Richard e sonntag, gordon j van wylen introduction to thermodynamics, classical and statistical wiley (1991)

The firstthermodynamic properties to be defined Chapter 2 are those that can be readilymeasured: pressure, specific volume, and temperature.. In addition, new analysis and the correlatio

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INTRODUCTION TO THERMODYNAMICS

CLASSICAL AND

STATISTICAL

JOHN WILEY & SONS

New York Chichester Brisbane Toronto Singapore

John Wiley & Sons, Inc to have books of

enduring value published in the United

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Copyright © 1971, 1982, 1991, by John Wiley & Sons, Inc.

All rights reserved Published simultaneously in Canada.

Reproduction or translation of any part of

this work beyond that permitted by Sections

107 and 108 of the 1976 United States Copyright

Act without the permission of the copyright

owner is unlawful Requests for permission

or further information should be addressed to

the Permissions Department, John Wiley & Sons.

Library of Congress Cataloging-in-Publication Data

Sonntag, Richard Edwin.

Introduction to thermodynamics: classical and statisticalf

Richard E Sonntag, Gordon J Van Wylen.-3rd ed.

p cm.

Includes bibliographical references and index.

ISBN 0-471-61427-0 (alk paper)

I Thermodynamics 2 Statistical thermodynamics.

Gordon John II Title.

In this third edition we have retained the basic objective of the previous editions:

to present a comprehensive and rigorous treatment of thermodynamics while taining an engineering perspective and, in so doing, to provide a textbook thatoffers considerable flexibility for the inclusion of material on statistical thermo-dynamics It is clear that engineers of the twenty-first century will find increasingapplications of phenomena and devices based on atomic-scale principles, and someintroduction and incorporation of such approaches to problems will be an im-portant part of their educational experience

re-We have deliberately directed our presentation to students New concepts anddefinitions are presented in the context in which they are first relevant The firstthermodynamic properties to be defined (Chapter 2) are those that can be readilymeasured: pressure, specific volume, and temperature In Chapter 3 tables of ther-modynamic properties are introduced, but only in regard to these measurableproperties Internal energy and enthalpy are introduced in connection with thefirst law, entropy in connection with the second law, and the Helmholtz and Gibbsfunctions in the section on availability Many examples have been included in thebook to assist the student in gaining an understanding of thermodynamics, andthe problems at the end of each chapter have been carefully sequenced to correlatewith the subject matter and provide some progression in difficulty

We have presented the subject matter so that there are several arrangements

by which the material can be covered, both within the classical section, Chapters

I to 14, and within the statistical section, Chapters 15 to 18 This has been donenot only for the amount of material from each part to be studied, but also for thesequence in which the topics may be taken up

The principal changes of our philosophy and direction in this edition are twofold:

an increased awareness and emphasis on environmental issues and ~oncernsthroughout the text and in the text problems; and a recognition of the steadilygrowing use of computers in the study of thermodynamics and also in the solution

of thermodynamic problems The use of computers is reflected in our inclusion ofthe entire appendix material on classical thermodynamics, Tables A.I throughA.16, on computer disks, and also in the inclusion there of FORTRAN subroutinesfor the properties of substances listed in these tables, Tables A.I through A.6, A.II,A.12, and A.14 This allows a considerable flexibility for studying many problems

in thermodynamics in terms of the variable quantities involved, and for creatingmany new design-oriented problems as well There are of course many other changes

in detail in the new edition, but the general organization and order of text materialremains the same as in the previous edition

Throughout the book we have attempted to maintain an engineering perspective,particularly in the choice of examples and problems One of the major changesfrom the previous edition is in the problems Although a number of the earlierproblems have been retained, most are new or have been significantly revised Anumber of new problems requiring a computer-based solution have been addedthroughout the book, beginning in Chapter 2, so that instructors who wish toincorporate these problems into the course may do so at any time throughout theterm Several different classes of applications of thermodynamics are introduced

in the first chapter, and these then serve as a basis for many of the problems inlater chapters We have retained a chapter on cycles (Chapter 10) because we findthat many students enjoy this subject, and it can also serve to strengthen effectivelythe student's understanding of the first and second laws of thermodynamics, and

to introduce him or her to engineering design and practice Many of the related problems are in this chapter, as are problems concerning a number ofmodern and relevant applications: heat pumps, cogeneration, topping and bot-toming cycles, two-stage systems, combined cycles, and many others We have alsoincluded comments and problems that relate thermodynamics to environmentalconcerns, as mentioned earlier

computer-There has been a general updating of text material, definitions, and dynamic data, in an effort to remain consistent with current practice in the field.For example, the new temperature scale, ITS-90, is included in Chapter 2, a con-ceptual approach to the introduction of thermodynamic tables has been presented

thermo-in Chapter 3, and new ideal-gas tables consistent with the most recent JANAFtables are introduced in Chapter 5, as well as new air tables that are consistentwith these tables In addition, new analysis and the correlation between thermo-dynamic and ideal-gas temperature scales are included in Chapter 7, a simplifiedaccount of developments concerning thermodynamic irreversibility and availability

is presented in Chapter 9, more accurate three-parameter generalized correlationsare introduced into Chapter 12, and thermochemical properties and equilibriumconstants are made internally consistent with the earlier-mentioned gas tables.Applications of statistical thermodynamics in Chapter 18 have been shortenedsomewhat, and the appendix tables and data have been thoroughly revised andextended

In regard to the symbols used in this text, we were guided by two tions First, we have used the symbols commonly found in the general literature

considera-of both classical and statistical thermodynamics; second, we have tried to maintain

a consistency of symbols throughout the book In a limited number of cases, wehave used a given symbol for more than one purpose We believe, however, thatthe context will clarify the meaning of these symbols

