Chemical Thermodynamics

Chemical Thermodynamics

.

Erno˝ Keszei

Chemical Thermodynamics

An Introduction

Dr. Erno˝ Keszei

Dept. Physical Chemistry

Lab. Chemical Kinetics

Eo¨tvo¨s Lora´nd University (ELTE)

Budapest, Hungary

keszei@chem.elte.hu

ISBN 978-3-642-19863-2 e-ISBN 978-3-642-19864-9

DOI 10.1007/978-3-642-19864-9

Springer Heidelberg Dordrecht London New York

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Preface

According to an anecdote, the German physicist Arnold Sommerfeld said the

following in the 1940s: “Thermodynamics is a funny subject. The first time you

go through it, you don’t understand it at all. The second time you go through it, you

think you understand it, except for one or two small points. The third time you go

through it, you know you don’t understand it, but by that time you are so used to it,

it doesn’t bother you any more.”

Things have changed much since then. University education has become avail￾able for a large number of students, and the Bologna process has led to a three-tier

system also in the European Higher Education Area. As a result, most of the

students of natural sciences or engineering do not have the opportunity any more

to study subjects such as thermodynamics over and over again in order to gain

deeper knowledge. Fortunately enough, in the second half of the twentieth century a

new approach for teaching the foundations of thermodynamics emerged. This

postulatory approach does not lead the student through a tedious historical devel￾opment of the subject, but rather introduces thermodynamics by stating four concise

postulates. These postulates facilitate the understanding of the subject by develop￾ing an abstract mathematical foundation from the beginning. This however rewards

the student with an easy understanding of the subject, and the postulates are directly

applicable to the solving of actual thermodynamic problems.

This book follows the postulatory approach used by Herbert B. Callen in

a textbook first published in 1960. The basics of thermodynamics are described

as briefly as possible whilst ensuring that students with a minimal skill of calculus

can also understand the principles, by explaining all mathematical manipulations

in enough detail. Subsequent chapters concerning chemical applications always

refer to a solid mathematical basis derived from the postulates. The concise and

easy-to-follow structure has been maintained – also in the chapters on applications

for chemically important topics.

Though the text has been written primarily for undergraduate students in

chemistry, I also kept in mind the needs of students studying physics, material

sciences and biochemistry, who can also find a detailed introduction to the

chemical aspects of thermodynamics concerning multi-component systems useful.

The book has been intended to cover a considerably wide range of topics, enough

v

for a chemistry major course. However, some sections can be considered as

optional and may be omitted even during a standard physical chemistry course.

Examples are the fundamental equation of the ideal van der Waals fluid

(Sect. 2.2.6), the equations of state of real gases, fluids and solids (Sect. 4.5),

practical usage of engines and refrigerators (Sect. 5.4), or multi-component phase

diagrams (Sect. 7.7). These omitted parts however can also be useful as a reference

for the student during further studies in more specific branches of physical chemistry.

The material covered in the appendix serves mostly to provide technical help in

calculus, but it also contains a treatise of the “classical” laws of thermodynamics. It

is important to be familiar with this aspect of thermodynamics to understand

classical texts and applications that make reference to these laws. As this material

is not necessary to understand postulatory thermodynamics, it is best left in the

appendix. However, it is highly advisable to include it in the course material.

Though the chapter on statistical thermodynamics could be skipped without any

consequence to understanding the rest of the book, it is also advised to include it in

a standard course. Quantum chemistry along with statistical thermodynamics

is essential to help the student develop a solid knowledge of chemistry at the

molecular level, which is necessary to understand chemistry in the twenty-first

century.

This material is a result of 4 years of teaching thermodynamics as part of the new

undergraduate chemistry curriculum introduced as the first cycle of the three-tier

Bologna system. It has been continually improved through experience gained from

teaching students in subsequent semesters. A number of students who studied from

the first versions contributed to this improvement. I would like to mention two of

them here; Tibor Nagy who helped to rectify the introductory chapters, and Soma

Vesztergom who helped a great deal in creating end-of-chapter problems. I am also

indebted to colleagues who helped to improve the text. Thanks are due to Professor

Jo´zsef Cserti and Tama´s Te´l for a critical reading of the introductory chapters

and phase transitions. Professor Ro´bert Schiller helped to keep the chapter on the

extension of interactions concise but informative.

