Commonly asked questions in thermodynamics

Commonly Asked Questions in

THERMODYNAMICS

CRC Press is an imprint of the

Taylor & Francis Group, an informa business

Boca Raton London New York

Marc J. Assael

Aristotle University, Thessaloniki, Greece

Anthony R. H. Goodwin

Schlumberger Technology Corporation, Sugar Land,Texas, USA

Michael Stamatoudis

Aristotle University, Thessaloniki, Greece

William A. Wakeham

University of Southampton, United Kingdom

Stefan Will

Universitat Bremen, Bremen, Germany

Commonly Asked Questions in

THERMODYNAMICS

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Library of Congress Cataloging-in-Publication Data

Commonly asked questions in thermodynamics / Marc J. Assael … [et al.].

p. cm.

Summary: “Accurate and clearly explained answers to common questions. Every scientist

and engineer encounters problems that may be solved at least in part using the principles of

thermodynamics. The importance of thermodynamics is often so fundamental to life that

we should all have a fairly detailed understanding of this core field. This clearly written,

easy-to-follow guide allows even nonscientists considering use of alternative fuel sources to

achieve a solid grounding in thermodynamics. The authors cover topics spanning from energy

sources to the environment to climate change. A broad audience of general readers, students,

industry professionals, and academic researchers will appreciate the answers found in this

book”-- Provided by publisher.

Includes bibliographical references and index.

ISBN 978-1-4200-8695-9 (pbk.)

1. Thermodynamics--Miscellanea. I. Assael, Marc J.

QC319.C66 2011

536’.7--dc22 2010050698

Visit the Taylor & Francis Web site at

http://www.taylorandfrancis.com

and the CRC Press Web site at

http://www.crcpress.com

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Th e authors are indebted individually and collectively to a

large body of students whom they have taught in many

universities in diff erent countries of the world. It is the

continually renewed inquisitiveness of students that provides

both the greatest challenge and reward from teaching in a

university. It is not possible for us to single out individual

students who have asked stimulating and interesting questions

over a career of teaching in universities.

