Introduction to the thermodynamics of materials 6th ed

1.7 Equilibrium Phase Diagrams and Thermodynamic Components 1.8 Laws of Therm odynam ics.... 7.4 The Gibbs Free Energy as a Function of Temperature and Pressure 7-5 Equilibrium between t

David R Gaskall Dauid E Laughlin

The Laws of Thermodynamics

t Oth Law

Introduces the thermodynamic intensive variable o f temperature (T)

• 1st Law

Conservation and conversion o f energy

Defines extensive thermodynamic state variable o f internal energy (U)

Introduction to the Thermodynamics

of Materials

Sixth Edition

Introduction to the Thermodynamics

of Materials

School of Materials Engineering

Purdue University West Lafayette, IN

David E LaughlinALCOA Professor of Physical M etallurgy

Department of Materials Science and Engineering

Carnegie Mellon University

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Title: Introduction to the thermodynamics o f materia s,

David E Laughlm Tay)or & F rancis,

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Preface xvii

A uthors

Part I Thermodynamic Principles Chapter 1 Introduction and Definition of T erm s

1.1 Introduction

1.2 The Concept of State

1.3 Example of Equilibrium

1.4 The Equation of State of an Ideal G a s

1.5 The Units of Energy and W o rk

1.6 Extensive and Intensive Therm odynam ic Variables

1.7 Equilibrium Phase Diagrams and Thermodynamic Components 1.8 Laws of Therm odynam ics

1.8.1 The First Law of T herm odynam ics

1.8.2 The Second Law of Therm odynam ics

1.8.3 The Third Law of T herm odynam ics

1.9 Sum m ary

1.10 Concepts and Terms Introduced in Chapter 1

1.11 Qualitative Example Problems

1.12 Quantitative Example Problem s

P ro b le m s

3

3

4

8

9

12 13 13 16 17 17 17 17 18 19 20 21 Chapter 2 The First Law of Therm odynam ics

2.1 Introduction

2 2 The Relationship between Heat and W ork

2 3 Internal Energy and the First Law of Therm odynam ics

2.4 Constant-Volume P rocesses

2.5 Constant-Pressure Processes and the Enthalpy, H

2.6 Heat C apacity

2.7 Reversible Adiabatic Processes

2.8 Reversible Isothermal Pressure or Volume Changes of an Ideal Gas 2.9 Other Forms of W ork

2.9.1 M agnetic Work on a Paramagnetic M aterial

2.9.2 Electrical Work on a Dielectric M aterial

2.9.3 Work to Create or Extend a S urface

2.10 S u m m ary

2.11 Concepts and Terms Introduced in Chapter 2

23 23 24 25 29 30

31 37 40 41 41 42 42

43 45

C O N TEN TS

2.12 Qualitative Example Problems

2.13 Quantitative Example Problems

Problems

Appendix 2A: Note on the Sign Convention of 8w

Chapter 3 The Second Law of Thermodynamics

3.1 Introduction

3.2 Spontaneous or Natural Processes

3.3 Entropy and the Quantification of Irreversibilitỵ

3.4 Reversible Processes

3.5 Illustration of Reversible and Irreversible Processes

3.5.1 The Reversible Isothermal Expansion of an Ideal G as

3.5.2 The Free Expansion of an Ideal Gas •

3.6 Further Differences between Reversible and Irreversible Expansion 3.7 Compression of an Ideal G as

3.7.1 Reversible Isothermal Compression

3.8 The Adiabatic Expansion of an Ideal Gas

3.9 Summary Statements

3.10 The Properties of Heat Engines

3.11 The Thermodynamic Temperature Scalẹ

3.12 The Second Law of Thermodynamics

3.13 Maximum Work

3.14 Entropy and the Criterion for Equilibrium

3.15 The Combined Statement of the First and Second Laws of Thermodynamics

316 Summarỵ

317 Concepts and Terms Introduced in Chapter 3

3-1^ Qualitative Example Problems

^49 Quantitative Example Problems

Problems

Chapter 4

The Statistical Interpretation of Entropỵ

4.1 Introduction c - t

4.2 Entropy and Disorder on an Atomic v ca e

4.3 The Concept of Microstatẹ

4.4 The Microcanonical Approach *" Sites with Different 4.4.1 Identical Particles on Distinguishablệ

Assigned Energies Vniffering Moms »n a C r y s ta l-4.4.2 Configurational Entropy °1 Snins on an 4.4 J c mU w a*™*»

Array of Atoms

4 5 The Boltzmann Distribution

45 47 51 54 57

57

58

59

„61

„61 62 63 64 65 65 66 67 67 71 74 76 78 79 81 83 83 85 90

„9 3

„93

„ 9 4

„ 9 5

„ 9 6

„96

„98 102 104

C O N TEN TS

ix

4.6 The Influence of Tem perature

4.7 4.8 Therm al Equilibrium and the Boltzmann E q u atio n

Heat Flow and the Production of E n tro p y

4.9 4.10 S u m m ary

Concepts and Terms Introduced in Chapter 4 113

4.11 4.12 Qualitative Example Problem s

Quantitative Exairmle Problem s 115

P ro b le m s 116

119

Chapter 5 Fundam ental Equations and Their Relationships 1

5.1 Introduction

5.2 The Enthalpy, H

5.3 The Helmholtz Free Energy, A

5.4 The Gibbs Free Energy, G

5.5 The Fundam ental Equations for a Closed System 129

5.6 The Variation of the Composition within a Closed System 131

5.7 The Chemical Potential 131

5.8 Therm odynam ic R elations 134

5.9 M axwell’s R elations 135

5.10 Examples of the Application of Maxwell R elation s 137

5.10.1 The First TdS E q u a tio n 137

5.10.2 The Second TdS E quation 139

5 10.3 S and V as Dependent Variables and T and P as Independent Variables 141

5.10.4 An Energy Equation (Internal Energy) 142

5.10.5 Another Energy Equation (E nthalpy) 143

5.10.6 A M agnetic Maxwell R elation 143

5.10.7 S, K and M with Independent Variables T, P, and M 144

5.1 1 A nother Important Form ula 145

5.12 The G ibbs-H elm holtz E q u atio n 145

5.13 S um m ary 147

5.14 Concepts and Terms Introduced in Chapter 5 148

5.15 Qualitative Example Problem s 148

5.16 Quantitative Example Problem s 150

P ro b le m s 152

Chapter 6 Heat Capacity, Enthalpy, Entropy, and the Third Law of T herm odynam ics 155