Since the time I first presented the text to Springer, I have experienced the

constant support of Ms. Elizabeth Hawkins, editor in chemistry. I would like to

thank her for her patience and cooperation which helped me to produce the

manuscript on time and in a suitable format for printing.

Budapest, Hungary Erno˝ Keszei

vi Preface

Contents

1 Introduction ............................................................... 1

Further Reading ............................................................ 2

2 Postulates of Thermodynamics .......................................... 3

2.1 Thermodynamic Systems: Postulate 1 ................................. 4

2.1.1 Constrained Systems and the Measurability

of Energy via Mechanical Work ............................... 6

2.2 The Conditions of Equilibrium: Postulates 2, 3 and 4 ................ 8

2.2.1 Properties of the Entropy Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . 10

2.2.2 Properties of the Differential Fundamental Equation . . . . . . . . . 13

2.2.3 The Scale of Entropy and Temperature . . . . . . . . . . . . . . . . . . . . . . . 15

2.2.4 Euler Relation, Gibbs–Duhem Equation

and Equations of State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17

2.2.5 The Fundamental Equation of an Ideal Gas . . . . . . . . . . . . . . . . . . . 18

2.2.6 The Fundamental Equation of an Ideal

van der Waals Fluid . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 22

Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28

3 Thermodynamic Equilibrium in Isolated and Isentropic Systems .... 29

3.1 Thermal Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 32

3.2 Thermal and Mechanical Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36

3.3 Thermal and Chemical Equilibrium . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 37

Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 41

4 Thermodynamic Equilibrium in Systems with Other Constraints .... 43

4.1 Equilibrium in Constant Pressure Systems:

The Enthalpy Function . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44

4.2 Equilibrium in Constant Temperature and Constant

Volume Systems: The Free Energy Function . . . . . . . . . . . . . . . . . . . . . . . . 46

vii

4.3 Equilibrium in Constant Temperature and Constant

Pressure Systems: The Gibbs Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48

4.4 Summary of the Equilibrium Conditions: Properties

of the Energy-like Potential Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50