Our philosophy regarding units in this edition has been to organize the book

so that the course or sequence can be taught entirely in SI units (Le SystemeInternational d'Unites) Thus, all the text examples are in SI units, as are thecomplete problem sets and the thermodynamic tables In recognition, however, ofthe continuing need for engineering graduates to be familiar with English Engi-neering units, we have included an introduction to this system in Chapter 2 Wehave also repeated a sufficient number of problems and tables in these units, whichshould allow for suitable practice for those who wish to use these units For dealingwith English units, there is the problem of distinguishing between force and mass

units The symbols Ibf and Ibm have been used for pound force and pound mass

to emphasize this distinction in the English system Such symbols as Ibf/in.2 havebeen used for pressure (rather than psi) and ft3/lbm for specific volume (rather than

cu ft/lb) in order to stress the fundamental units involved in the various ters The force-mass conversion constant gc is treated as being implicit, to enableequations including kinetic or potential energy terms to be handled in a consistentmanner with regard to units In dealing with SI units, we have commonly used thebasic units for pressure (pascal) and volume (cubic meter), although we have usedthe liter extensively as a convenient volume unit Others may wish to use the barmore extensively as the pressure unit, and we trust that such flexibility in theseunits will present no particular difficulties to the student Concerning the extensiveproperties, a lowercase letter (v, u, h,s) designates the property per unit mass (eitherpound mass or kilogram); an uppercase letter (V.!.U, H, S) the property for theentire system; a lowercase letter with a bar (v, u,h, :5)the property per unit mole(either the pound mole or Ib m~},~r the_kilogram mole or kmol, in this text); and

parame-an uppercase letter with a bar (V, U, H, S) the partial molal property in a mixture.Following this pattern, we have found it convenient to designate the total heat

transfer as Q, the heat transfer per unit mass of the system as q, the total work as

J¥, and the work per unit mass of the system as w

Furthermore, we represent the rate of flow across a system boundary or controlsurface by a dot over the given quantity Thus, Q represents a rate of heat transferacross the system boundary; Wthe rate at which work crosses the system boundary(that is, the power); and mthe mass rate of flow across a control surface (ri is used

when the mass rate of flow is expressed in moles per unit time) We realize that

we have departed from the usual mathematical use of a dotted symbol, in whichthe dotted symbol typically refers to a derivative with respect to time However,

we have used the dotted symbol to indicate only a flow of heat and work across

a system boundary and a flow of heat, work, and mass across a control surface,and not in any other context We believe that these designations have contributed

to a simple and consistent use of symbols for this book

As was stated at the beginning of this preface to the third edition, the authorsbelieve that an introduction to contemporary applications concerning atomic-scalephenomena and devices is crucial to today's engineering education With this view

in mind, the last four chapters of the book have been written and organized sothat the subject of statistical thermodynamics can be introduced in one of severalways, at different depths of coverage

The minimum coverage includes the development of an understanding of theimportant basic concepts of thermodynamic equilibrium and of entropy and canreasonably be achieved in four class periods This minimum coverage would includeSections 15.1 to 15.4, 16.1, 16.5, and 17.1 to 17.3

The next level of coverage, in two additional class periods, applies to the erties of monatomic gases and includes the additional material of Sections 15.5and 15.6, 17.5, 18.1 and 18.2, and 18.4 A greater depth of understanding can beachieved by taking additional time to include some or all of Sections 15.8, 16.2 to16.4, 17.4, and 18.3

prop-Beyond the basic coverage just discussed, the remainder of the material in thispart of the text consists of special applications for those who wish to spend ad-ditional time on this subject These topics include Maxwell-Boltzmann velocity

distribution and free molecular flow (Sections 18.5 and 18.6), diatomic gases (15.7and 18.7), polyatomic gas (18.8), electron gas (18.9), gas mixtures (18.10), andchemical reactions (18.11) These topics are independent of one another and can

be chosen as desired

We acknowledge with appreciation the suggestions, counsel, and encouragement

of many colleagues, both at the University of Michigan and elsewhere This sistance has been very helpful to us during the writing of this edition, as it waswith the earlier editions of the book Several secretaries have aided us immeasurablythroughout, and we acknowledge this assistance with many thanks Both under-graduate and graduate students have been of particular assistance, for their per-ceptive questions have often caused us to rewrite or rethink a given portion of thetext, or to try to develop a better way of presenting the material in order to anticipatesuch questions or difficulties We must single out two graduate students at theUniversity of Michigan who have been of particular help with this project, especially

as-in the development of the computer programs, former doctoral student Dr YoungMoo Park and current doctoral student Mr Kyoung Kuhn Park We appreciatetheir many valuable contributions to this materia! Finally, for each of us, theencouragement and patience of our wives and families have been indispensable,and have made this time of writing pleasant and enjoyable, in spite of the pressures

of the project

Our hope is that this book will contribute to the effective teaching of modynamics to students who face very significant challenges and opportunitiesduring their professional careers Your comments, criticism, and suggestions willalso be appreciated

ther-Ann Arbor, Michigan

June 1990

Richard E SonntagGordon J Van Wylen

Symbols xv

1 SOME INTRODUCTORY COMMENTS

1.1 The Simple Steam Power Plant

1.2 Fuel Cells 5

1.3 The Vapor-Compression Refrigeration Cycle

1.4 The Thermoelectric Refrigerator 9

1.5 The Air Separation Plant 12

1.6 The Chemical Rocket Engine 13

1.7 Environmental Issues 14

2 SOME CONCEPTS AND DEFINITIONS

8

162.1

The Thermodynamic Systemand the Control Volume

Macroscopic versus Microscopic Point of View 17

Properties and State of a Substance 18

3 PROPERTIES OF A PURE SUBSTANCE 37

3.1 The Pure Substance 37

3.2 Vapor-Liquid-Solid-Phase Equilibrium in a Pure Substance 373.3 Independent Properties of a Pure Substance 44

3.4 Equations of State for the Vapor Phaseof a Simple

Compressible Substance 44

3.5 Tablesof Thermodynamic Properties 49

3.6 Thermodynamic Surfaces 53

4 WORK AND HEAT 63

4.1 Definition of Work 63

4.2 Units for Work 64

4.3 Work Done at the Moving Boundary of a SimpleCompressibleSystemin

4.9 Comparison of Heat and Work 78

5 THE FIRST LAW OF THERMODYNAMICS 86

5.1 The First Law of Thermodynamicsfor a SystemUndergoing a Cycle 865.2 The First Law of Thermodynamicsfor a Change in State of a System 875.3 Internal Energy-A Thermodynamic Property 91