6.1 Introduction 155

6.2 Theoretical Calculation of the Heat C apacity 156

6.3 The Empirical Representation of Heat C apacities 162

6.4 Enthalpy as a Function of Temperature and C om position 162

X C O N TE N TS

Thermodynamics 172

6.5.1 Development of the Third Law of Thermodynamics 172

6.5.2 Apparent Contradictions to the Third Law of Thermodynamics 175

6.6 Experimental Verification of the Third Law 177

6.7 The influence of Pressure on Enthalpy and Entropy 182

6.8 Summary 184

6.9 Concepts and Terms Introduced in Chapter 6 185

6.10 Qualitative Example Problems 1 ^

6.11 Quantitative Example Problems 187

Problems ^ 3

Appendix 6A 1^4 Part II Phase Equilibria Chapter 7 ^ 199 Phase Equilibrium in a One-Component System

199

7.1 Introduction n 7.2 The Variation of Gibbs Free Energy with Temperature at Constan ^ Pressure

7.3 The Variation of Gibbs Free Energy with Pressure at Constant Temperature

7.4 The Gibbs Free Energy as a Function of Temperature and Pressure 7-5 Equilibrium between the Vapor Phase and a Condensed P hase

7.6 Graphical Representation of Vapor Phase and Condensed Phase Equilibria

7.7 Solid-Solid Equilibria

7-S The El feet of an Applied Magnetic Field on the P-T D iag ram

7-9 Sum m ary /

7 J0 Concepts and Terms Introduced in Chapter 7

' Qualitative Example Problems

P«)blc.ma.r! ,.,a.tiVe EXample Pr°bIemS

.204 205 2 1 0 212 .212 217 218 .219 .220 222 226 Chapter 8 The Behavior of Gases 229

8.1 Introduction 2 2 9 8.2 The P-V-l Relationships of Gases ^

8.3 The Thermodynamic Properties of Ideal Gases and Mixtures o Ideal Gases 23U 8.3.1 Mixtures ofldeal Gases 230 8.3.1.1 Mole Fraction 2 3 ^

XI

8 3.1.2 Daltons L a w of P a r tia l P r e s s u r e s

8 3.1.3 Partial Molar Quantities_

8 3 9 The Enthalpy o f Mixing o f Ideal G ^ - - - —

8 l l The Gibbs Free Energy o f M m n g o f deal G ases

g a The r 4 Deviation From Ideality ana n q « s The Van Der Waals Fluid " " ^ 8.6 Other Equations of State for^Nom » Nonideal G ases ' " ' " r 7 Further Therm odynam ic Treatmen g.8 Summary ; T ’^rhonter 8

8 9 Concepts and Terms Introduced i P 8.10 Qualitative Example Problem s

8.11 Quantitative Example Problem s

P ro b le m s

231

232

234

235

.236 236 240 250 251 259 260 260 261 265 Chapter 9 The Behavior of Solutions 267

9.1 Introduction 267

9.2 Raoult’s Law and H enry’s L a w 267

9.3 The Therm odynam ic Activity of a Component in S o lu tio n 271

9.4 The G ibbs-D uhem E q u a tio n 273

9.5 The Gibbs Free Energy of Formation of a Solution 275

9.5.1 The M olar Gibbs Free Energy of a Solution and the Partial Molar Gibbs Free Energies of the Components of the Solution 275

9.5.2 The Change in Gibbs Free Energy due to the Formation of a S o lution 277

9.5.3 The M ethod of Tangential Intercepts 278

9.6 The Properties of Ideal Solutions 279

9.6.1 The Change in Volume Accompanying the Form ation of an Ideal Solution 279

9.6.2 The Enthalpy of Formation of an ideal S o lu tio n 281

9.6.3 The Entropy of Formation of an Ideal Solution 282

9.7 Nonideal Solutions 285

9.8 Application of the G ibbs-D uhem Relation to the D eterm ination of A c tiv ity 288

9.8.1 The Relationship between H enry’s and R aoult’s L aw s 289

9.8.3 Direct Calculation of the Total Molar Gibbs Free Energy of M ixing 290

9.9 Regular Solutions 292

9.10 A Statistical Model of S olutions 298

9 10.1 Extensions of the Regular Solution Model: The Atomic Order Param eter 303

9.10.2 Including Second-Neighbor Interactions 306

xii C O N TE N TS

9.11 Subregular Solutions

9.12 Modified Regular Solution Model for Application to Polymers 9.12.1 The Flory-Huggins Model

9.13 Summary

9.14 Concepts and Terms Introduced in Chapter 9

9.15 Qualitative Example Problems

9.16 Quantitative Example Problems

Problems

307 309 309 310 313 313 315 317 Chapter 10 Gibbs Free Energy Composition and Phase Diagrams of Binary Systems 10.1 Introduction

10.2 Gibbs Free Energy and Thermodynamic Activity

10.3 Qualitative Overview of Common Binary Equilibrium Phase Diagrams

10.3.1 The Lens Diagram: Regular Solution Model

10.3.2 Unequal Enthalpies of Mixing

10.3.3 The Low-Temperature Regions in Phase D iagram s

10.3.4 The Eutectic and Eutectoid Phase Diagrams

10.3.5 The Peritectic and Peritectoid Phase Diagrams

10.4 Liquid and Solid Standard States

10.5 The Gibbs Free Energy of Formation of Regular Solutions

10.6 Criteria for Phase Stability in Regular Solutions

10.7 Phase Diagrams, Gibbs Free Energy, and Thermodynamic A ctivity

10.8 The Phase Diagrams of Binary Systems That Exhibit Regular Solution Behavior in the Liquid and Solid States

10.9 Summary

10.10 Concepts and Terms Introduced in Chapter 10

10.11 Qualitative Example Problems

10.12 Quantitative Example Problems

Problems / .

Appendix 10A

Appendix .

.321 322 3 2 4 3 2 4 325 326 327 329 331 338 341 3 4 6 356 362 3 6 4 3 6 4 3 6 6 371 373 37 6 Part HI Reactions and Transformations of Phases Chapter 11 .381

Reactions Involving Gases 381

11.1 Introduction i-uriiim C o n stan t 382

11.2 Reaction Equilibrium in a Gas Mixture and the Equ 1 . 388

11.3 The Effect of Temperature on the Equili num o n ' .390

11.4 The Effect of Pressure on the Equilibrium ons , Entropy 391

11.5 Reaction Equilibrium as a Compromise between Enthalpy andbHtropy ^

11.6 Reaction Equilibrium in the System S 0 2(g) 3<g> ug)

xiii

11.6.1 The Effect of Tem perature

11.6.2 The Effect of P re ssu re

11.6.3 The Effect of Changes in Temperature and Pressure

11.7 Equilibrium in H20 - H 2 and C 0 2- C 0 M ix tu res G

11.8 S u m m a r y .

11.9 Concepts and Terms Introduced in Chapter 11

11.10 Qualitative Example Problem s

11.11 Quantitative Example Problem s

P ro b lem s 404All) Reactfons Involving Pure Condensed Phases and a Gaseous Phase