4.4.1 Calculation of Heat and Work from Thermodynamic

Potential Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 52

4.4.2 Calculation of Entropy and Energy-like Functions

from Measurable Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 53

4.4.3 Calculation of Thermodynamic Quantities from the

Fundamental Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57

4.5 Equations of State of Real Gases, Fluids and Solids . . . . . . . . . . . . . . . . . 58

4.5.1 Chemical Potential and Fugacity of a Real Gas . . . . . . . . . . . . . . . 64

Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 68

5 Thermodynamic Processes and Engines . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69

5.1 Quasistatic, Reversible and Irreversible Processes . . . . . . . . . . . . . . . . . . . 69

5.2 Heat Engines: The Carnot Cycle and the Carnot Engine . . . . . . . . . . . . 72

5.3 Refrigerators and Heat Pumps: The Carnot Refrigerating

and Heat-Pump Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75

5.4 Heat Engines and Refrigerators Used in Practice . . . . . . . . . . . . . . . . . . . . 77

5.4.1 Heat Engines Based on the Rankine Cycle . . . . . . . . . . . . . . . . . . . 77

5.4.2 Refrigerators and Heat Pumps Based

on the Rankine Cycle . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 79

5.4.3 Isenthalpic Processes: The Joule–Thompson Effect . . . . . . . . . . 80

Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85

6 Thermodynamics of Mixtures (Multicomponent Systems) . . . . . . . . . . . 87

6.1 Partial Molar Quantities . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87

6.1.1 Chemical Potential as a Partial Molar Quantity . . . . . . . . . . . . . . . 89

6.1.2 Determination of Partial Molar Quantities

from Experimental Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90

6.2 Thermodynamics of Ideal Mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

6.2.1 Ideal Gas Mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93

6.2.2 Properties of Ideal Mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95

6.2.3 Alternative Reference States . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98

6.2.4 Activity and Standard State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 101

6.3 Thermodynamics of Real Mixtures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

6.3.1 Mixtures of Real Gases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103

6.3.2 The Chemical Potential in Terms of Mole Fractions . . . . . . . . 106

6.3.3 The Chemical Potential in Terms of Solute Concentration ... 108

6.3.4 Activity and Standard State: An Overview . . . . . . . . . . . . . . . . . . 109

6.3.5 Thermodynamic Properties of a Real Mixture . . . . . . . . . . . . . . . 115

6.4 Ideal Solutions and Ideal Dilute Solutions . . . . . . . . . . . . . . . . . . . . . . . . . 118

Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 122

viii Contents

7 Phase Equilibria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 125

7.1 Stability of Phases . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 127

7.2 Phase Equilibria of Pure Substances . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 129

7.2.1 Phase Diagrams of Pure Substances . . . . . . . . . . . . . . . . . . . . . . . . . . 135

7.2.2 Calculation of the Quantity of Coexisting phases:

the Lever Rule . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139

7.2.3 Calculation of Equilibrium Temperature and Pressure;

the Clausisus–Clapeyron Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . 141

7.2.4 First-Order and Second-Order Phase Transitions . . . . . . . . . . . . 144

7.3 Liquid–Vapor Equilibrium of Ideal Binary Mixtures . . . . . . . . . . . . . . 147

7.4 Liquid–Vapor Equilibrium of Real Binary Mixtures . . . . . . . . . . . . . . 154

7.5 Solid–Liquid Equilibrium of Ideal Binary Mixtures . . . . . . . . . . . . . . . 158

7.6 Equilibrium of Partially Miscible Binary Mixtures . . . . . . . . . . . . . . . . 159

7.6.1 Liquid–Liquid Phase Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 161

7.6.2 Solid–Liquid Phase Diagrams . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 163

7.6.3 Colligative Properties: Equilibrium of a Binary Mixture

Phase and a Pure Phase Containing One of the Mixture

Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 178

7.7 Phase Diagrams of Multicomponent Systems . . . . . . . . . . . . . . . . . . . . . . 185

7.8 Separation of Components Based on Different Phase Diagrams .... 190

Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 200

8 Equilibria of Chemical Reactions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 201

8.1 Condition of a Chemical Equilibrium at Constant Temperature

and Pressure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202

8.1.1 Relation of the Equilibrium Constant and the

Stoichiometric Equation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 205

8.1.2 Affinity: The Driving Force of Chemical Reactions . . . . . . . . . 206

8.2 The Equilibrium Constant in Terms of Different Activities . . . . . . . 211

8.2.1 Heterogeneous Reaction Equilibria

of Immiscible Components . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 214

8.3 Calculation of the Equilibrium Constant from

Thermodynamic Data ................................................ 218

8.4 Temperature and Pressure Dependence of the Equilibrium

Constant . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 221

8.4.1 The Le Chaˆtelier–Braun Principle . . . . . . . . . . . . . . . . . . . . . . . . . . . . 223

Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 226

9 Extension of Thermodynamics for Additional Interactions

(Non-Simple Systems) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 227

9.1 Thermodynamics of Interfaces: Two-Dimensional

Equations of State . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 231

9.1.1 Thermodynamic Properties of Curved Surfaces . . . . . . . . . . . . . 234

Contents ix

9.2 Thermodynamic Description of Systems Containing

Electrically Charged Particles . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241

9.2.1 Thermodynamic Consequences of the Electroneutrality

Principle: The Chemical Potential of Electrolytes

and the Mean Activity Coefficient . . . . . . . . . . . . . . . . . . . . . . . . . . . 244

9.2.2 Chemical Potential of Ions in an Electric Field:

The Electrochemical Potential . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 251

9.2.3 Heterogeneous Electrochemical Equilibria:

The Galvanic Cell . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 253

9.2.4 Electrodes and Electrode Potentials . . . . . . . . . . . . . . . . . . . . . . . . . . 259

Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 264

10 Elements of Equilibrium Statistical Thermodynamics . . . . . . . . . . . . . . 265

10.1 The Microcanonical Ensemble . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 266

10.1.1 Statistical Thermodynamics of the Einstein Solid

in Microcanonical Representation . . . . . . . . . . . . . . . . . . . . . . . . 269

10.1.2 Statistical Thermodynamics of a System

of Two-State Molecules in Microcanonical

Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 272

10.2 The Canonical Ensemble . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 274

10.2.1 Calculation of the Canonical Partition Function

from Molecular Data . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 280

10.2.2 Statistical Thermodynamics of the Einstein

Solid and the System of Two-State Molecules

in Canonical Representation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 281