5.4 ProblemAnalysisand Solution Technique 93

5.5 The Thermodynamic Property Enthalpy 96

5.6 The Constant-Volume and Constant-PressureSpecific Heats 1005.7 The Internal Energy, Enthalpy, and Specific Heat ofIdeal Gases 1025.8 The First Law as a Rate Equation 109

5.9 ConseNation of Mass 110

6 FIRST-LAW ANALYSIS FOR A CONTROL VOLUME 120

6.1 ConseNation of Massand the Control Volume 120

6.2 The First Law of Thermodynamicsfor a Control Volume 124

6.3 The Steady-State,Steady-Flow Process 128

6.4 The Joule-Thomson Coefficient and the Throttling Process 138

6.5 The Uniform-State, Uniform-Flow Process 141

7 THE SECOND LAW OF THERMODYNAMICS 159

7.1 Heat Engines and Refrigerators 159

7.2 Second Law of Thermodynamics 164

7.3 The ReversibleProcess 164

7.4 Factors That Render ProcessesIrreversible 167

CONTENTS xi

7.5 The Carnot Cycle 170

7.6 Two Propositions Regarding the Efficiency of a CarnotCycle 173

7.7 The Thermodynamic Temperature Scale 174

7.8 TheIdeal-Gas Temperature Scale 177

7.9 Equivalence of Ideal-Gasand Thermodynamic Temperature Scales 179

Entropy-A Property of a System 189

The Entropy of a Pure Substance 191

Entropy Change in ReversibleProcesses 194

Two Important Thermodynamic Relations 197

Entropy Change of a SystemDuring an Irreversible Process

Lost Work 200

Principle of the Increase of Entropy 202

Entropy Change of a Solid or Liquid 205

Entropy Change of an Ideal Gas 206

The ReversiblePolytropic Processfor an Ideal Gas 212

199

9 SECOND-LAW ANALYSIS FOR A CONTROL VOLUME 224

9.1 The Second Law of Thermodynamics for a Control Volume 224

9.2 The Steady-State,Steady-Flow Processand the Uniform-State,

Uniform-Flow Process 227

9.3 The ReversibleSteady-State,Steady-Flow Process 232

9.4 Principle of the Increase of Entropy 235

9.5 Efficiency 236

9.6 Available Energy, ReversibleWork, and Irreversibility 239

9.7 Availability and Second-Law Efficiency 244

9.8 ProcessesInvolving Chemical Reactions 250

9.9 Some General Comments Regarding Entropy 251

10 SOME POWER AND REFRIGERATION CYCLES 264

VAPOR POWER CYCLES 265

10.1 The Rankine Cycle 265

10.2 Effect of Pressureand Temperature on the Rankine Cycle 268

10.3 The Reheat Cycle 271

10.4 The Regenerative Cycle 273

10.5 Deviation of Actual Cycles from Ideal Cycles 279

VAPOR REFRIGERATIONCYCLES 283

10.6 Vapor-Compression Refrigeration Cycles 283

10.7 Working Fluids for Vapor-Compression Refrigeration Systems 28510.8 Deviation of the Actual Vapor-Compression Refrigeration Cycle from the

Ideal Cycle 28610.9 The Ammonia Absorption Refrigeration Cycle 289

AIR-STANDARDPOWER CYCLES 290

10.10 Air-Standard Cycles 290

10.11 The Air-Standard Carnot Cycle 291

10.12 The Air-Standard Otto Cycle 293

10.13 The Air-Standard Diesel Cycle 297

10.14 The Ericsson and Stirling Cycles 300

10.15 The Brayton Cycle 302

10.16 The Simple Gas-Turbine Cycle with a Regenerator 308

10.17 The Ideal Gas-Turbine Cycle Using Multistage Compression with

Intercooling, Multistage Expansion with Reheating, and aRegenerator 311

10.18 The Air-Standard Cycle for Jet Propulsion 311

AIR-STANDARDREFRIGERATIONCYCLE 315

10.19 The Air-Standard Refrigeration Cycle 315

11 AN INTRODUCTION TO THE THERMODYNAMICS OF

MIXTURES 336

11.1 General Considerations and Mixtures of Ideal Gases 336

11.2 A Simplified Model of a Mixture of Gasesand a Vapor 343

11.3 The First Law Applied to Gas-Vapor Mixtures 347

11.4 The Adiabatic Saturation Process 349

11.5 Wet-Bulb and Dry-Bulb Temperatures 351

11.6 The Psychrometric Chart 352

12 THERMODYNAMIC RELATIONS 362

12.1 Two Important Relations 362

12.2 The Maxwell Relations 365

12.3 The Property Relation for Mixtures 368

12.4 The Clapeyron Equation 370

12.5 Some Thermodynamic Relations Concerning Enthalpy, Internal

Energy, and Entropy 37212.6 Some Thermodynamic Relations Concerning Specific Heat 378

12.7 Volume Expansivityand Isothermal and Adiabatic Compressibility 380

12.8 Developing Tables of Thermodynamic Properties from Experimental

J2.J3 Fugacity and the Generalized Fugacity Table/Chart 403

J2.14 Equations of State and Pseudocritical State for Mixtures 406

13 CHEMICAL REACTIONS 421

J 3 J Fuels 421

13.2 The Combustion Process 424

13.3 Enthalpy of Formation 431

J3.4 First-LawAnalysis of Reacting Systems 433

13.5 Adiabatic Flame Temperature 438

13.6 Enthalpy and the Internal Energy of Combustion; Heat of Reaction 440

13.7 The Third Law of Thermodynamics and Absolute Entropy 444

13.8 Second-Law Analysis of Reacting Systems 445

13.9 Evaluation of Actual Combustion Processes 454

14 INTRODUCTION TO PHASE AND CHEMICAL EQUILIBRIUM 467

Requirements for Equilibrium 467

Equilibrium Between Two Phasesof a Pure Substance

Equilibrium of a Multicomponent, Multiphase System

The Gibbs Phase Rule (Without Chemical Reaction)