12.2 Reaction Equilibrium in a System Containing Pure Condensed Phases and a Gas P h a s e 77

12.3 The Variation of the Standard Gibbs Free Energy Change with T em perature 419

12.4 Ellingham D iagram s 422

12.5 The Effect of Phase Transform ations 430

12.5.1 Example of the Oxidation o f C opper 431

12.5.2 Example of the Chlorination of Iron 433

19 The Oxides of C arbon 43d 12 6 1 The Equilibrium 2CO + O, = 2 C 0 2 440

12.7 Graphical Representation of Equilibria in the System M e ta l-C a rb o n - ^ O xygen 447

12.9 Concepts and Terms introduced in Chapter .448

12.10 Qualitative Example Problem s

12.11 Quantitative Example Problem s ^

P ro b lem s

Appendix 12 A 4sq Appendix 12B

Chapter 13 Reaction Equilibria in Systems Containing Components in Condensed Solution 467

13.1 Introduction 467

13.2 The Criteria for Reaction Equilibrium in Systems C ontaining Components in Condensed Solution 469

13.3 Alternative Standard States 477

13.4 The Gibbs Equilibrium Phase R u le 484

13.5 Phase Stability D iagram s 489

13.6 Binary Systems Containing C om pounds 503

13.7 Graphical Representation of Phase E quilibria 516

13.7.1 Phase Equilibria in the System M g -A I-0 516

13.7.2 Phase Equilibria in the System A l-C -O -N Saturated with Carbon 520

13.8 The Formation of Oxide Phases of Variable Composition 523

13.9 The Solubility of Gases in Metals 532

13.10 Solutions Containing Several Dilute Solutes 537

13.11 Summary 547

13.12 Concepts and Terms Introduced in Chapter 13 550

13.13 Qualitative Example Problems 550

13.14 Quantitative Example Problems 551

Problems 5 61 xiv C O N TE N TS Chapter 14 Electrochemistry

14.1 Introduction

14.2 The Relationship between Chemical and Electrical Driving Forces

14.3 The Effect of Concentration on EM F

14.4 Formation Cells

145 Concentration Cells

14.6 The Temperature Coefficient of the EMF

14.7 Thermal Energy (Heat) Effects

14.8 The Thermodynamics of Aqueous Solutions

14-9 The Gibbs Free Energy of Formation of Ions and Standard Reduction Potentials

14.9.1 Solubility Products

14.9.2 The Influence of Acidity

14.10 Pourbaix Diagrams

14.10.] The Pourbaix Diagram for Aluminum

14.10.2 The Equilibrium between the Two Dissolved Substances

14.10.3 The Equilibrium between the Two Solids

14.10.4 One Solid in Equilibrium with a Dissolved Substance

14.10.5 The Solubility of Alumina in Aqueous Solutions

l4-ll Summary

■.12 Concepts and Terms introduced in Chapter 14

4- 3 Q u a lity Example Problem

Chapter 15 Thermodynamics of Phase T ransform ations 6 2 1 15.1 Thermodynamics and Driving Force •••• ^22

15.1.1 Phase Transformations with N o C h an ge in Composition 6 2 2 15.1.2 Phase Transformations w ith C hange in C o m p o s it io n 6 2 4 15.2 Use o f the T, Curves 6 2 6

.567 567 569 574 57 6 577 584 586 587 591 .596 .599 .601 .603 .60 4 .605 .607 .609 611 .613 .613 .6 1 4 .618

x v

15.2.1 M artensitic T ransform ation

15.2.2 Massive T ransform ations

15.2.3 The Formation of Amorphous Phases from the r *• .628

15.3 Surface E nergy lciu id 629

15.3.1 Equilibrium S h a p e .630

15.4 Nucléation and Surface Energy

15.4.1 Homogeneous N ucléation .632

15.4.2 Heterogeneous N ucléation 632

15.5 Capillarity and Local E quilibrium ~

) 5.6 Therm odynam ics of the Landau Theory of Phase Transform ations

15.7 S um m ary ^

15.8 Concepts and Terms Introduced in Chapter 15

15.9 Qualitative Example Problem s

P ro b le m s

Appendix A: Selected Therm odynam ic and Therm ochem ical Data Appendix B: Exact Differential E quations

Appendix C: The Generation of Additional Therm odynam ic Potentials as

Legendre T ransform ations

N om enclature ^ g Answers to Selected Problem s

Index

In preparing this new edition, I have endeavored to retain the substance o f the previous five editions while adding some flavors of my own These additions are ones which reflect my research interests (in macjnetism and phase transform ations) and are also relevant to current m aterials science students A dditions to this book

include the role of work term s other than P-V wor (e.g., m agnetic work), along with

their attendant aspects o f entropy, Maxwell relations, and the role o f such applied fields on phase diagrams Also, there is an increased emphasis on the therm odynam ­ics of phase transformations These topics are sprinkled throughout the text, and an entirely new chapter (Chapter 15) has been included which collects specific therm o­dynamic applications to the study o f phase transformations To m ake the agreed-

Perhaps they will see the light of day in the seventh edition

The text is written for undergraduate m aterials science students and can be uti­lized by m aterials-related graduate students who have not taken such a course in their undergraduate studies It has been more than 40 years since I used the first edi­tion of the text when teaching my first class in therm odynam ics at Carnegie Mellon University I also used the text in the mid-1990s in several sum m er school classes on therm odynam ics at CMU Experience makes me aware that it is impossible to make

it through the entire text in a one-sem ester course In this edition, I have divided the

Principles”) and as much as possible of the second section ( Phase Equilibria ) be

h eluded in a one-semester undergraduate course The third section ( f a c t i o n s and Transformations”) can make its way into other courses of the curriculum that deal

requisite for any course that utilizes tnecompu

learned at least half as much from me as I have fiom im

XVII

xviii PREFACE

some 4 years after David’s death May the text continue to train materials students well in the basics of thermodynamics

David E Laughlin

ALCOA Professor o f Physical Metallurgy Department of Materials Science and Engineering

Carnegie Mellon University

that you find Send all tvDos'tnr v u !'St °f typos’ Please feel free to send me any

lypos to Gaskell.Laughlin@gniaii.c0m

David R Gaskell received a BSc in metallurgy and technical chem istry from the

University of Glasgow, Scotland, and a PhD from M cMaster University, Ham ilton

ON Dr Gaskell’s first faculty position was at the University of Pennsylvania, where

he taught from 1967 to 1982 in metallurgy and materials science In 1982 he was recruited at the rank of professor by Purdue University, West Lafayette, IN where he taught until 2013 During Dr Gaskell’s career, he served as a visiting professor at the National Research Council of Canada, Atlantic Regional Laboratory, Halifax, NS (1975-1976), and as a visiting professor at the G C W illiams Co-operative Research Centre for Extraction Metallurgy, in the Department of Chemical Engineering, University of Melbourne, Australia (1995) He also held a position during his sab­batical in Australia as a visiting scientist at the Commonwealth Scientific and Industrial Research Organisation (CSIRO) in Clayton, Victoria Dr Gaskell authored

the textbooks Introduction to Metallurgical Thermodynamics, Introduction to

the Thermodynamics o f Materials, and Introduction to Transport Phenom ena in Materials Engineering.

