throttling Calorimeter . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 182

6.8 Heat Exchangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 184

6.9 Shaft Work Machines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 187

6.10 Open System Unsteady State Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 197

CHAPTER 7 Second Law of Thermodynamics and Entropy Transport

and Production Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .205

7.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205

7.2 What Is Entropy? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 206

7.3 The Second Law of Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 207

7.4 Carnot’s Heat Engine and the Second Law of Thermodynamics . . . . . . . . . . . . . . . . . . . . . 208

7.5 The Absolute Temperature Scale . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212

viii Contents

7.6 Heat Engines Running Backward . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 216

7.7 Clausius’s Definition of Entropy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 218

7.8 Numerical Values for Entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221

7.9 Entropy Transport Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227

7.10 Differential Entropy Balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227

7.11 Heat Transport of Entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 229

7.12 Work Mode Transport of Entropy. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231

7.13 Entropy Production Mechanisms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231

7.14 Heat Transfer Production of Entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 232

7.15 Work Mode Production of Entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 235

7.16 Phase Change Entropy Production. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 239

7.17 Entropy Balance and Entropy Rate Balance Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . 240

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241

CHAPTER 8 Second Law Closed System Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249

8.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 249

8.2 Systems Undergoing Reversible Processes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 250

8.3 Systems Undergoing Irreversible Processes. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 256

8.4 Diffusional Mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 271

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 273

CHAPTER 9 Second Law Open System Applications . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279

9.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279

9.2 Mass Flow Transport of Entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 279

9.3 Mass Flow Production of Entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280

9.4 Open System Entropy Balance Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280

9.5 Nozzles, Diffusers, and Throttles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 284

9.6 Heat Exchangers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 289

9.7 Mixing . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 293

9.8 Shaft Work Machines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 296

9.9 Unsteady State Processes in Open Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 297

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 308

Final Comments on the Second Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 310

CHAPTER 10 Availability Analysis. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319

10.1 What Is Availability? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319

10.2 Fun with Scalar, Vector, and Conservative Fields . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 320

10.3 What are Conservative Forces? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 321

10.4 Maximum Reversible Work . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322

10.5 Local Environment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 322

10.6 Availability. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 323

10.7 Closed System Availability Balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327

10.8 Flow Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331

10.9 Open System Availability Rate Balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334

10.10 Modified Availability Rate Balance Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 335

10.11 Energy Efficiency Based on the Second Law . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 339

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 351

CHAPTER 11 More Thermodynamic Relations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361

11.1 Kynning (Introduction) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 361

11.2 Two New Properties: Helmholtz and Gibbs Functions. . . . . . . . . . . . . . . . . . . . . . . . . . . . 362

11.3 Gibbs Phase Equilibrium Condition . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 366

11.4 Maxwell Equations. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 367

11.5 The Clapeyron Equation. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 370

11.6 Determining u, h, and s from p, v, and T . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 372

11.7 Constructing Tables and Charts. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 378

11.8 Thermodynamic Charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 380

Contents ix

11.9 Gas Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 382

11.10 Compressibility Factor and Generalized Charts . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 384

11.11 Is Steam Ever an Ideal Gas?. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 396

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 398

CHAPTER 12 Mixtures of Gases and Vapors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405

12.1 Wprowadzenie (Introduction). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 405

12.2 Thermodynamic Properties of Gas Mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 406

12.3 Mixtures of Ideal Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 412

12.4 Psychrometrics. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 417

12.5 The Adiabatic Saturator . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 420

12.6 The Sling Psychrometer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 421

12.7 Air Conditioning . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 424

12.8 Psychrometric Enthalpies. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 426

12.9 Mixtures of Real Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 430

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 438

CHAPTER 13 Vapor and Gas Power Cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 447

13.1 Bevezetésének (Introduction) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 448

13.2 Part I. Engines and Vapor Power Cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 448

13.3 Carnot Power Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 456

13.4 Rankine Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 457

13.5 Operating Efficiencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 459

13.6 Rankine Cycle with Superheat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 466

13.7 Rankine Cycle with Regeneration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 469

13.8 The Development of the Steam Turbine. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 474

13.9 Rankine Cycle with Reheat . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 477

13.10 Modern Steam Power Plants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 480

13.11 Part II. Gas Power Cycles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486

13.12 Air Standard Power Cycles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 486

13.13 Stirling Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 488

13.14 Ericsson Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 490

13.15 Lenoir Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 493

13.16 Brayton Cycle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 495

13.17 Aircraft Gas Turbine Engines. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 499

13.18 Otto Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 502

13.19 Atkinson Cycle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 508

13.20 Miller Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 509

13.21 Diesel Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 512

13.22 Modern Prime Mover Developments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 516

13.23 Second Law Analysis of Vapor and Gas Power Cycles. . . . . . . . . . . . . . . . . . . . . . . . . .518

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 525

CHAPTER 14 Vapor and Gas Refrigeration Cycles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535