15 QUANTUM MECHANICS 506

15.1 The Bohr Theory of the Atom 506

15.2 Wave Characteristics of Electrons and the Heisenberg Uncertainty

Principle 507

15.3 The Schrbdinger Wave Equation 509

15.4 Translation 511

15.5 Application of the Wave Equation to Molecules 514

15.6 Electronic States of Atoms 515

15.7 Molecular Rotation and Vibration 523

15.8 The Pauli Exclusion Principle 524

16 MOLECULAR DISTRIBUTIONS AND MODELS 528

16 1 Introduction 528

16.2 Mathematical Probability 529

16.3 Permutations, Combinations, and Repeated Trials 533

16.4 Distribution Functions, Mean Values, and Deviations 538

16.5 Molecular Distributions and Models 542

11 STATISTICAL MECHANICS AND THERMODYNAMICS 552

17.1 The Thermodynamic Equilibrium State 552

17.2 The First Law of Thermodynamics 557

The Maxwell-Boltzmann Velocity Distribution 583

Free Molecular Flow 589

The Diatomic Gas 592

The Polyatomic Gas 600The Electron Gas in a Metal 603Mixtures of Gases 607

Chemical Reaction and Equilibrium 611

579

Appendix A Tables, Figures, and Charts 625

Appendix B Computer-Aided Thermodynamics 754

Some Selected References 767

Answers to Selected Problems 768

Index 773

constant-pressure specific heat

constant-volume specific heat

zero-pressure, constant-pressure specific heat

zero-pressure, constant-volume specific heat

electron state sym bol

total dissociation energy

atomic term symbol

observed dissociation energy

electron charge

specific energy and total energy

electron state symbol

acceleration due to gravity

specific Gibbs function and total Gibbs function

a constant that relates force, mass, length, and timejth energy level degeneracy

molecular rotational quantum number

atomic total angular momentum number

specific heat ratio: CplCv

m rh

NO

P P

w, W

W

W rev

xx

polytropic exponentnumber of particlesAvogadro's numberelectron state symbolmathematical probabilityatomic term symbolpressure

partial pressure of component i in a mixture

potential energyheat transfer per unit mass and total heat transferrate of heat transfer

heat transfer with high-temperature body and heat transfer with temperature body; sign determined from context

low-radiusmolecular equilibrium separationgas constant

universal gas constantelectron state symbolspecific entropy and total entropyatomic term symbol

timetemperaturespecific internal energy and total internal energyzero-point energy per mole

molecular vibration quantum numberspecific volume and total volumevolume fraction

velocitythermodynamic probability-number of microstateswork per unit mass and total work

rate of work, or powerreversible work between two states assuming heat transfer with sur-roundings

qualityliquid-phase or solid-phase mole fractionvapor-phase mole fraction

partition function

Cfi' number of components

NCfi'M combinations of N, M at a time

{3T

I'J

Il III

SUBSCRIPTS

c

c.v

e e

f f fg

g

volume expansivitycoefficient of performance for a refrigeratorcoefficient of performance for a heat pumpadiabatic compressibility

isothermal compressibilityefficiency

chemical potentialJoule-Thomson coefficientstoichiometric coefficientdensity

relative humidityavailability for a systemavailability associated with a steady-state, steady-flow processhumidity ratio or specific humidity

property at the critical pointcontrol volume

electronicstate of a substance leaving a control volumeformation

property of saturated liquiddifference in property for saturated vapor and saturated liquidproperty of saturated vapor

energy statestate of a substance entering a control volumeproperty of saturated solid

ig difference in property for saturated vapor and saturated solid

bar over symbol denotes property on a molal basis (over V, H, S,

U, A, G, the bar denotes partial molal property)property at standard-state condition

ideal gasliquid phasesolid phasevapor phase

a rocket engine, and an air separation plant In this introductory chapter a briefdescription of this equipment is given There are at least two reasons for includingsuch a chapter First, many students have had limited contact with such equipment,and the solution of problems will be more meaningful when they have somefamiliarity with the actual processes and the equipment Second, this chapter willprovide an introduction to thermodynamics, including the use of certain terms(which will be more formally defined in later chapters), some of the problems towhich thermodynamics can be applied, and some of the things that have beenaccomplished, at least in part, from the application of thermodynamics.

Thermodynamics is relevant to many other processes than those cited in thischapter It is basic to the study of materials, chemical reactions, and plasmas Thestudent should bear in mind that this chapter is only a brief and necessarily veryincomplete introduction to the subject of thermodynamics

1.1 THE SIMPLE STEAM POWER PlANT

A schematic diagram of a simple steam power plant is shown in Fig 1.1 pressure superheated steam leaves the boiler, which is also referred to as a steamgenerator, and enters the turbine The steam expands in the turbine and, in doing

High-so, does work, which enables the turbine to drive the electric generator The pressure steam leaves the turbine and enters the condenser, where heat is transferredfrom the steam (causing it to condense) to the cooling water Because large quantities

low-of cooling water are required, power plants are frequently located near rivers orlakes This transfer of heat to the water in lakes and rivers leads to the thermalpollution problem, which has been studied extensively in recent years During ourstudy of thermodynamics we will gain an understanding of why this heat transfer

is necessary and how it can be minimized When the supply of cooling water islimited, a cooling tower may be used In the cooling tower some of the coolingwater evaporates in such a way that it lowers the temperature of the water thatremains as a liquid

Cooling water out

Low-pressure steam

High-pressure low-temperature water to boiler

High-pressure superheated steam Economizer

Superheater

Steam generator Fuel

Warm

air

Stack Air in gases

out

Cooling water from river or lake or cooling tower

Pump

FIGURE 1.1 Schematic diagram of a steam power plant.