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vii

Contents

Preface xv

Authors xvii

1 Defi nitions and the 1st Law of Thermodynamics 1

1.1 Introduction 1

1.2 What Is Th ermodynamics? 2

1.3 What Vocabulary Is Needed to Understand Th ermodynamics? 3

1.3.1 What Is a System? 3

1.3.2 What Is a State? 3

1.3.3 What Are the Types of Property: Extensive and Intensive? 4

1.3.4 What Is a Phase? 4

1.3.5 What Is a Th ermodynamic Process? 5

1.3.6 What Is Adiabatic? 5

1.3.7 What Is Work? 5

1.3.8 What Is a Reversible Process or Reversible Change? 6

1.3.9 What Are Th ermal Equilibrium and the Zeroth Law of

Th ermodynamics? 7

1.3.10 What Is Chemical Composition? 8

1.3.11 What Is the Amount of Substance? 8

1.3.12 What Are Molar and Mass or Specifi c Quantities? 9

1.3.13 What Is Mole Fraction? 10

1.3.14 What Are Partial Molar Quantities? 10

1.3.15 What Are Molar Quantities of Mixing? 12

1.3.16 What Are Mixtures, Solutions, and Molality? 12

1.3.17 What Are Dilution and Infi nite Dilution? 13

1.3.18 What Is the Extent of Chemical Reaction? 14

1.4 What Are Intermolecular Forces and How Do

We Know Th ey Exist? 14

1.4.1 What Is the Intermolecular Potential Energy? 14

1.4.2 What Is the Origin of Intermolecular Forces? 17

1.4.3 What Are Model Pair Potentials and Why Do We Need Th em? 18

1.4.3.1 What Is a Hard-Sphere Potential? 18

1.4.3.2 What Is a Square Well Potential? 19

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viii Contents

1.4.3.3 What Is a Lennard-Jones (12–6) Potential? 20

1.4.3.4 What Is the Potential for Nonspherical Systems? 21

1.4.4 Is Th ere Direct Evidence of the Existence of Intermolecular

Forces? 22

1.5 What Is Th ermodynamic Energy? 23

1.6 What Is the 1st Law of Th ermodynamics? 23

1.7 Questions Th at Serve as Examples of Work and the 1st Law of

Th ermodynamics? 24

1.7.1 How Does a Dewar Flask Work? 24

1.7.2 In a Th ermally Isolated Room Why Does the Temperature

Go Up When a Refrigerator Powered by a Compressor Is

Placed Within? 26

1.7.3 What Is the 1st Law for a Steady-State Flow System? 27

1.7.4 What Is the Best Mode of Operation for a Gas Compressor? 30

1.7.5 What Is the Work Required for an Isothermal Compression? 31

1.7.6 What Is the Work Required for an Adiabatic Compression? 32

1.8 How Are Th ermophysical Properties Measured? 35

1.8.1 How Is Temperature Measured? 36

1.8.2 How Is Pressure Measured? 37

1.8.3 How Are Energy and Enthalpy Diff erences Measured? 37

1.8.4 How Is the Energy or Enthalpy Change of a Chemical

Reaction Measured? 39

1.8.5 How Is Heat Capacity Measured? 39

1.8.6 How Do I Measure the Energy in a Food Substance? 41

1.8.7 What Is an Adiabatic Flow Calorimeter? 43

1.9 What Is the Diff erence between Uncertainty and Accuracy? 45

1.10 What Are Standard Quantities and How Are Th ey Used? 46

1.11 What Mathematical Relationships Are Useful in Th ermodynamics? 51

1.11.1 What Is Partial Diff erentiation? 51

1.11.2 What Is Euler’s Th eorem? 54

1.11.3 What Is Taylor’s Th eorem? 54

1.11.4 What Is the Euler–MacLaurin Th eorem? 55

1.12 References 55

2 What Is Statistical Mechanics? 59

2.1 Introduction 59

2.2 What Is Boltzmann’s Distribution? 61

2.3 How Do I Evaluate the Partition Function q? 62

2.4 What Can Be Calculated Using the Molecular Partition Function? 66

2.4.1 What Is the Heat Capacity of an Ideal Diatomic Gas? 66

2.4.2 What Is the Heat Capacity of a Crystal? 67

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Contents ix

2.4.3 What Is the Change of Gibbs Function Associated with the

Formation of a Mixture of Gases? 68

2.4.4 What Is the Equilibrium Constant for a Chemical Reaction

in a Gas? 70

2.4.5 What Is the Entropy of a Perfect Gas? 72

2.5 Can Statistical Mechanics Be Used to Calculate the Properties of

Real Fluids? 73

2.5.1 What Is the Canonical Partition Function? 74

2.5.2 Why Is the Calculation so Diffi cult for Real Systems? 77

2.6 What Are Real, Ideal, and Perfect Gases and Fluids? 78

2.7 What Is the Virial Equation and Why Is It Useful? 81

2.7.1 What Happens to the Virial Series for Mixtures? 86

2.8 What Is the Principle of Corresponding States? 87

2.8.1 How Can the Principle of Corresponding States Be Used

to Estimate Properties? 91

2.9 What Is Entropy S? 94

2.9.1 How Can I Interpret Entropy Changes? 96

2.10 References 96

3 2nd Law of Thermodynamics 101

3.1 Introduction 101

3.2 What Are the Two 2nd Laws? 101

3.2.1 What Is Law 2a? 102

3.2.2 What Is Law 2b? 102

3.3 What Do I Do if Th ere Are Other Independent Variables? 104

3.3.1 Is Zero a Characteristic Th ermodynamic Function? 106

3.4 What Happens When Th ere Is a Chemical Reaction? 107

3.5 What Am I Able To Do Knowing Law 2a? 109

3.5.1 How Do I Calculate Entropy, Gibbs Function, and

