Thư viện - ĐH Quy Nhơn 600 / Г 00150 ° David R Gaskall Dauid E Laughlin ® CRC Press Taylor Francis G r o u p Tai ngay!!! Ban co the xoa dong chu nay!!! The Laws of Thermodynamics t Oth Law Introduces the thermodynamic intensive variable of temperature (T) • 1st Law Conservation and conversion of energy Defines extensive thermodynamic state variable of internal energy ( U) dU = Sq - Sw' • 2nd Law Defines the extensive thermodynamic state variable of entropy (S) dSuniverse >0 • 3rd Law For systems in internal equilibrium, sets the zero o f entropy at the minimum in temperature (OK) and at the minimum in internal energy The Three TdS Equations TdS = c d T + -7T-dV PT TdS - c dT - TVadP P T d S - c ^ d P +^ i V Fundamental Equations (extensive) for Magnetic Materials dU ’ = TdS'- PdV' + V 'fifld M + Efi.dn dH ’ = TdS' + V'dP - V 'fijv td tt + Eyidn dA ' = -S 'd T - P d V ' + V 'n fld M + E ^dn dG' = -S 'd T + V 'd P - VdJddOT + E^dti Maxwell Relations for Single Component fd P ( * r U v, s ~{ ÔS fdT> (a n [ d P ys W ( dS ) ,dvj r dP | T ) \ ' dS fd V r°p ) T dT Introduction to the Thermodynamics of Materials Sixth Edition Introduction to the Thermodynamics of Materials Sixth Edition David R Gaskell School of Materials Engineering Purdue University West Lafayette, IN David E Laughlin ALCOA Professor of Physical Metallurgy Department of Materials Science and Engineering Carnegie Mellon University Pittsburgh, PA TRt/ÔNG 0AI HQC QUY HtlÖK TH Ü V i È N CRC Press T a y lo r & Francis C r o u p Boca Raton London N ew York CRC Press is an im print of the Taylor & Francis Group, an inform a business CRC Press Taylor & Francis Group 6000 Broken Sound Parkway NW, Suite 300 Boca Raton, FL 33487-2742 © 2018 by Taylor & Francis Group, LLC CRC Press is an imprint of Taylor & Francis Group, an Informa business No claim to original U.S Government works Printed on acid-free paper International Standard Book Number-13: 978-1-4987-5700-3 (Hardback) been made to^ubf in^ nial‘on G a in e d from authentic and highly regarded sources R eason ab le e ffo r ts have for the validity of 'n ^ * • C data and information’ but the author and publisher cannot a ssu m e r e s p o n sib ility * trace the copyright* bokT ^1^ ^ ^ conseiluences ° f their use The authors and p u blishers have a ttem p te d to permission to publish^ CJlS 0^a^ mater^ reproduced in this publication and a p o lo g ize to c o p y r ig h t h o ld er s i f please write and ^ T 'S ^°rm has not ^cen S ta in e d If any copyright m aterial has not been a c k n o w le d g e d US novv so we may rectify in any future reprint ted, or utilized i n ^ U^ Cr Copyright Law, no part o f this book may be reprinted, rep rod u ced , tran sm it- including p h o to c o ^ 0rm ^ 3ny e^ectronic’ mechanical, or other m eans, now k n ow n or h ereafter in v e n ted , out written permission^ m,Cro^ min£’ and recording, or in any inform ation storage or retrieval s y ste m , w ith - For permission to photocopy or use material electronically from this work, (http://www.copyright.com/) or contact the Copyright Clearance en , Danvers, MA 01923,978-750-8400 CCC is a not-for-profit o rg a n iz a tio P for a variety of users For organizations that have been grante a p o system of payment has been arranged (C Caccess C ) 2w2 wRwo.copyright.com se w o o d D r iv e , ^ c e n s e s an reg istr a tio n by the C C C , a sep a te Trademark Notice: Product or corporate names may be trademarks or regis • ered tradem arks, and are u s e d only for identification and explanation without intent to infringe u ,„ „ „ Names Gaskcll David R„ 1940- author 1Laughlm, D a v G a s k e l l & Title: Introduction to the thermodynamics o f materia s, David E Laughlm Tay)or & F rancis, Description: Sixth edition 1Boca Raton, FL CKC r ic , 12017] 1Includes index _ Identifiers: LCCN 20170116231 ISBN 9781498757003 (hard ic r n j 9781315119038 (e-book) ợ ô m n o rties M e ta llu rg y Subjects: I.CSH: Thermodynamics I Matcrials-Thcrmal pr p Classification: LCC TN673 G33 2017 1D D C /1 - c LC record available at https://lccn.loc.gov/20l7011623 Visit the Taylor & Francis Web site at http://www.tavlorandfrancis.