The pressure of the condensate leaving the condenser is increased in the pumpand thus enables the condensate to flow into the steam generator In many steamgenerators an economizer is used An economizer is simply a heat exchanger inwhich heat is transferred from the products of combustion (just before they leavethe steam generator) to the condensate The temperature of the condensate isincreased, but no evaporation takes place In other sections of the steam generator,heat is transferred from the products of combustion to the water, causing it toevaporate The temperature at which evaporation occurs is called the saturationtemperature The steam then flows through another heat exchanger, known as asuperheater, where the temperature of the steam is increased well above the sat-uration temperature

In many power plants the air that is used for combustion is preheated in theair preheater by transferring heat from the stack gases as they are leaving thefurnace This air is then mixed with fuel-which might be coal, fuel oil, naturalgas, or other combustible material-and combustion takes place in the furnace

As the products of combustion pass through the furnace, heat is transferred to thewater in the superheater, the boiler, the economizer, and to the air in the airpreheater The products of combustion from power plants are discharged to theatmosphere, which is one of the facets of the air pollution problem we now face

A large power plant has many other pieces of equipment, some of which will

be considered in later chapters

Figure 1.2 shows a steam turbine and the generator that it drives Steam turbinesvary in capacity from less than 10 kilowatts to more than 1 000000 kilowatts.Figure 1.3 shows a cutaway view of a condenser The steam enters at the topand the condensate is collected in the hot well at the bottom while the coolingwater flows through the tubes A large condenser has a tremendous number oftubes, as shown in Fig 1.3

Figure 1.4 shows a large steam generator The flow of air and products ofcombustion are indicated The condensate, also called the boiler feedwater, enters

at the economizer inlet, and the superheated steam leaves at the superheater outlet.The number of operating nuclear power plants has increased substantially inrecent years In these power plants the reactor replaces the steam generator of theconventional power plant, and the radioactive fuel elements replace the coal, oil,

or natural gas

There are several different reactor designs in current use One of these is theboiling-water reactor, such as the system shown in Fig 1.5 In other nuclear powerplants a secondary fluid circulates from the reactor to the steam generator, whereheat is transferred from the secondary fluid to the water, which in turn goes through

a conventional steam cycle Safety considerations and the necessity to keep theturbine, condenser, and related equipment from becoming radioactive are alwaysmajor considerations in the design and operation of a nuclear power plant

FIGURE 1.3 A condenser used in a large power plant (Courtesy Westinghouse Electric Corp.).

ECONOMIZER OUTLET

SUPERHEATER OUTLET

STEAM TO SUPERHEATER

FIGURE '.4 A large steam generator (Courtesy Babcock and Wilcox Co.).

We might well ask whether all the equipment in the power plant, such as thesteam generator, the turbine, the condenser, and the pump, is necessary Is it possible

to produce electrical energy from the fuel in a more direct manner?

The fuel cell accomplishes this objective Figure 1.7 shows a schematic ment of a fuel cell of the ion-exchange membrane type In this fuel cell hydrogen

arrange-_Water _ Stt'am-waler mixture Steam

Ele<lr~

~-::!.::~~"';'Shielding

1381tV

transm;swn line

FIGURE 1.5 Schematic diagram of the Big Rock Point nuclear plant of Consumers Power Company

at Charlevoix Michigan (Courtesy Consumers Power Company).

and oxygen react to form water Let us consider the general features of the operation

of this type of fuel cell

The flow of electrons in the external circuit is from anode to cathode Hydrogenenters at the anode side, and oxygen enters at the cathode side At the surface ofthe ion-exchange membrane the hydrogen is ionized according to the reaction

2Hz •4H+ +

4e-Products of combustion Fuel

Air

Power plant

Heat transfer to cooling water

rv Electrical energy (work)

FIGURE 1.6 Schematic diagram of a power plant.

The electrons flow through the external circuit and the hydrogen ions flow throughthe membrane to the cathode, where the following reaction takes place.

4H+ + 4e- + Oz-+2HzOThere is a potential difference between the anode and cathode, and thus there is

a flow of electricity through a potential difference; this, in thermodynamic terms,

is called work There may also be a transfer of heat between the fuel cell and thesurroundings

At the present time the fuel used in fuel cells is usually either hydrogen or amixture of gaseous hydrocarbons and hydrogen The oxidizer is usually oxygen.However, current development is directed toward the production of fuel cells thatuse hydrocarbon fuels and air Although the conventional (or nuclear) steam powerplant is still used in large-scale power-generating systems, and conventional pistonengines and gas turbines are still used in most transportation power systems, thefuel cell may eventually become a serious competitor The fuel cell is already beingused to produce power for space and other special applications

Thermodynamics plays a vital role in the analysis, development, and design ofall power-producing systems, including reciprocating internal-combustion enginesand gas turbines Considerations such as the increase of efficiency, improved designoptimum operating conditions, environmental pollution, and alternate methods ofpower generation involve, among other factors, the careful application of the fun-damentals of thermodynamics

Catalytic electrodes

Hydrogen~

Ion-exchange membrane Gas chambers

~Oxygen

FIGURE 1.7 Schematic arrangement of an ion-exchange membrane type of fuel cell.

1.3 THE VAPOR-COMPRESSION REFRIGERATION CYCLE

A simple vapor-compression refrigeration cycle is shown schematically in Fig 1.8.The refrigerant enters the compressor as a slightly superheated vapor at a lowpressure It then leaves the compressor and enters the condenser as a vapor atsome elevated pressure, where the refrigerant is condensed as heat is transferred

to cooling water or to the surroundings The refrigerant then leaves the condenser

as a high-pressure liquid The pressure of the liquid is decreased as it flows throughthe expansion valve and, as a result, some of the liquid flashes into cold vapor.The remaining liquid, now at a low pressure and temperature, is vaporized in theevaporator as heat is transferred from the refrigerated space This vapor thenreenters the compressor

In a typical home refrigerator the compressor is located in the rear near thebottom of the unit The compressors are usually hermetically sealed, that is, themotor and compressor are mounted in a sealed housing, and the electric leads forthe motor pass through this housing This seal prevents leakage of the refrigerant.The condenser is also located at the back of the refrigerator and is arranged sothat the air in the room flows past the condenser by natural convection Theexpansion valve takes the form of a long capillary tube, and the evaporator islocated around the outside of the freezing compartment inside the refrigerator

Heat transfer to ambient air or to cooling water

High-pressure liquid Expansion valve Low-pressure mixture of liquid and vapor

Heat transfer from refrigerated space

High-pressure vapor

Compressor

~Work

Low-pressure vapor

FIGURE 1.8 Schematic diagram of a simple refrigeration cycle.