10.2.3 The Translational Partition Function. Statistical

Thermodynamics of a Monatomic Ideal Gas . . . . . . . . . . . . . 283

10.2.4 Calculation of the Rotational, Vibrational,

and Electronic Partition Functions . . . . . . . . . . . . . . . . . . . . . . . . 287

10.2.5 Statistical Characterization of the Canonical Energy . . . . . 291

10.2.6 The Equipartition Theorem . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 294

10.3 General Statistical Definition and Interpretation of Entropy . . . . . 297

10.4 Calculation of the Chemical Equilibrium Constant

from Canonical Partition Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 300

Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 306

11 Toward Equilibrium: Elements of Transport Phenomena . . . . . . . . . . 307

11.1 Transport Equations for Heat, Electricity, and Momentum . . . . . . 309

11.2 Equations for the Diffusive Material Transport . . . . . . . . . . . . . . . . . . . 311

11.2.1 Fick’s First Law: The Flux of Diffusion . . . . . . . . . . . . . . . . . . 312

11.2.2 Fick’s Second Law: The Rate of Change

of the Concentration Profile . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 312

11.3 Principle Transport Processes and Coupled Processes . . . . . . . . . . . 316

Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 318

x Contents

Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 319

A1 Useful Relations of Multivariate Calculus . . . . . . . . . . . . . . . . . . . . . . . . . . 319

A.1.1 Differentiation of Multivariate Functions . . . . . . . . . . . . . . . . . . 319

A.1.2 Differentiation of Composite Functions . . . . . . . . . . . . . . . . . . . . 322

A.1.3 Differentiation of Implicit Functions . . . . . . . . . . . . . . . . . . . . . . . 323

A.1.4 Integration of Multivariate Functions . . . . . . . . . . . . . . . . . . . . . . 324

A.1.5 The Euler Equation for Homogeneous

First-Order Functions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 325

A2 Changing Extensive Variables to Intensive Ones:

Legendre Transformation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 326

A.2.1 Legendre Transformations . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 327

A.2.2 Legendre Transformation of the Entropy Function . . . . . . . . 329

A3 Classical Thermodynamics: The Laws . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 331

A.3.1 Zeroth Law and Temperature . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 332

A.3.2 First Law and Energy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 334

A.3.3 Second Law and Entropy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 336

A.3.4 Third Law and the Uniqueness of the Entropy Scale . . . . . . 341

Further Reading . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 341

Index . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 343

Contents xi

Chapter 1

Introduction

Physical chemistry deals with general properties common in different materials

despite their chemical diversity. Properties referring to materials stored in a con￾tainer – i.e., materials “at rest,” without temporal changes – have a special impor￾tance. These materials are told to be in an “equilibrium state” and are described by

the science called thermodynamics. Equilibrium states can be very different

depending on the circumstances; thus, one of the major aims of thermodynamics

is to quantitatively characterize materials within different conditions and the

changes accompanying their transition to a new state. The term “thermodynamics”

has a historical origin. At the beginning of the nineteenth century, there was an

attempt to understand the underlying principles of the efficiency of steam engines

already in operation. The basic problem of the investigations was the transformation

of heat into mechanical work. The Greek word yerm
[therme] means hotness (heat),

while another Greek word, dunamiς [dynamis] means the ability to act (power).

Putting the two words together expressed the basic direction of this research. (The

branch of mechanics dealing with movements is also called dynamics, originating

from the same Greek word. Based on this, some authors criticize the name thermo￾dynamics and propose thermostatics instead, as the underlying Greek word (stasiς

[stasis] ¼ state) refers more directly to equilibrium states. These critics are not

really relevant since actual names of branches of science are arbitrary, having a

historical origin.) The term “thermodynamics” survived, even though this science

explains a lot more than the efficiency of heat engines.

There are other branches of physics dealing with the characterization of

equilibria; mechanics with equilibria of mechanical interactions, electrostatics

with that of electric interactions, magnetostatics with that of magnetic interactions,

and the calculations of interaction energies. Thermodynamics includes all these

interactions but includes in addition the influence on interaction energies of the

state of “hotness” (or coldness) of matter. It will be clear from molecular (or

statistical) thermodynamics that the temperature-dependent energy involves

changes in the molecular modes hidden at the macroscopic level. These molecular

modes cannot be observed directly by measuring macroscopic quantities only, but

the consequences of their changes are accessible for macroscopic observations.