14.1 Introduksjon (Introduction). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 535

14.2 Part I. Vapor Refrigeration Cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 536

14.3 Carnot Refrigeration Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 537

14.4 In the Beginning There Was Ice. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 539

14.5 Vapor-Compression Refrigeration Cycle. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 542

14.6 Refrigerants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 547

14.7 Refrigerant Numbers . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 549

14.8 CFCs and the Ozone Layer . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 552

14.9 Cascade and Multistage Vapor-Compression Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . 554

14.10 Absorption Refrigeration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 560

14.11 Commercial and Household Refrigerators . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 562

14.12 Part II. Gas Refrigeration Cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 568

x Contents

14.13 Air Standard Gas Refrigeration Cycles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 568

14.14 Reversed Brayton Cycle Refrigeration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 569

14.15 Reversed Stirling Cycle Refrigeration . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 572

14.16 Miscellaneous Refrigeration Technologies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 575

14.17 Future Refrigeration Needs . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 578

14.18 Second Law Analysis of Refrigeration Cycles. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 579

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 582

CHAPTER 15 Chemical Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 591

15.1 Einführung (Introduction). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 591

15.2 Stoichiometric Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 593

15.3 Organic Fuels. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 596

15.4 Fuel Modeling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 599

15.5 Standard Reference State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 603

15.6 Heat of Formation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 604

15.7 Heat of Reaction. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 607

15.8 Adiabatic Flame Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 613

15.9 Maximum Explosion Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 619

15.10 Entropy Production in Chemical Reactions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 621

15.11 Entropy of Formation and Gibbs Function of Formation. . . . . . . . . . . . . . . . . . . . . . . . . . . 625

15.12 Chemical Equilibrium and Dissociation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 626

15.13 Rules for Chemical Equilibrium Constants . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 634

15.14 The van’t Hoff Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 635

15.15 Fuel Cells . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 636

15.16 Chemical Availability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 641

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 642

CHAPTER 16 Compressible Fluid Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 651

16.1 Introducerea (Introduction). . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 651

16.2 Stagnation Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 652

16.3 Isentropic Stagnation Properties . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 653

16.4 The Mach Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 655

16.5 Converging-Diverging Flows . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 660

16.6 Choked Flow . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 665

16.7 Reynolds Transport Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 669

16.8 Linear Momentum Rate Balance . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 673

16.9 Shock Waves . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 675

16.10 Nozzle and Diffuser Efficiencies . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 681

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 685

CHAPTER 17 Thermodynamics of Biological Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 693

17.1 Introdução (Introduction) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 693

17.2 Living Systems. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 693

17.3 Thermodynamics of Biological Cells. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 695

17.4 Energy Conversion Efficiency of Biological Systems . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 699

17.5 Metabolism . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 702

17.6 Thermodynamics of Nutrition and Exercise . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 705

17.7 Limits to Biological Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 711

17.8 Locomotion Transport Number . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 714

17.9 Thermodynamics of Aging and Death . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 716

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 721

CHAPTER 18 Introduction to Statistical Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 727

18.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 727

18.2 Why Use a Statistical Approach? . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 728

18.3 Kinetic Theory of Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 728

18.4 Intermolecular Collisions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 732

Contents xi

18.5 Molecular Velocity Distributions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 734

18.6 Equipartition of Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 738

18.7 Introduction to Mathematical Probability . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 741

18.8 Quantum Statistical Thermodynamics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 747

18.9 Three Classical Quantum Statistical Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 749

18.10 Maxwell-Boltzmann Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 750

18.11 Monatomic Maxwell-Boltzmann Gases. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 751

18.12 Diatomic Maxwell-Boltzmann Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 753

18.13 Polyatomic Maxwell-Boltzmann Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 756

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 758

CHAPTER 19 Introduction to Coupled Phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 763

19.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 763

19.2 Coupled Phenomena . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 763

19.3 Linear Phenomenological Equations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 765

19.4 Thermoelectric Coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 767

19.5 Thermomechanical Coupling . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 776

Summary . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 783

APPENDIX A Physical Constants and Conversion Factors. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 787

APPENDIX B Greek and Latin Origins of Engineering Terms . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 789

INDEX . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 793

xii Contents

Preface

TEXT OBJECTIVES

This textbook has two main objectives. The first is to provide students with a clear presentation of the

fundamental principles of basic and applied engineering thermodynamics. The second is to help students develop

skills as engineering problem solvers by nurturing the development of their confidence with basic engineering

principles through the use of numerous solved example problems. Problem-solving skills are not necessarily

learned simply by routinely solving more and more problems. The understanding of proven problem-solving

strategies and techniques greatly accelerates the development of problem-solving skills. Throughout the text, learn￾ing assessment exercises are included that have proven to be effective in helping students to understand and

develop confidence in their ability to solve engineering thermodynamics problems.