ỗom and the CRC Press Web site at http://www.crcpress.com Dedication Grandchildren are the crown of,he aged (Proverbs 17:6) Sadie, Gabe, Rowan, Sawyer, Ramona, Adam, Charlie, Astrid, and Reuben The LORD bless you and may you (also) see your children’s children (Psalm 128:5ff.) Contents Preface xvii A uthors Part I Thermodynamic Principles Chapter Introduction and Definition of T erm s 1.1 1.2 1.3 1.4 1.5 1.6 1.7 1.8 Introduction The Concept of State Example of Equilibrium The Equation of State of an Ideal G a s The Units of Energy and W ork Extensive and Intensive Thermodynamic Variables Equilibrium Phase Diagrams and Thermodynamic Components Laws of Thermodynamics 1.8.1 The First Law of Therm 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 1.11 Qualitative Example Problems 1.12 Quantitative Example Problems P ro b lem s 3 12 13 13 16 17 17 17 17 18 19 20 21 Chapter The First Law of Therm odynam ics 23 2.1 Introduction 2 The Relationship between Heat and W ork 23 Internal Energy and the First Law of Therm odynam ics 2.4 Constant-Volume Processes 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 Magnetic 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 Surface 2.10 Sum m ary 2.11 Concepts and Terms Introduced in Chapter 23 24 25 29 30 31 37 40 41 41 42 42 43 45 v ii VIII 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 45 47 51 54 Chapter The Second Law of Thermodynamics 57 3.1 3.2 3.3 3.4 3.5 3.6 3.7 3.8 3.9 3.10 3.11 3.12 3.13 3.14 3.15 316 317 3-1^ ^49 Introduction Spontaneous or Natural Processes Entropy and the Quantification of Irreversibility Reversible Processes 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 • Further Differences between Reversible and Irreversible Expansion Compression of an Ideal Gas 3.7.1 Reversible Isothermal Compression The Adiabatic Expansion of an Ideal Gas Summary Statements The Properties of Heat Engines The Thermodynamic Temperature Scale The Second Law of Thermodynamics Maximum Work Entropy and the Criterion for Equilibrium The Combined Statement of the First and Second Laws of Thermodynamics Summary Concepts and Terms Introduced in Chapter Qualitative Example Problems Quantitative Example Problems Problems Chapter 81 83 83 85 90 „93 „93 „94 „95 „9 4.1 4.2 4.3 Introduction c - t Entropy and Disorder on an Atomic vca e The Concept of Microstate 4.4 The Microcanonical Approach *" Sites with Different 4.4.1 Identical Particles on Distinguishable^ 45 79 The Statistical Interpretation of Entropy Assigned Energies Vniffering Moms »n a C ry s ta lSnins on an cm U w a*™*» Array of Atoms The Boltzmann Distribution 4.4.2 4.4J 57 58 59 „61 „61 62 63 64 65 65 66 67 67 71 74 76 78 Configurational Entropy °1 „96 „98 102 104 CONTENTS ix The Influence of Tem perature 4.6 Thermal Equilibrium and the Boltzmann E quation 4.7 Heat Flow and the Production of E n tro p y 4.8 Sum m ary 4.9 4.10 Concepts and Terms Introduced in Chapter 4.11 Qualitative Example Problem s 4.12 Quantitative Exairmle Problem s P ro b lem s .113 115 116 119 Chapter Fundamental Equations and Their Relationships 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 