Enthalpy Changes? 109

3.5.2 How Do I Calculate Expansivity and Compressibility? 113

3.5.3 What Can I Gain from Measuring the Speed of Sound in

Fluids? 115

3.5.4 What Can I Gain from Measuring the Speed of Sound in

Solids? 117

3.5.5 Can I Evaluate the Isobaric Heat Capacity from the

Isochoric Heat Capacity? 118

3.5.6 Why Use an Isentropic Expansion to Liquefy a Gas? 119

3.5.7 Does Expansion of a Gas at Constant Energy Change Its

Temperature? 119

3.5.8 What Is a Joule-Th omson Expansion? 121

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x Contents

3.6 What Am I Able to Do Knowing Law 2b? 122

3.6.1 How Are Th ermal Equilibrium and Stability Ensured? 122

3.6.2 How Are Mechanical Equilibrium and Stability Ensured? 123

3.6.3 How Are Diff usive Equilibrium and Stability Ensured? 124

3.7 Is Th ere a 3rd Law? 126

3.8 How Is the 2nd Law Connected to the Effi ciency of a Heat Engine? 128

3.9 What Is Exergy Good For? 131

3.10 References 136

4 Phase Equilibria 139

4.1 Introduction 139

4.1.1 What Is the Phase Rule? 140

4.2 What Is Phase Equilibrium of a Pure Substance? 141

4.2.1 What Does Clapeyron’s Equation Have to Do with

Ice-Skating? 146

4.2.2 How Do I Calculate the Chemical Potential? 148

4.3 What Is the Condition of Equilibrium between Two Phases of a

Mixture of Substances? 150

4.3.1 What Is the Relationship between Several Chemical

Potentials in a Mixture? 151

4.3.2 What Can Be Done with the Diff erences in Chemical

Potential? 151

4.3.3 How Do I Measure Chemical Potential Diff erences (What

Is Osmotic Pressure)? 151

4.4 Do I Have to Use Chemical Potentials? What Is Fugacity? 154

4.4.1 Can Fugacity Be Used to Calculate (Liquid + Vapor) Phase

Equilibrium? 156

4.5 What Are Ideal Liquid Mixtures? 158

4.6 What Are Activity Coeffi cients? 159

4.6.1 How Do I Measure the Ratio of Absolute Activities at a

Phase Transition? 165

4.6.2 What Is Th ermodynamic Consistency? 167

4.6.3 How Do I Use Activity Coeffi cients Combined with Fugacity

to Model Phase Equilibrium? 168

4.6.4 How Do We Obtain Activity Coeffi cients? 169

4.6.5 Activity Coeffi cient Models 170

4.6.6 How Can I Estimate the Equilibrium Mole Fractions of a

Component in a Phase? 172

4.7 How Do I Calculate Vapor + Liquid Equilibrium? 173

4.7.1 Is Th ere a Diff erence between a Gas and a Vapor? 173

4.7.2 Which Equations of State Should Be Used in Engineering

VLE Calculations? 179

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Contents xi

4.7.3 What Is a Bubble-Point or Dew-Point Calculation and

Why Is It Important? 183

4.7.4 What Is a Flash Calculation? 186

4.7.4.1 What Is an Isothermal Flash? 186

4.7.4.2 What Is an Isenthalpic Flash? 189

4.7.4.3 What Is an Isentropic Flash? 189

4.8 Would Practical Examples Help? 190

4.8.1 What Is the Minimum Work Required to Separate Air into

Its Constituents? 190

4.8.2 How Does a Cooling Tower Work? 194

4.9 What Is the Temperature Change of Dilution? 196

4.10 What about Liquid + Liquid and Solid + Liquid Equilibria? 202

4.10.1 What Are Conformal Mixtures? 202

4.10.2 What Are Simple Mixtures? 202

4.10.3 What Are Partially Miscible Liquid Mixtures? 203

4.10.4 What Are Critical Points in Liquid Mixtures? 204

4.10.5 What about the Equilibrium of Liquid Mixtures and Pure

Solids? 206

4.11 What Particular Features Do Phase Equilibria Have? 206

4.11.1 What Is a Simple Phase Diagram? 207

4.11.2 What Is Retrograde Condensation (or Evaporation)? 208

4.11.3 What Is the Barotropic Eff ect? 208

4.11.4 What Is Azeotropy? 209

4.12 What Are Solutions? 210

4.12.1 What Is the Activity Coeffi cient at Infi nite Dilution? 210

4.12.2 What Is the Osmotic Coeffi cient of the Solvent? 211

4.13 References 212

5 Reactions, Electrolytes, and Nonequilibrium 217

5.1 Introduction 217

5.2 What Is Chemical Equilibrium? 217

5.2.1 What Are Enthalpies of Reaction? 218

5.3 What Are Equilibrium Constants? 222

5.3.1 What Is the Temperature Dependence of the Equilibrium

Constant? 223

5.3.2 What Is the Equilibrium Constant for a Reacting

Gas Mixture? 224

5.3.3 What Is the Equilibrium Constant for Reacting Liquid or

Solid Mixtures? 226

5.3.4 What Is the Equilibrium Constant for Reacting Solutes in

Solution? 227

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xii Contents

5.3.5 What Are the Enthalpy Changes in Mixtures with

Chemical Reactions? 229

5.3.6 What Is the diff erence between ΔrGm and ΔrG⦵

m ? 230

5.4 What Is Irreversible Th ermodynamics? 232

5.5 What Are Galvanic Cells? 234

5.5.1 What Is a Standard Electromotive Force? 238

5.6 What Is Special about Electrolyte Solutions? 239

5.7 What Can Be Understood and Predicted for Systems Not at

Equilibrium? 242

5.8 Why Does a Polished Car in the Rain Have Water Beads?