David E Laughlin is the ALCOA Professor of Physical M etallurgy in the

Department of Materials Science and Engineering of Carnegie Mellon University (CMU), Pittsburgh, PA, and also has a courtesy appointment in the Electrical and

Computer Engineering Department He was the principal editor of M etallurgical

and Materials Transactions from 1987 to 2016 David is a graduate of Drexel

University, Philadelphia, PA (1969), and the Massachusetts Institute of Technology, Cambridge, MA (1973) He is a fellow of the M inerals, Metals and M aterials Society (TMS), an honorary member of the American Institute of M ining M etallurgical, and Petroleum Engineers (AIME), and a fellow of ASM International He is also the recipient of several CMU awards for teaching and research excellence and was named a distinguished scientist of the TMS Electronic, Magnetic and Photonic Materials Division He has authored more than 400 technical publications in the field of phase transformations, physical metallurgy, and magnetic m aterials, has been awarded 12 patents and has edited or coedited seven books, including the fifth

edition of Physical Metallurgy.

PART I

Thermodynamic Principles

CHAPTER 1 Introduction and Definition of Terms

1.1 INTRODUCTION

T he term therm odynam ics is related to the two G reek w ords therm e and

d ynam ikos, which translate into English as “ heat” and “ pow er” (or “ m ovem ent” ),

respectively Therm odynam ics is the physical science that focuses on the relation­ship betw een energy and work as well as the equilibrium states and variables o f system s that are being investigated Im portantly, therm odynam ics defines heat and identifies it as the process in which energy is transferred from one region to another

down a tem perature gradient In this text, we w ill m ainly use the phrase therm al

energy to identify this form o f energy transfer, but som etim es the word heat will be

used Therm odynam ics deals with the conservation of energy as well as the conver­

sion of the various form s o f energy into each other or into work T herm odynam ics

is concerned with the behavior o f and interactions betw een portions o f the universe

denoted as system s and those portions o f the universe called the surroundings or the environm ent The system is that part o f the universe wc w ish to investigate in

detail, and the surroundings is that part of the universe outside the system w hich may interact w ith it by exchanging energy or matter T he system m ay perform work on the surroundings or have work perform ed on it by the surroundings T he boundary

or wall betw een the system and the surroundings is w hat allow s such interactions

In what we will call sim ple therm odynam ic system s, the surroundings interacts with

the system only via pressure and tem perature changes T h e com position rem ains constant in sim ple systems

It is convenient to characterize systems by the k inds ol interactions that are allow ed betw een them and their surroundings

1 Iso la te d sy ste m s: In th ese sy ste m s, no w ork is d o n e o n or b y th e sy ste m In ad d i­

tio n , e n e r g y or m atter m ay not en ter or lea v e it T h u s, th e e n e r g y o f th e s e sy ste m s

r em a in s co n sta n t, as d o e s th e o v e r a ll c o m p o s itio n Is o la te d s y s te m s are th erefore

u n a ffe c te d by c h a n g e s in th e su rrou n d in gs.

2 C lo se d sy ste m s: T h e se are sy ste m s w h ich m ay r e c e iv e (or g iv e o f f ) en erg y from

(or to) th'c su rro u n d in g s T h e b o u n d a ries are c a lle d d a th e r m a l: that is th ey a llo w

th erm al e n erg y to tran sfer th rou gh th em into or o u t o f th e sy s te m H ow ever, the

3

INTRODUCTION t o t h e t h e r m o d y n a m ic s o f MATERIALS, SIXTH EDITION

boundaries are impermeable to matter; hence, the amount o f matter is con.

remain constant The boundaries are both permeable and diatherma

The boundaries or walls of the system are cla ssified as fo llo w s

• Adiabatic: No thermal energy can pass through.

• Diathennai. Thermal energy can pass through.

• Permeable: Matter can pass through.

• Semipermeable: Some components are able to pass through, w 1 e o

It is evident that when evaluating a system , it is im p o rta n t th at i

The macroscopic property of system s c a lle d te m p e ra tu re is a ^ ^ e c h a n i _

tory physics courses The discovery that m ech an ical en e r g y c o u c ^ t jie r _ thermal energy (via friction) was an im portant early step in th e d e v e o f o t ^ e r modynamics Later, the conversion o f thermal en ergy in to m e c h a n i c a ^ ^ d i s c u s s e d

in the introduction to the First Law o f T h erm od yn am ics in C h a p ter • ^ jn te r e s t to The system may be a machine (heat engine) or a d e v ic e (trans u c e ^ c o m p o s e d

of matter, which is anything that has m ass and o c c u p ie s sp a c e M a ® ^ s(jc h temperature, pressure, and chemical com position, as w e ll as p h y stc a P ' ^ ^ c e n t r a l

as thermal expansion, compressibility, heat capacity, v is c o s ity , an s u r r o u n d aim of applied thermodynamics is the determ ination o f th e e f f e c t o j n te r a c t s

with the system by transferring or receiving various io rm s o f e n e r g y 01^ ^ ^ ^ ^

it, another locus of applied therm odynam ics is the e sta b lish m e n t o „ u e n c e s w h ic h which exist between the equilibrium state o f a given sy ste m and th e in

have been brought to bear on it.

1.2 THE CONCEPT OF STATE

If it w^Un^amema^ COnccP* *n thermodynamics is that of the therm odynam ic state.

weie possible to know the masses, velocities, positions, and all modes o f m otion trans ational, rotational, etc.) of all of the constituent particles in a system , this

now edge would serve to describe the microscopic state of the system, w hich, in

turn, would determine, in principle, all of the thermodynamic variables o f the sys­tem that can be measured (energy, temperature, pressure, etc.) For system s with macroscopic dimensions, this would entail more than 1024 coordinates, w hich is

IN TR O D U C TIO N AND D EFIN ITIO N OF TER M S

5

substance of fixed com position is being considered, the fixing of the* val'ues^of i

variables Thus, only two therm odynam ic variables are independent which c

o f t h e o t h e r v a r ia b l e s a r e dependent variables T h e t h e r m o d v n n m ^ * ^ ,

system is thus uniquely determ ined when the values o f the two independent vari­

however, when more independent variables are needed— for exam ple when therm odynam ic fields other than tem perature and pressure are present Such fields include electric or m agnetic fields