Figure 1.9 shows a large centrifugal unit that is used to provide refrigerationfor an air-conditioning unit In this unit, water is cooled and then circulated toprovide cooling where needed

1.4 THE THERMOELECTRIC REFRIGERATOR

We may well ask the same question about the vapor-compression refrigerator that

we asked about the steam power plant-is it possible to accomplish our objective

in a more direct manner? Is it possible, in the case of a refrigerator, to use theelectrical energy (which goes to the electric motor that drives the compressor) toproduce cooling in a more direct manner, and to avoid the cost of the compressor,condenser, evaporator, and all the related piping?

The thermoelectric refrigerator is such a device This is shown schematically inFig 1.10 The thermoelectric device, like the conventional thermocouple, uses twodissimilar materials There are two junctions between these two materials in athermoelectric refrigerator One is located in the refrigerated space and the other

in ambient surroundings When a potential difference is applied, as indicated, thetemperature of the junction located in the refrigerated space will decrease and thetemperature of the other junction will increase Under steady-state operating con-ditions, heat will be transferred from the refrigerated space to the cold junction.The other junction will be at a temperature above the ambient, and heat will betransferred from the junction to the surroundings

A thermoelectric device can also be used to generate power by replacing therefrigerated space with a body that is at a temperature above the ambient Such

a system is shown in Fig 1.11

drive motor

~ Centrifugal refrigerant compressor

Compressed refrigerant condenses around condenser water tubes

Cold refrigerant liquid boils around water cooler tubes Cold refrigerant liquid

flow control to water cooler

Vl

o

5:

mZ

m

Zvi

1.4 THE THERMOELECTRIC REFRIGERATOR 11

Heat transfer from refrigerated space

FIGURE I lOA thermoelectric refrigerator.

The thermoelectric refrigerator cannot yet compete economically with the ventional vapor-compression units However, in certain special applications, thethermoelectric refrigerator is already in use and, in view of research and devel-opment efforts under way in this field, it is quite possible that thermoelectricrefrigerators will be much more extensively used in the future

con-Heat transfer from a high-temperature body

1.5 THE AIR SEPARATIONPlANT

One process of great industrial significance is the air separation plant, in whichair is separated into its various components The oxygen, nitrogen, argon, and raregases so produced are used extensively in various industrial, research, space, andconsumer goods applications The air separation plant can be considered an ex-ample from two major fields, the chemical process industry and cryogenics Cryo-genics is a term applied to technology, processes, and research at very low tem-peratures (in general, below 150 K) In both chemical processing and cryogenics,thermodynamics is basic to an understanding of many phenomena that occur and

to the design and development of processes and equipment

A number of different designs of air separation plants have been developed.Consider Fig 1.12, which shows a somewhat simplified sketch of a type of plantthat is frequently used Air from the atmosphere is compressed to a pressure of 2

to 3 mega pascals It is then purified, particularly to remove carbon dioxide (whichwould plug the flow passages as it solidifies when the air is cooled to its liquefactiontemperature) The air is then compressed to a pressure of 15 to 20 mega pascals,cooled to the ambient temperature in the aftercooler, and dried to remove thewater vapor (which would also plug the flow passages as it freezes)

The basic refrigeration in the liquefaction process is provided by two differentprocesses In one process the air in the expansion engine expands During this

Distillation column

Aftercooler

Low-pressure compressor

Hydrocarbon

absorber

Fresh air intake

FIGURE 1.12 A simplified diagram of a liquid oxygen plant.

1.6 THE CHEMICAL ROCKET ENGINE 13

process the air does work and as a result the temperature of the air is reduced In

the other refrigeration process air passes through a throttle valve that is so designedand so located that there is a substantial drop in the pressure of the air and,associated with this, a substantial drop in the temperature of the air

As shown in Fig 1.12, the dry, high-pressure air enters a heat exchanger Theair temperature drops as it flows through the heat exchanger At some intermediatepoint in the heat exchanger, part of the air is bled off and flows through theexpansion engine The remaining air flows through the rest of the heat exchangerand through the throttle valve The two streams join (both are at the pressure of0.5 to 1 megapascal) and enter the bottom of the distillation column, which isreferred to as the high-pressure column The function of the distillation column is

to separate the air into its various components, principally oxygen and nitrogen.Two streams of different composition flow from the high-pressure column throughthrottle valves to the upper column (also called the low-pressure column) One ofthese streams is an oxygen-rich liquid that flows from the bottom of the lowercolumn and the other is a nitrogen-rich stream that flows through the subcooler.The separation is completed in the upper column Liquid oxygen leaves from thebottom of the upper column and gaseous nitrogen from the top of the column.The nitrogen gas flows through the subcooler and the main heat exchanger It isthe transfer of heat to this cold nitrogen gas that causes the high-pressure airentering the heat exchanger to become cooler

Not only is a thermodynamic analysis essential to the design of the system as

a whole, but essentially every component of such a system, including the pressors, the expansion engine, the purifiers and driers, and the distillation column,operates according to the principles of thermodynamics Inthis separation process

com-we are also concerned with the thermodynamic properties of mixtures and theprinciples and procedures by which these mixtures can be separated This is thetype of problem encountered in the refining of petroleum and many other chemicalprocesses It should also be noted that cryogenics is particularly relevant to manyaspects of the space program, and a thorough knowledge of thermodynamics isessential for creative and effective work in cryogenics

1.6 THE CHEMICAL ROCKET ENGINE

The advent of missiles and satellites brought to prominence the use of the rocketengine as a propulsion power plant Chemical rocket engines may be classified aseither liquid propellant or solid propellant, according to the fuel used

Figure 1.13 shows a simplified schematic diagram of a liquid propellant rocket.The oxidizer and fuel are pumped through the injector plate into the combustionchamber where combustion takes place at high pressure The high-pressure, high-temperature products of combustion expand as they flow through the nozzle, and

as a result they leave the nozzle with a high velocity The momentum changeassociated with this increase in velocity gives rise to the forward thrust on thevehicle

The oxidizer and fuel must be pumped into the combustion chamber, and some

auxiliary power plant is necessary to drive the pumps In a large rocket this auxiliary

Oxidizer tank

Fuel tank

Auxiliary power plant Pump

FIGURE 1.13 Simplified schematic diagram of a liquid-propellant rocket engine.