E. Keszei, Chemical Thermodynamics,

DOI 10.1007/978-3-642-19864-9_1, # Springer-Verlag Berlin Heidelberg 2012

1

Thermodynamics differs basically from other branches of physics by considering

this thermal energy and other thermal properties.

Chemical thermodynamics – in addition to what physicists and civil engineers

usually learn as thermodynamics – deals with materials and properties where the

chemical composition and its change are especially important. Quantitative

relations concerning composition and its change are usually rather complicated.

There is a special role of traditions and conventions established during the devel￾opment of this science to describe the “chemical” aspects. This book – after a

concise introduction to the principles of thermodynamics – concentrates on the

thermodynamic description depending on the composition of equilibrium states and

a detailed discussion of the underlying conventions. To establish the general

principles is unavoidable before actual applications to chemically interesting

systems, thus the first part of the book describes the very foundations of

thermodynamics.

As mentioned before, the science of thermodynamics was developed by the

interpretation of how steam engines, or in a wider sense and after later inventions,

heat engines in general operate. This is the reason why its traditional treatment is

based on conclusions drawn from the operation of those engines. This treatment is

quite complicated and is not best suited to develop the principles underlying

chemical applications. There is another possibility to set the foundations of a

science, as it is common practice, e.g., in geometry, number theory, probability

theory, or in physical sciences like mechanics, electrodynamics, and quantum

mechanics. This is the postulatory foundation when a few postulates (or axioms)

are formulated, from which all theorems can be proved or all important relations

derived. Already at the end of the nineteenth century, the American physicist Josiah

Willard Gibbs proposed mathematically sound foundations of thermodynamics, but

a genuine system of postulates has only been formulated in the middle of the

twentieth century, mainly due to La´szlo´ Tisza, an American physicist of Hungarian

origin. The treatment of this book concerning the foundations of thermodynamics is

closely related to the frequently referred textbook by Herbert B. Callen (a former

student of Tisza) published 1960 with the title “Thermodynamics,” as well as its

second edition published 1985. In addition to this – concerning especially statistical

thermodynamics and chemical applications – a number of other textbooks have

been used as resources, which are listed at the end of the chapters.

Further Reading

Callen HB (1985) Thermodynamics and an introduction to thermostatistics, 2nd edn. Wiley,

New York

2 1 Introduction

Chapter 2

Postulates of Thermodynamics

Thermodynamics is a general theory; it deals with the properties of all kinds of

matter where the behavior of a large number of microscopic particles (such as

molecules, atoms, ions, etc.) determines the macroscopic properties. It is stated

sometimes that this branch of science deals with the transformation of the thermal

energy hidden in the internal structure and modes of movements of the enormously

large number of particles that build up macroscopic bodies, into other forms of

energy. As the microscopic structure of matter, the modes of movements and the

interactions of particles have further consequences than simply determining the

energy of a macroscopic body; thermodynamics has a more general relevance to

describe the behavior of matter.

The number of particles in a macroscopic piece of matter is in the order of

magnitude of the Avogadro constant (6.022 141 79
1023/ mol). Obviously, there

is no question of describing the movement of individual particles; we should

content ourselves with the description of the average behavior of this large popula￾tion. Based on our actual knowledge on probability theory, we would naturally use

a statistical description of the large population to get the average properties. By

comparing the calculated averages – more precisely, the expected values – with

macroscopic measurements, we could determine properties that “survive” averag￾ing and manifest at the macroscopic level. There are not many such properties; thus,

this treatment of the ensemble of particles would lead to practically useful results.

This probabilistic approach is called statistical thermodynamics or, in a broader

sense, statistical physics.

However, as it has been mentioned before (and is described in details in

Appendix 3), thermodynamics had been developed in the middle of the nineteenth

century while attempting to theoretically solve the problem of efficiency of

transforming heat into mechanical work. The “atomistic” theory of matter was of

very little interest in those days, thus thermodynamics developed only by inspection

and thorough investigation of macroscopic properties. This is reflected in the term

phenomenological thermodynamics, which is related to the Latin word of Greek

origin phenomenon (an observable event). This “classical” thermodynamics used

terms relevant to heat engines to formulate a few “laws” from which relations

E. Keszei, Chemical Thermodynamics,

DOI 10.1007/978-3-642-19864-9_2, # Springer-Verlag Berlin Heidelberg 2012

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