The values of the therm odynam ic variables of a system are not functions of the history of the system; that is, they are independent of the path over w hich the process has taken the system in changing it from its previous state to its present state These

therm odynam ic variables are thus intrinsic to the state of the system Such therm o­ dynam ic variables are functions of state and can be expressed as exact differentialsr

o f their dependent variables There are, of course, tim es when the system has proper­

ties which do depend on its history; these properties are com m only called extrinsic

properties They are not equilibrium properties of the system; given time, they may change It should be noted that some of these extrinsic properties can be m anipulated

to produce m aterials with optim um chaiacteiistics

Consider the volume, V, of 1 mole of a pure gas T he value of the volume is

dependent on the values o f the pressure, P, and tem perature, T, o f the gas The rela­ tionship betw een the dependent variable V and the independent variables P and T

can be expressed as

In a three-dim ensional diagram , the coordinates of which are volum e, pressure, and

tem perature, the points in V-P-T space which represent the equilibrium states of

existence of the system lie on a surface This is shown in Figure 1.1 for 1 mole of a simple gas Fixing the values of any two of the three variables fixes the value of the third variable of the system when it is in equilibrium

Consider a process which changes the state of the gas from state 1 to.state 2 This process causes the volume of the gas to change by

:!; P ie r r e M a u r ic e M a r ie D u h e m ( 1 8 6 1 - 1 9 1 6 )

ol which, 1 -> a -> T and 1 -* b -+ 2, are shown in Figure

W = W ^ a + W a^ 2

W ={Va-Vi) + (V2-V a)

&V V2-V^

\ - > Cl occurs at the constant pressure, P,

a -* 2 occurs at the constant temperature, T ,

We can express these changes as

and

INTRODUCTION AND DEFINITION OF TERMS

the gas between the states This is because the volume of the gas s a state function

and Equation 1.4 is an exact differential of the volume, which is a therm odynam ic

^ T h e 'p a r t i a l differentials which relate the change in volume to changes in the

intensive thermodynamic variables (P and T) are related to the properties of the

gas— namely,

pr = - i f — 1 , the isothermal compressibility with dimensions of P~'

Equation 1.1:

(1.4)

and

8 INTRODUCTION TO THE THERMODYNAMICS OF MATERIALS, SIXTH EDITION

Thus, the complete differential of Equation 1.4 can be written as

dV = a V d T -§ TVdP

This equation can be easily integrated over the ranges in T and P, where p7 and oc

are assumed to be constant

In Figure 1.1, the equilibrium states of the system are shown to lie on a surface

in V-P-T space This means that equilibrium exists at unique combinations of P and

T such that P and T satisfy the equation for the V(P,T) surface.

A particularly simple system is illustrated in Figure 1.2 In this figure, 1 mole of

a gas is shown to be contained in a cylinder by a movable piston The system is at equilibrium when

1 The pressure exerted by the gas on the piston equals the pressure exerted b y the

piston on the gas.

2 The temperature of the gas is the same as the temperature o f the surroundings (p ro­ vided that thermal energy can be transferred through the boundary o f the cy lin d er, that is, the boundaries of the cylinder are diathermal).

The state of the gas is thus fixed, and equilibrium occurs as a result of the estab­lishment of a balance between the tendency of the external influences acting on the system to cause a change in the system (i.e., the temperature and pressure) and the tendency of the system to resist such a change Fixing the pressure of the gas at P,

Figure 1.2 One mole of a gas is shown to be contained in a cylinder by a p is to n T h e w a lls

of the cylinder are diathermal, and W is the m ass that is e x e rtin g p re s s u re o n

1.3 EXAMPLE OF EQUILIBRIUM

Gas

and T x determ ines the state o f the system and hence fixes the

V\ I f, a t c o n s t a n t t e m p e r a t u r e , b y a s u i t a b le i n c r e a s e in t h e at t h e v a lu e

piston, the pressure exerted on the gas is increased to P 0 (FioUre^l * ^ ace<^ on

gas causes the piston to move into the cylinder This process dec ^ CXerte<^ on t*ie

until equalization o f the pressures is restored As a result o f this pr F S ° n t*ie P*ston

o f the gas decreases from V, to Vb Therm odynam ically, the i s o t h e r m a l^ V° lu n lf pressure from P , to P 2 changes the state of the system from state I (c h ^ °

p \ * T \) to s t a t e b ( c h a r a c t e r iz e d b y P 2, T x\ a n d th e v o l u m e , a s a d e p e n ^ n t T a i f a b k '

decreases from the value V , to Vh T his shows that work was nerfv^™ ^

by the piston

ture gradient across the cylinder wall causes the transfer o f therm al ener» from the

pressure P 2 causes the expansion o f the gas, w hich pushes the piston out o f the c 1 inder W hen the gas is uniform ly at the tem perature 7 \, the volum e o f the oa s is V Again, therm odynam ically, the increasing of the tem perature from T t o V at the constant pressure P 2 changes the state o f the system from state b (P^ p ) to ^ ta te 2 (P 2, P 2), and the volume as a dependent variable increases from Vb in the state b to

V2 in the state 2 In this case, work was perform ed on the piston by the expanding

gas Since volume is a state function, the final volume V2 w ould be the sam e if the state were first changed from 1 to a and then from a to 2

IN T R O D U C T IO N AND D EFIN IT IO N O F T E R M S

9

1.4 THE EQUATION OF STATE OF AN IDEAL GAS

The pressure-volum e relationship of a gas at constant tem perature was determ ined

experim entally in 1660 by Robert Boyle (1627—1691), who found that, at constant T ,

Рос —

V

T his is know n as Boyle* s law Similarly, the volum e—tem perature relationship o f a gas

at constant pressure was determ ined experim entally in 1787 by Jacques-A lexandre-

C esar Charles (1746-1823) This relationship, which is know n as C h a rle s* la w , is

that, at constant pressure,

10 INTRODUCTION TO THE THERMODYNAMICS OF MATERIALS, SIXTH EDITION

at constant P produce straight lines in a V versus T plot These sections are shown

in Figure 1.3a and b

In 1802, Joseph-Luis Gay-Lussac (1778-1850) observed that the therm al

coefficient of what were called permanent gases was a constant Previously, we

noted that the coefficient of thermal expansion, a, is defined as the fractional increase of the volume of the gas, with the change in tem perature at constant pressure; that is,

Figure 1.3 (a) The variation, with pressure, of the volume of 1 mole of ideal g a s a t 3 0 0 a n d