power plant must be very reliable and have a relatively high power output, yet itmust be light in weight The oxidizer and fuel tanks occupy the largest part of thevolume of an actual rocket, and the range and payload of a rocket are determinedlargely by the amount of oxidizer and fuel that can be carried Many different fuelsand oxidizers have been considered and tested, and much effort has gone into thedevelopment of fuels and oxidizers that will give a higher thrust per unit mass rate

of flow of reactants Liquid oxygen is frequently used as the oxidizer in propellant rockets, and liquid hydrogen is frequently used as the fuel

liquid-Much work has also been done on solid-propellant rockets They have beenvery successfully used for jet-assisted takeoffs of airplanes, military missiles, andspace vehicles They are much simpler in both the basic equipment required foroperation and the logistic problems involved in their use, but they are more difficult

to control

1.7 ENVIRONMENTAL ISSUES

In the first six sections of this chapter, we have introduced and discussed a number

of devices, each of which produces certain effects for the use and convenience ofhumankind For example, the construction and operation of the steam power plant

1.7 ENVIRONMENTAl ISSUES 15

creates electricity, which is so deeply entrenched in our society that we take itsready availability for granted Inrecent years, however, it has become increasinglyapparent that we need to consider seriously the effects of such an operation onour environment Combustion of hydrocarbon fuels releases carbon dioxide intothe atmosphere, where its concentration is increasing Carbon dioxide, as well asother gases, absorbs infrared radiation from the surface of the earth, holding itclose to the planet and creating the "greenhouse effect", which in turn is believed

to cause global warming and critical climatic changes around the earth Powerplant combustion, particularly of coal, releases sulfur dioxide, which is absorbed

in clouds and later falls as acid rain in many areas Refrigeration and tioning systems, as well as other industrial processes, use certain chlorofluorocar-bons that eventually find their way to the upper atmosphere and destroy theprotective ozone layer

air-condi-These are only some of the many environmental problems caused by our efforts

to produce goods and effects intended to improve our way of life During our study

of thermodynamics, which is the science of the conversion of energy from one form

to another, we must continue to reflect on these issues We must consider how wecan eliminate or at least minimize damaging effects, as well as use our naturalresources efficiently and responsibly

One excellent definition of thermodynamics is that it is the science of energy andentropy Since we have not yet defined these terms, an alternate definition in alreadyfamiliar terms is: thermodynamics is the science that deals with heat and work andthese properties of substances that bear a relation to heat and work Like allsciences, the basis of thermodynamics is experimental observation In thermody-namics these findings have been formalized into certain basic laws, which are known

as the first, second, and third laws of thermodynamics In addition to these laws,the zeroth law of thermodynamics, which in the logical development of thermo-dynamics precedes the first law, has been set forth

In the chapters that follow, we will present these laws and the thermodynamicproperties related to these laws, and apply them to a number of representativeexamples The objective of the student should be to gain both a thorough under-standing of the fundamentals and an ability to apply these fundamentals to ther-modynamic problems The examples and problems further this twofold objective

It is not necessary for the student to memorize numerous equations, for problemsare best solved by the application of the definitions and laws of thermodynamics

In this chapter some concepts and definitions basic to thermodynamics are sented

pre-2.1 THE THERMODYNAMIC SYSTEM AND

THE CONTROL VOLUME

A thermodynamic system is defined as a quantity of matter of fixed mass andidentity on which attention is focused for study Everything external to the system

is the surroundings, and the system is separated from the surroundings by thesystem boundaries These boundaries may be either movable or fixed

In Fig 2.1 the gas in the cylinder is considered the system If a Bunsen burner

is placed under the cylinder, the temperature of the gas will increase and the pistonwill rise As the piston rises, the boundary of the system moves As we will seelater, heat and work cross the boundary of the system during this process, but thematter that comprises the system can always be identified

An isolated system is one that is not influenced in any way by the surroundings.This means that no heat or work cross the boundary of the system

16

FIGURE 2.1 Example of a system.

In many cases a thermodynamic analysis must be made of a device, such as anair compressor, which has a flow of mass into it, out of it, or both, as shownschematically in Fig 2.2 The procedure followed in such an analysis is to specify

a control volume that surrounds the device under consideration The surface ofthis control volume is referred to as a control surface Mass, as well as heat andwork (and momentum), can flow across the control surface

Thus, a system is defined when dealing with a fixed quantity of mass, and acontrol volume is specified when a flow of mass is to be analyzed The difference

in these two approaches is considered in detail in Chapter 6 The terms closedsystem and open system are sometimes used as the equivalent of the terms system(fixed mass) and control volume (involving a flow of mass) The procedure thatwill be followed in the presentation of the first and second laws of thermodynamics

is first to present these laws for a system and then to make the necessary formations to apply them to a control volume

trans-2.2 MACROSCOPIC VERSUS MICROSCOPIC POINT OF VIEW

An investigation into the behavior of a system may be undertaken from either amicroscopic or a macroscopic point of view Let us briefly describe a system from

a microscopic point of view Consider a system consisting of a cube 25 mm on aside and containing a monatomic gas at atmospheric pressure and temperature.This volume contains approximately 1020 atoms To describe the position of each

Heat

Air compressor Motor

High-pressure air out

,

I I

FIGURE 2.2 Example of a control volume.

atom, we need to specify three coordinates; to describe the velocity of each atom,

we specify three velocity components

Thus, to describe completely the behavior of this system from a microscopicpoint of view we must deal with at least 6 x 1020 equations Even with a largedigital computer, this is a quite hopeless computational task However, there aretwo approaches to this problem that reduce the number of equations and variables

to a few that can be computed relatively easily One approach is the statisticalapproach, in which, on the basis of statistical considerations and probability theory,

we deal with "average" values for all particles under consideration This is usuallydone in connection with a model of the atom under consideration This is theapproach used in the disciplines known as kinetic theory and statistical mechanics.The other approach that reduces the number of variables to a few that can behandled is the macroscopic point of view of classical thermodynamics As the wordmacroscopic implies, we are concerned with the gross or average effects of manymolecules These effects can be perceived by our senses and measured by instru-ments However, what we really perceive and measure is the time-averaged influence

of many molecules For example, consider the pressure a gas exerts on the walls

of its container This pressure results from the change in momentum of the molecules

as they collide with the wall From a macroscopic point of view, however, we arenot concerned with the action of the individual molecules but with the time-averaged force on a given area, which can be measured by a pressure gage In fact,these macroscopic observations are completely independent of our assumptionsregarding the nature of matter