(Interfacial Tension) 245

5.9 References 247

6 Power Generation, Refrigeration, and Liquefaction 249

6.1 Introduction 249

6.2 What Is a Cyclic Process and Its Use? 249

6.3 What Are the Characteristics of Power Cycles? 251

6.3.1 Why Does a Diesel Car Have a Better Fuel Effi ciency

Th an a Gasoline Car? 257

6.3.2 Why Do Power Plants Have Several Steam Turbines? 263

6.3.3 What Is a Combined Cycle? 267

6.4 What Is a Refrigeration Cycle? 273

6.4.1 What Is a Vapor-Compression Cycle? 273

6.4.2 What Is an Absorption Refrigerator Cycle? 278

6.4.3 Can I Use Solar Power for Cooling? 280

6.5 What Is a Liquefaction Process? 282

6.6 References 284

7 Where Do I Find My Numbers? 285

7.1 Introduction 285

7.2 What Kind of Numbers Are We Searching For? 286

7.2.1 How Uncertain Should the Values Be? 286

7.2.2 Should the Numbers Be Internationally Agreed upon

Values? 287

7.2.3 Should I Prefer Experimental or Predicted (Estimated)

Values? 291

7.3 Is the Internet a Source to Find Any Number? 293

7.3.1 What about Web Pages? 293

7.3.2 What about Encyclopedias and Compilations

(Databases and Books)? 294

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Contents xiii

7.3.3 What Software Packages Exist for the Calculation of

Th ermophysical Properties? 295

7.3.3.1 What Is the NIST Th ermo Data Engine? 295

7.3.3.2 What Is the NIST Standard Reference Database

23, REFPROP? 296

7.3.3.3 What Is the NIST Standard Reference Database

4, SUPERTRAPP? 297

7.3.3.4 What Is the NIST Chemistry Web Book? 297

7.3.3.5 What Is the DIPPR Database 801? 297

7.3.3.6 What Is the Landolt-Börnstein? 298

7.3.3.7 What Is NIST STEAM? 298

7.3.4 How about Searching in Scientifi c and Engineering

Journals? 298

7.4 How Can I Evaluate Reported Experimental Values? 299

7.4.1 What Are the Preferred Methods for the Measurement of

Th ermodynamic Properties? 299

7.4.1.1 How Do I Measure Density and Volume? 300

7.4.1.2 How Do I Measure Saturation or Vapor Pressure? 304

7.4.1.3 How Do I Measure Critical Properties? 306

7.4.1.4 How Do I Measure Sound Speed? 307

7.4.1.5 How Do I Measure Relative Electric Permittivity? 309

7.4.2 What Are the Preferred Methods for the Measurement of

Transport Properties? 310

7.4.2.1 How Do I Measure Viscosity? 312

7.4.2.2 How Do I Measure Th ermal Conductivity? 313

7.4.2.3 How Do I Measure Diff usion Coeffi cients? 314

7.5 How Do I Calculate Th ermodynamic Properties? 315

7.5.1 How Do I Calculate the Enthalpy and Density of a Nonpolar

Mixture? 315

7.5.2 How Do I Calculate the Enthalpy and Density of a Polar

Substance? 316

7.5.3 How Do I Calculate the Boiling Point of a Nonpolar Mixture? 317

7.5.4 How Do I Calculate the VLE Diagram of a Nonpolar

Mixture? 318

7.5.5 How Do I Calculate the VLE of a Polar Mixture? 319

7.5.6 How Do I Construct a VLE Composition Diagram? 321

7.5.7 How Do I Construct a LLE Composition Diagram? 322

7.6 How Do I Calculate Transport Properties? 322

7.7 References 325

Index 329

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xv

Preface

Th e concept of a series of books entitled Commonly Asked Questions in . . . is

inherently attractive in an educational context, an industrial context, or even a

research context. Th is is, of course, at least in part because the idea of a tutorial

on a topic to be studied and understood provides a means of seeking personal

advice and tuition on special elements of the topic that cannot be understood

through the primary medium of education. Th e primary means can be a lecture,

a text book, or a practical demonstration. Equally the motivation for the study

can be acquisition of an undergraduate degree, professional enhancement, or

the development of a knowledge base beyond one’s initial fi eld to advance a

technical project or a research activity. Th us, the spectrum of motivations and

the potential readership is rather large and at very diff erent levels of experi￾ence. As the authors have developed this book, they have become acutely aware

that this is especially the case for thermodynamics and thermophysics. Th e

subjects of thermodynamics and thermophysics play a moderate role in every

other discipline of science from the nanoscale to the cosmos and astrophysics

with biology and life sciences in between. Furthermore, while some aspects

of thermodynamics underpin the very fundamentals of these subjects, oth￾ers aspects of thermodynamics have an impact on almost every application in

engineering. In consequence, the individuals who may have questions about

thermodynamics and its applications encompass most of the world’s scientists

and engineers at diff erent levels of activity ranging from the undergraduate to

the research frontier.