1000 K (b) The variation, with temperature, of the volum e of 1 m o le of id e a l g a s

IN T R O D U C T IO N AND D E F IN IT IO N O F T E R M S

11

a =

(1.5)

w here V is the volum e o f 1 m ole o f the gas at 0 C G ay -L ussac o b ta in e d a value

o f 1/267 for a , but m ore refined ex p erim en tatio n by H e n ri V ic to r R eg n au lt (1810-1878) in 1847 show ed a to have the value 1/273 L ater, it w as found that the accu racy w ith w hich B oyle’s and C harles laws d e scrib e the b e h a v io r o f d if­ferent gases varies from one gas to another G enerally, gases w ith low er b o ilin g

po in ts obey the laws m ore closely th an do gases w ith h ig h er b o ilin g points It was also found that the law s are m ore closely obeyed by all gases as the p ressu re o f the gas is d e creased It was thus found convenient to invent a h y p o th etic a l gas

w hich obeys B oyle’s and C h a rle s’ laws exactly a t a ll te m p e ra tu re s a n d p r e s ­

su res T h is hyp o th etical gas is ca lled the p e r fe c t or id ea l g a s , and it has a value

T he existence o f a finite coefficient o f th erm al expansion th erefo re sets a lim it

on the therm al contraction o f the ideal gas; that is, since a = 1 /2 7 3 1 5 , then the fractional d ecrease in the volum e o f the gas, p e r d egree d e c re a se in tem p eratu re,

is 1/273.15 o f the volum e at 0°C T hus, at -2 7 3 1 5 °C , the volum e o f the gas

w ould be zero, and hence the lim it o f tem p e ra tu re d ecrease, -2 7 3 1 5 °C , is the absolute zero o f tem perature T his defines an absolute scale o f tem p e ra tu re ca lled

the ideal gas tem perature s c a le , w hich is related to the a rb itra ry C elsius scale by

the equation

T (degrees absolute) = T (degrees C e lsiu s)+ 273.15

A com bination of Boyle’s law:

P 0 = standard pressure (1 atm osphere [atm])

V{PyT) = volume at pressure P and tem perature T

gives

P V = P0V

INTRODUCTION TO THE THERMODYNAMICS OF MATERIALS, SIXTH EDITION

From Avogadro’s (Lorenzo Avogadro, 1776-1856) hypothesis, the volume per

gram-mole* of all ideal gases at 0°C and 1 atm pressure (termed standard tem pera­

ture and pressure [STP]) is 22.414 liters Thus, the constant in Equation 1.6 has the

value

P0Va _ 1 atm-22.414 liters = 0 082057

This constant is given the symbol R, the gas constant, and, bein^> aPP' ^

idea! gas law Because of the simple form of it s equation o s a

be assigned a single-valued function to designate the intensity o i s

the temperature gradient is nonzero, there is a tendency to

the high-temperature system to the low-temperature system, commonly « ilteo tear

transfer We will see that temperature is a measure of the energy o

which compose the system

1.5 THE UNITS OF ENERGY AND WORK

The unit liter atm occurring in the units of R is an energy term W ork is done

when a force moves a body through a distance Work and energy have the dim en­sions force-distance Pressure is force per unit area; hence, work and energy can have

is the joule, which is the work done when a force of 1 newton moves a distance o f 1 meter Liter-atm are converted to joules as follows:

1 atm = 101,325

meters2

ra vnoofiro1 s number of molecules ot the

A gram-mole (g-mole or mole) o f a substance is the mass g e-mole of C has a mass of 12 g substance expressed in grams Thus, a g-m ole o f 0 2 has a mass o f 3 2 g, a g mo

and a g-mole of CO, has a mass of 4 4 g.

IN T R O D U C T IO N AND D E F IN IT IO N O F T E R M S

13

M ultiplying both sides by liters ( 10~3 m eters3) gives

1 liter • atm = 101.325 newton-meters = 101.325 j ouje

discussed as they arise in the course or the text

1.6 EXTENSIVE AND INTENSIVE THERM ODYNAM IC VARIABLES

T herm odynam ic state variables are either extensive or in te n siv e Extensive vari­

ables have values which depend on the size of the system , w hereas values o f intensive variables are independent o f the size o f the system Volume is an extensive variable, and tem perature and pressure are intensive variables T he values o f extensive vari­ables, expressed per unit volume or unit m ass o f the system , have the characteristics

o f intensive variables; for example, the volum e per unit m ass (specific volume) and the volume per mole (m olar volume) are variables whose values are independent o f

the size of the system For a system o f n moles o f an ideal gas, the equation o f state is

P V ' = n R T

where V" is the total volume o f the system Per mole ol the system , the equation o f state reduces to Equation 1.7:

P V = R T

where V, the m olar volume of the gas, equals V '/n -T h e m olar volum e o f an ideal gas

at Standard Tem perature Pressure (STP) is 22.414 liters

1.7 EQUILIBRIUM PHASE DIAGRAMS AND THERMODYNAMIC COMPONENTS

O f the several ways to graphically represent the equilib riu m states o f the exis­

tence of a system , the constitution or equilibrium phase diagram is the rhost popular

and convenient The com plexity of a phase diagram is d eterm in ed prim arily by the

num ber of com ponents which occur in the system, w here com ponents are chem i­

cal species of fixed com position T he sim plest com ponents are chem ical elements

INTRODUCTION TO THE THERMODYNAMICS OF MATERIALS, S IX TH E D ITIO N

'9 e 1.4 Schematic representation of part of the p res su re -tem p eratu re equilibrium p h a s e

9 or H20 The melting point is designated as m an d the boiling point as b.

St01C^ om^ c cornPounds Systems are prim arily categorized by the nu m ber o f

(quaternary) systems, and so on.

'^hT ^ aSe ^ a£rarn °f a one-component system with only two independent state a es ,s a two-dimensionaI representation of the dependence of the equilibrium Wlt ^ 6 tW° inc^ePenc^ent variables as the coordinate axes Pressure and tem - U,r?*dre norrna^^ chosen as the two independent variables Figure 1.4 shows a

J * ? ' ™ ^ area A 0B ' the equilibrium state of the H 20 is a liquid Sim ilarly,

the kc \V 1 6 ^ an^ ^ 0W l^e COB curve, the equilibrium states are, respectively,

if V 1S Sai t0 ^ ^<)mo8eneous' that is, it consists of only one phase o f water

another StM L QUV^ A 0 ' the 1!quid and solid H20 coexist in eq u ilib riu m w ith o n e

variable*-" ^nitc! vo ume ln the physical system within which the th e rm o d y n a m ic

in D'K^inr* fC Uni ° rrn^ constant; that is, they do not experience any ab ru p t c h a n g e

ih c c w H ° ne P°!m in the V0,Ume t0 an°

ther-m iinion CUr' C e u ,cPresents t^le sither-multaneous variation of P and T req u ired fo r th e

the i in a,nCe ° 1 e etiu'iihnum between solid and liquid H 20 , and thus rep resen ts