To meet these objectives, explanations are occasionally more detailed than those found in other texts, because

common learning difficulties encountered by students have been anticipated. If students can understand the text

by simply reading it, then the instructor has more flexibility in selecting lecture material. For example, an

instructor might choose to develop a few salient points from the reading and then work a few interesting

example problems, rather than present a complete derivation of all the assigned reading material.

CULTURAL INFRASTRUCTURE

What engineers do has an enormous impact on society and the world. Understanding how the great challenges

of engineering were met in the past can help students understand the importance of the theory and practice of

modern engineering principles. This text presents the historical background, the current uses, and the future

importance of the thermodynamic topics treated. By understanding where ideas come from, how they were

developed, and what external forces shaped the resulting technology, students will better understand their role

as engineers of the future.

Engineering is an exciting and rewarding career. However, students occasionally become disenchanted with their

engineering course work because they are unable to see the connection between what they are studying and

what an engineer really does. To combat this problem, the thermodynamic concepts in this text are presented in

a straightforward logical manner, and then applied to real-world engineering situations that are both timely and

interesting.

TEXT COVERAGE

This text was designed for use in a standard two-semester engineering thermodynamics course sequence. The first

part of the text (Chapters 1–10) contains material suitable for a Basic Thermodynamics course that can be taken

by engineers from all majors. The second part of the text was designed for an Applied Thermodynamics course

in a mechanical engineering program. Chapters 17, 18, and 19 present several unique topics (biothermody￾namics, statistical thermodynamics, and coupled phenomena) for those wishing to glimpse the future of the

subject.

xiii

TEXT FEATURES

1. Style. To make the subject as understandable as possible, the writing is somewhat conversational and the

importance of the subject is evidenced in the enthusiasm of the presentation. The composition of the

engineering student body has been changing in recent years, and it is no longer assumed that the students

are all men and that they inherently understand how technologies (e.g., engines) operate. Consequently, the

operation of basic technologies is explained in the text along with the relevant thermodynamic material.

2. Significant figures. One of the unique features of this text is the treatment of significant figures. Professors

often lament about the number of figures provided by students on their homework and examinations. The

rules for determining the correct number of significant figures are introduced in Chapter 1 and are followed

consistently throughout the text. An example from Chapter 1 follows.

EXAMPLE 1.6

The inside diameter of a circular water pipe is measured with a ruler to two significant figures and is found to be 2.5 inches.

Determine the cross-sectional area of the pipe to the correct number of significant figures.

Solution

The cross-sectional area of a circle is A = πD2

/4, so Apipe = π(2.5 inches)2

/4 = 4.9087 in2

, which must be rounded to 4.9 in2

,

since the least accurate value in this calculation is the pipe diameter (2.5 inches), which has only two significant figures.

3. Chapter overviews. Each chapter begins with an overview of the material contained in the chapter.

4. Problem-solving strategy. A proven technique for solving thermodynamic problems is discussed early in the

text and followed throughout in the solved examples. The technique follows these steps:

5. Solved example problems. Over 200 solved example problems are provided in the text. These examples

were carefully designed to illustrate the preceding text material. A sample from Chapter 5 follows.

EXAMPLE P.1

Read the problem statement. An incandescent lightbulb is a simple electrical device. Using the energy rate balance on a

lightbulb, determine the heat transfer rate of a 100. W incandescent lightbulb.

Solution

Step 1. Identify and sketch the system (see Figure P.1 on the following page).

Step 2. Identify the unknowns. The unknown is Q_ :

Step 3. Identify the type of system. It is a closed system.

Step 4. Identify the process connecting the system states. The bulb does not change its thermodynamic state, so its

properties remain constant. The process path (after the bulb has warmed to its operating temperature) is U = constant.

SUMMARY OF THE THERMODYNAMIC PROBLEM￾SOLVING TECHNIQUE

Begin by carefully reading the problem statement completely through.

Step 1. Make a sketch of the system and put a dashed line around the system boundary.

Step 2. Identify the unknown(s) and write them on your system sketch.

Step 3. Identify the type of system (closed or open) you have.

Step 4. Identify the process that connects the states or stations.

Step 5. Write down the basic thermodynamic equations and any useful auxiliary equations.

Step 6. Algebraically solve for the unknown(s).

Step 7. Calculate the value(s) of the unknown(s).

Step 8. Check all algebra, calculations, and units.

Sketch → Unknowns → System → Process → Equations → Solve → Calculate → Check

xiv Preface