The theory and development of thermodynamics in this book will be presentedfrom both the macroscopic and the microscopic points of view Chapters 3 through

14 cover the principles and a number of applications of classical thermodynamics;Chapters 15 through 18 constitute an introduction to the subject of statisticalthermodynamics

A few remarks should be made regarding the continuum From the macroscopicview, we are always concerned with volumes that are very large compared tomolecular dimensions and, therefore, with systems that contain many molecules.Because we are not concerned with the behavior of individual molecules, we cantreat the substance as being continuous, disregarding the action of individualmolecules; this is called a continuum The concept of a continuum, of course, isonly a convenient assumption that loses validity when the mean free path of themolecules approaches the order of magnitude of the dimensions of the vessel, as,for example, in high-vacuum technology In much engineering work the assumptionofa continuum is valid and convenient, and goes hand in hand with the macroscopicview

2.3 PROPERTIES AND STATE OF A SUBSTANCE

If we consider a given mass of water, we recognize that this water can exist invarious forms If it is a liquid initially, it may become a vapor when it is heated

or a solid when it is cooled Thus, we speak of the different phases of a substance

A phase is defined as a quantity of matter that is homogeneous throughout When

more than one phase is present, the phases are separated from each other by thephase boundaries Ineach phase the substance may exist at various pressures andtemperatures or, to use the thermodynamic term, in various states The state may

be identified or described by certain observable, macroscopic properties; somefamiliar ones are temperature, pressure, and density In later chapters other prop-erties will be introduced Each of the properties of a substance in a given state hasonly one definite value, and these properties always have the same value for agiven state, regardless of how the substance arrived at that state Infact, a propertycan be defined as any quantity that depends on the state of the system and isindependent of the path (that is, the prior history) by which the system arrived atthe given state Conversely, the state is specified or described by the properties,and later we will consider the number of independent properties a substance canhave, that is, the minimum number of properties that must be specified to fix thestate of the substance

Thermodynamic properties can be divided into two general classes, intensiveand extensive properties An intensive property is independent of the mass; thevalue of an extensive property varies directly with the mass Thus, if a quantity ofmatter in a given state is divided into two equal parts, each part will have thesame value of intensive properties as the original, and half the value of the extensiveproperties Pressure, temperature, and density are examples of intensive properties.Mass and total volume are examples of extensive properties Extensive propertiesper unit mass, such as specific volume, are intensive properties

Frequently we will refer not only to the properties of a substance but to theproperties of a system When we do so we necessarily imply that the value of theproperty has significance for the entire system, and this implies equilibrium Forexample, if the gas that comprises the system in Fig 2.1 is in thermal equilibrium,the temperature will be the same throughout the entire system, and we may speak

of the temperature as a property of the system We may also consider mechanicalequilibrium, which is related to pressure If a system is in mechanical equilibrium,there is no tendency for the pressure at any point to change with time as long asthe system is isolated from the surroundings There will be a variation in pressurewith elevation because of the influence of gravitational forces, although underequilibrium conditions there will be no tendency for the pressure at any location

to change However, in many thermodynamic problems, this variation in pressurewith elevation is so small that it can be neglected Chemical equilibrium is alsoimportant and will be considered in Chapter 14

When a system is in equilibrium regarding all possible changes of state, we saythat the system is in thermodynamic equilibrium

2.4 PROCESSES AND CYCLES

Whenever one or more of the properties of a system change, we say that a change

in state has occurred For example, when one of the weights on the piston in Fig.2.3 is removed, the piston rises and a change in state occurs, for the pressuredecreases and the specific volume increases The path of the succession of statesthrough which the system passes is called the process

_ _ _ J

Gas

Piston -1~w~<::z2:22;:Z=ZLZ:Z~

r I

System :

"'""''''1

FIGURE 2.3 Example of a system that may undergo a quasiequilibrium process.

Let us consider the equilibrium of a system as it undergoes a change in state.The moment the weight is removed from the piston in Fig 2.3, mechanical equi-librium does not exist, and as a result the piston is moved upward until mechanicalequilibrium is again restored The question is this: Since the properties describethe state of a system only when it is in equilibrium, how can we describe the states

of a system during a process if the actual process occurs only when equilibriumdoes not exist? One step in the answer to this question concerns the definition of

an ideal process, which we call a quasi-equilibrium process A quasi-equilibriumprocess is one in which the deviation from thermodynamic equilibrium is infini-tesimal, and all the states the system passes through during a quasi-equilibriumprocess may be considered equilibrium states Many actual processes closely ap-proach a quasi-equilibrium process, and may be so treated with essentially noerror If the weights on the piston in Fig 2.3 are small and are taken off one byone, the process could be considered quasi-equilibrium On the other hand, if allthe weights were removed at once, the piston would rise rapidly until it hit thestops This would be a nonequilibrium process, and the system would not be inequilibrium at any time during this change of state

For nonequilibrium processes, we are limited to a description of the systembefore the process occurs and after the process is completed and equilibrium isrestored We are unable to specify each state through which the system passes orthe rate at which the process occurs However, as we will see later, we are able todescribe certain overall effects that occur during the process

Several processes are described by the fact that one property remains constant.The prefix iso- is used to describe this process An isothermal process is a constant-temperature process, an isobaric (sometimes called isopiestic) process is a constant-pressure process, and an isochoric process is a constant-volume process

When a system in a given initial state goes through a number of different changes

of state or processes and finally returns to its initial state, the system has undergone

a cycle Therefore, at the conclusion of a cycle, all the properties have the samevalue they had at the beginning Steam (water) that circulates through a steampower plant undergoes a cycle

A distinction should be made between a thermodynamic cycle, which has justbeen described, and a mechanical cycle A four-stroke cycle internal-combustionengine goes through a mechanical cycle once every two revolutions However, theworking fluid does not go through a thermodynamic cycle in the engine, since air