* * ue^Cc °* pressure on the melting temperature of ice Similarly, the cu rv es C O

e maintenance of the equilibrium between solid and vapor H 20 and betw een liq u id

U)

INTRODUCTION AND DEFINITION OF TERMS 15

and vapor H->0 The curve CO is thus the variation, with temperature, of the saturated

vapor pressure of solid ice or alternatively, the variation, with pressure, of the sublima­

tion temperature of water vapor The curve OB is the variation, with temperature, of

the saturated vapor pressure of liquid water or, alternatively, the variation, with pres­sure, of the dew point of water vapor The three two-phase equilibrium curves meet

at the point O (the triple point), which thus represents the unique values of P and T

required for the establishment of the three-phase (solid + liquid + vapor) equilibrium

The path amb indicates that if a quantity of ice is heated at a constant pressure

of l atm, melting occurs at the state m, which, by definition, is the normal melting temperature of ice Boiling occurs at the state b, which is the normal boiling tem ­

perature of water

We have seen that phases may be solids, liquids, or gases Gases are single-phase solutions and, hence, are homogeneous phases Liquids may be homogeneous and single phase or they may divide into regions of different composition and therefore be composed of two or more phases Likewise, solids may be single phase or may also

be composed of more than one phase It is common to call a metal composed of more than one component an alloy Alloys may be single phase or multiphase A single­phase crystalline alloy consists of two or more components distributed randomly on

a single crystal structure Such single-phase alloys are called solid solutions.

If the system contains two components, a composition axis must be included and, consequently, the complete diagram is three-dimensional, with the coordinates composition, temperature, and pressure.' In most cases of condensed phases, how­ever, it is sufficient to present a binary phase diagram as a constant-pressure sec­tion of the three-dimensional diagram The constant pressure chosen is normally

l atm, and the coordinates are composition and temperature Figure 1.5, which is

a typical simple binary phase diagram, shows the phase relationships occurring in

X Y

Weight percent

Figure 1.5 T h e tem p e ra tu re com position equilibrium p h a s e d ia g ra m for the system

INTRODUCTION TO THE THERMODYNAMICS OF MATERIALS, SIXTH EDITION

peratures below the melting temperature of Ah 3 I ’ nillt';on This r-,

Cr A are completely miscible in all Pr0P ° ^ ns ^ J S b i Uy a n d c o m p l e t e liq u id

two-phase system comprising a liquid solution o f c o m p o s itio n

equilibrium depend only on the overall c o m p o sitio n o f th e s y s t e m

and are determined by the lever rule, as follow s:

numerator and denominators of the e x p r e ssio n s are the len^m

the phase diagram.

the designation of the components o f a system is s o m e w h a t ar lt^a * H o w e v

the most convenient choice is not alw ays as o b v io u s, a n d th e g e n e

in selecting the components w ill be d iscu ssed later w h e n d e a li n g w i r 0x 1 e

phase diagrams.

1.8 J.AWS OF THERMODYNAMICS*

following subsections and will be the subject of study throug o

A very good summary of the Laws of Thermodynamics is found in Peter Atkins, The Laws o j

1 herm odxnam 'h s; A Very Short Introduction, Oxford University Press, Oxford, UK, 2010.

IN T R O D U C T IO N A ND D E F IN IT IO N O F T E R M S

1 7

1.8.1 The First Law of Thermodynamics

T he First Law not only states that the energy o f the universe is c o n se rv e d but it

also posits that the various form s o f energy (e.g., therm al, electrical, m agnetic, and

m echanical) can be co n verted into o th er form s o f energy W h en first delineated, it

was the fact that therm al energy (heat) could be converted to m echan ical work that was o f special interest (heat engines) T his law also defines an im p o rta n t extensive

th erm od y nam ic state function called the internal e n e rg y , U, o f the system under

investigation

1.8.2 The Second Law of Thermodynamics

A lthough the Second Law is the one that often gets the m ost attention in popu­lar discussions o f science, it is often incorrectly understood! C are m ust be taken in applying the law by delineating the system and the surroundings T h is law allow s us

to m ake im portant predictions o f the direction in w hich a system w ill evolve with tim e during spontaneous processes, if other im portant caveats are tak en into account

T he Second Law introduces another im portant extensive th erm o d y n am ic state func­

tion called e n tro p y , S A short version o f the Second Law is that the entropy o f the

universe never decreases

1.8.3 The Third Law of Thermodynamics

In its boldest form , the T h ird Law states that when a system w hich is in com plete internal equilibrium approaches the absolute zero in tem perature, all o f the aspects

o f its entropy approach zero Som etim es, the T hird Law is stated as follows: a system

can never be taken to the absolute zero in tem perature T his is also called the u n a t­

T he Laws of T herm odynam ics will be discussed in the follow ing chapters and applied to the therm odynam ic stability o f system s in later chapters o f the text

1.9 SUMMARY

In thermodynamics, the universe is divided into the system (that part of the universe

of interest to us) and the surroundings There are several kinds of walls between the system and the surroundings, and each type gives rise to a system with specific characteristics.

In thermodynamics, the equilibrium of the system is of interest in that, if it is known, one can determine if the state of the system will change and in which direc­ tion such a change would go.

The state of a simple system is determined by its temperature and pressure, the two intensive independent variables of the sy ilt!ftưỜNG ĐẠ I HOC o u v /\jH0 rv

TH U V iriN

4 Other thermodynamic variables are functions of pressure and temperature, and ' graphs may be plotted which display the equilibrium states o f the system as a func- tion of the independent variables.

5 The Zeroth Law of Thermodynamics introduces the intensive variable

stant, shows that different forms of energy may be converted into one ano er, an

7 The Second Law of Thermodynamics defines which processes may occur spon­

8 The Third Law of Thermodynamics states that all aspects of entropy approach the value of zero as the temperature of the system approaches zero, if the sys em is in complete internal equilibrium.

1-10 CONCEPTS AND TERMS INTRODUCED IN CHAPTER 1

The reader should write out brief d efinitions or d e s c r ip tio n s o f th e f o l l o w i n o terms Where appropriate, equations may be u sed.

IN T R O D U C T IO N AND D E F IN IT IO N O F T E R M S

19

Thermodynamic state functions

Thermodynamic state variables

change for n moles?

Solution to Qualitative Problem 1

T he surface would be shifted up to double the volum e at every point T he slopes and

curvatures o f the surface at 2V, rem ain the sam e as those at V,.