Th e task of writing a single text that attempts to answer all questions that

might arise from this group of people and this range of disciplines is evidently

impossible, partly because only one section of the text is likely to be of use to

most people, and partly because the sheer extent of the knowledge available in

this subject would be beyond the scope of the book.

We have therefore not attempted to write such a comprehensive text. We

have instead been selective about the areas and disciplines we have decided to

concentrate on: thermodynamics as opposed to thermophysics, chemical ther￾modynamics in particular, with a focus on chemists, chemical engineers, and

mechanical engineers. Of course, this focus represents the bias of the authors’

own backgrounds but this also covers the content required by a large number

of those who will wish to make use of the material. In addition, the nature of

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xvi Preface

the subject is such that even within the limited scope we have set, we have not

always been able to be deductive and take a rigorous pedagogical approach.

Th us in some sections the reader will fi nd references to substantive texts

devoted entirely to topics that we merely sketch.

It is our hope that this book will be useful to some of the wide audience who

might benefi t from answers to common questions in thermodynamics. It is

often true in this subject that the most common questions are also rather pro￾found and have engendered substantial debate both in the past and sometimes

even today. We indicate a pragmatic way forward with these topics in this text,

but we would not suggest that such a pragmatic approach should stifl e further

debate.

Accordingly, the fi rst chapter answers questions about the fundamentals

of the subject and provides some simple examples of applications. Th e second

chapter briefl y expounds the basis of statistical mechanics, which links the

macroscopic observable properties of materials in equilibrium with the prop￾erties and interactions of the molecules they are composed of. Chapter 3 deals

with the applications of the second law of thermodynamics and a range of ther￾modynamic functions. In Chapter 4 we consider the topic of phase equilibrium

and the thermodynamics of fl uid mixtures, which is vital for both chemists and

chemical engineers. Chapter 5 deals with the topic of chemical reactions and

systems that are not in equilibrium. Th is leads to Chapter 6 where we illustrate

the principles associated with heat engines and refrigeration. In both cases our

emphasis is on using examples to illustrate the earlier material.

Finally, we focus on the sources of data that a scientist or engineer can access

to fi nd values for the properties of a variety of materials that allow design and

construction of process machinery for various industrial (manufacturing)

or research purposes. Even here it is not possible to be comprehensive with

respect to the wide range of data sources now available electronically, but we

hope that the data sources we have listed will provide a route toward the end

point, which will continue to extend as the electronic availability of informa￾tion continues to expand. Here we are at pains to point out that each values

obtained from a particular data source has an uncertainity associated with it.

It is generally true that the uncertainty is at least as valuable as the data point

itself because it expresses the faith that a design engineer should place in the

data point and thus, in the end, on the fi nal design.

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xvii

Authors

Marc J. Assael, BSc, ACGI, MSc, DIC, PhD, CEng, CSci, MIChemE, is a professor

in thermophysical properties. He is also the vice-chairman of the Faculty of

Chemical Engineering at the Aristotle University of Th essaloniki in Greece.

Marc J. Assael received his PhD from Imperial College in 1980 (under the

supervision of Professor Sir William A. Wakeham) for the thesis “Measurement

of the Th ermal Conductivity of Gases.” In 1982 he was elected lecturer in heat

transfer in the Faculty of Chemical Engineering at the Aristotle University of

Th essaloniki, where he founded the Th ermophysical Properties Laboratory. In

1986 he was elected assistant professor, in 1991 associate professor, and in 2001

professor of thermophysical properties at the same faculty. During the years

1991–1994 he served as the vice-chairman of the faculty and during 1995–1997

he served as the chairman of the Faculty of Chemical Engineering. In 2005,

the laboratory was renamed Laboratory of Th ermophysical Properties and

Environmental Processes, to take into account the corresponding expansion

of its activities.

In 1998, Marc J. Assael was TEPCO Chair Visiting Professor in Keio

University, Tokyo, Japan, and from 2007 he has also been holding the position

of adjunct professor in Jiaotong University, Xi’an, China. He has published

more than 250 papers in international journals and conference proceedings,

20 chapters in books, and six books. In 1996, his book Th ermophysical Properties

of Fluids: An Introduction to their Prediction (coauthored by J. P. M. Trusler

and T. F. Tsolakis) was published by Imperial College Press (a Greek edition

was published by A. Tziola E.), while in 2009, his latest book, Risk Assessment:

A Handbook for the Calculation of Consequences from Fires, Explosions and

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