For n moles, the surface shifts up at every point by n V;— again, w ith the slopes

and curvatures rem aining the same

Qualitative Problem 2

O btain sim plified expressions for p r and a of an ideal gas

Solution to Qualitative Problem 2

1.11 QUALITATIVE EXAMPLE PROBLEMS

and

a = —

2 0 INTRODUCTION TO THE THERMODYNAMICS OF MATERIALS, SIXTH EDITI q ^

1.12 QUANTITATIVE EXAMPLE PROBLEMS

Quantitative Problem 1

Consider 1 mole of an ideal gas Using a y axis o f pressure and an a * a x is o f te m p e r a tu r e , plot the variations of pressure with temperature for volu m es o f 11.2 liters, 2 2 4 liters, and 44.8 liters Use ranges of pressure and temperature co n sisten t w ith F ig u r e 1.3.

Solution to Quantitative Problem 1

States of constant volume can be calculated using the id eal g a s la w (P V ' = n R T ) T h e

following table summarizes the calculations T h e plot is fou n d in F ig u r e 1.6.

P re s s u re (a tm ) Temperature (K) V = 11.2 liters V = 2 2 4 lite r s V = 4 4 8 lit e r s

IN T R O D U C T IO N AND D E F IN IT IO N O F T E R M S

Quantitative Problem 2

A rock w ith a m ass o f 10 lb falls 100 ft from a c liff to the floor o f a canyon W hat is

Solution to Quantitative Problem 2

curvatures of the surface are proportional to these second derivatives)

What are the signs of the curvatures? Explain

The expression for the total derivative of V with respect to the dependent vari-

ables P and T is

* th n m tn o b ta in th e e q u a t io n o f s t a t e fo r a n id e a l g a s

e q u a t io n a n d in te g r a te th e m to o D ia m h

1.3- The pressure temperature phase diagram in Figure 1.4 has no two-phase areas

(only two-phase curves), but the temperature compos.t.on diagram in F.gure 1.5 does have two-phase areas Explain

1.4* Calculate the value of the ratio oc/p, for an ideal gas in terms of its volume.

CHAPTER 2 The First Law of Thermodynamics

2.1 INTRODUCTION

The First Law of Therm odynam ics is som etim es thought to be merely an extension to the Law of Conservation of Energy, which was discovered in the late seventeenth century for m echanical systems It is, however, much more! The First

Law introduces the im portant therm odynam ic state variable internal energy U (also called a therm odynam ic p o tential), and the law posits that energy may be

converted from one of its forms to another form Furtherm ore, the law introduces the im portant concept that the transfer of therm al energy (heat) is a different kind

of energy than that which is done during a process of work First, we start with a

review of basic mechanics

Kinetic energy is conserved in a frictionless system of interacting rigid elastic

bodies A collision between two of these bodies results in a transfer of kinetic energy from one to the other; the work done by the one equals the work done on the other The total kinetic energy of the system is unchanged as a result of the collision If the kinetic system is in the intluence of a gravitational field, then the sum of the kinetic and potential energies of the bodies is constant Changes of position o f the bodies in the gravitational field, in addition to changes in the velocities of the bodies, do not alter the total dynamic energy of the system As the result of possible interactions,

kinetic energy may be converted to potential energy and vice versa, but the sum of

the two remains constant If, however, friction occurs in the system, then with con­tinuing collision and interaction among the bodies, the total dynamic energy of the

system decreases and thermal energy is produced It is thus reasonable to expect that

a relationship exists between the dynamic energy dissipated and the thermal energy

produced as a result of the effects of friction.

The establishment of such a relationship laid the foundations for the development

of the thermodynamic method As a subject, this has now gone far beyond simple considerations of the interchange of energy from one form to another— for example, from dynamic energy to thermal energy The development of therm odynam ics from

its early beginnings to its present state was achieved as the result of the invention

of convenient thermodynamic functions o f state In this chapter, the first two of these thermodynamic functions— the internal energy, U, and the enthalpy, H— are

introduced

23

24 INTRODUCTION TO THE THERMODYNAMICS OF MATERIALS, SIXTH E D ITIO N

2.2 THE RELATIONSHIP BETWEEN HEAT AND WORK

The relationship between heat (thermal energy) and work was suggested in 1798

boring was roughly proportional to the work, w, performed during the boring T h is suggestion was novel, as hitherto, heat had been regarded as being an invisible fluid

called caloric, which resided between the constituent particles of a substance In th e

caloric theory of heat, the temperature of a substance was considered to be d eter­mined by the quantity of caloric gas which it contained It was thought th at w hen tw o bodies of differing temperature were placed in contact with one anothei, they ca m e

to an intermediate common temperature as the result of caloric flowing betw een them Thermal equilibrium was thought to be reached when the p iessu ie o ca o ric gas in the one body equaled that in the other

Some 40 years would pass before the relationship between heat and w or w as

by James Prescott Joule (1818-1889) Joule conducted experim ents in w hich w o rk was performed in a certain quantity of adiabatically* contained w atei, and he th e n measured the resultant increase in the temperature of the water He o b se iv e d th a t

a direct proportionality existed between the work done and the resultan t in c re a s e

in temperature and that the same proportionality existed no m atter w a I m e a n s

included:

1 Rotating a paddle wheel immersed in the water

2 An electric motor driving a current through a c o il im m ersed in th e w a te i

3 Compressing a cylinder o f gas im m ersed in the w ater

4 Rubbing together two metal blocks im m ersed in the w ater

This proportionality between/the work performed and the rise in te m p e ra tu ie gave rise to the notion of a m e c h a n ic a l e q u iv a le n t o f h e a t, and foi t e p u rp o s e o f

the calorie for /5 ° c a lo rie), which is the quantity of therm al en erg y n e e d e d to b e transferred to 1 gram of water to increase the temperature of the w ater fro m 14.5 C

to 15.5°C On the basis of this definition, Joule determ ined the value o f th e m e c h a n i­

presently accepted value is 0.2389 calories (15° calories) per jou le R o u n d in g th is to0.239 calories per joule defines the t h e r m o c h e m i c a l c a l o r i e, w hich, u n til th e i n ti o - duction in 1960 of SI units, was the traditional energy unit used in th e rm o c h e m is ti y

: A n adiabatic vessel is one whi ch is c o n s t r u c t e d in s u c h a w a y a s to p r o h i b i t , o r a t l e a s t m i n i m i z e , t h e pas sag e o f thermal en e rg y through its w a l l s T h e m o s t f a m i l i a r e x a m p l e o f a n a d i a b a t i c v e s s e l i s t h e

Dew ar flask (k n o w n more popularly as a thermos flask ). T h e r m a l e n e r g y t r a n s m i s s i o n b y c o n d u c t i o n into or out of this vessel is m i n i m i z e d by u s i n g d o u b l e g l a s s w a l l s s e p a r a t e d b y a n e v a c u a t e d s p a c e , and a rubber or cork stopper T h e r m a l e n e r g y t r a n s m i t t e d by r a d ia t i o n is m i n i m i z e d b y u s i n g h i g h l y