Introduction The Enthalpy, H The Helmholtz Free Energy, A The Gibbs Free Energy, G The Fundamental Equations for a Closed System 129 The Variation of the Composition within a Closed System 131 The Chemical Potential 131 Therm odynam ic R elations 134 M axwell’s R elations 135 Examples of the Application of Maxwell R elations 137 5.10.1 The First TdS E quation 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 (Enthalpy) 143 5.10.6 A Magnetic Maxwell R elation .143 5.10.7 S, K and M with Independent Variables T, P, and M .144 5.1 Another Important Form ula .145 5.12 The Gibbs-H elm holtz E quation 145 5.13 Sum m ary 147 5.14 Concepts and Terms Introduced in Chapter 148 5.15 Qualitative Example Problems 148 5.16 Quantitative Example Problems 150 P roblem s 152 Chapter Heat Capacity, Enthalpy, Entropy, and the Third Law of T herm odynam ics .155 6.1 6.2 6.3 6.4 Introduction 155 Theoretical Calculation of the Heat Capacity 156 The Empirical Representation of Heat C apacities 162 Enthalpy as a Function of Temperature and C om position 162 C O N TEN TS X 6.5 The Dependence of Entropy on Temperature and the Third Law of 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 185 6.10 Qualitative Example Problems ^ 6.11 Quantitative Example Problems 187 Problems ^ Appendix 6A 1^4 Part II Phase Equilibria Chapter ^ 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 204 Temperature .205 7.4 The Gibbs Free Energy as a Function of Temperature and Pressure 210 7-5 Equilibrium between the Vapor Phase and a Condensed Phase 7.6 Graphical Representation of Vapor Phase and Condensed Phase 212 Equilibria .212 7.7 Solid-Solid Equilibria 217 7-S The El feet of an Applied Magnetic Field on the P-T D iagram 218 7-9 Sum m ary / 219 J0 Concepts and Terms Introduced in Chapter 220 ' Qualitative Example Problems P«)blc.ma.r! ,.,a.tiVe EXample Pr°bIemS .222 226 Chapter The Behavior of Gases 229 8.1 Introduction 2 8.2 8.3 The P-V-l Relationships of Gases ^ 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 ^ 680 ANSWERS TO SELECTED PROBLEMS 11* dQ = SdT+ PdV+ Ndji Q = Q (T,V,m) Chapter Seven 7.1 (a) The triple point for a-p-vapor is T = 1163 K, p = 2.52 x 10-10 atm, and the triple point for P-liquid-vapor is T = 1689 K, p = 8.35 x 10~5 atm (b) Th = 2776 K (c) A //(a_*P) = 4739 J, AHm = 29,770 J 7.2 p Hg.373 K = 3.55 X 10-4 atm 7.3 Condensation begins at 328 K; at 280 K 82.5% of the SiCl4 has condensed 7.4 Eq (I) gives the vapor pressure of solid zinc 7.5 A ///;,Fc =73.3 atm The triple-point pressure is 5.14 atm, and, as the atm isobar does not pass through the liquid-phase field, liquid C 02 is not stable at atmospheric pressure 7.7 P = 2822 atm 7.8 The slopes of the lines at the triple-point are obtained from dP/dT = AS/A V 7.9 Th = 523 K 7.12* 681 ANSWERS TO SELECTED PROBLEMS 7.13* S S+L L i Chapter Eight 8.1 The van der Waals equation containing the reduced variables is Zu = 0.375; ( d U / d W t = a / V : 8.2 n A/ n B - \ , P = 1-414 atm 8.3 The tank contains 565 moles of van der Waals oxygen and 511 moles of ideal gas oxygen As the gas is purchased by the tank-load, the same price purchases more moles of a van der Waals gas than it does an ideal gas 8.4 w = -1384 J 8.5 (a) b = 0.0567 l/mole, a = 6.7712-atm/mole2; (b) 0.170 1/mole; (c) P (van der Waals) = 65.5 atm, P (ideal gas) = 82.1 atm 8.6 With the virial equation w = -301 kJ, with the van der Waals equation vv = -309 kJ, with the ideal gas law vv = -272 kJ 8.7 (a)/ = 688 atm, (b) P = 1083 atm, (c) AG = 16,190 J with an nonideal con tribution of 790 J 8.9* Volume ANSWERS TO SELECTED PROBLEMS 682 10* dP = R d T - { RT ,- + ^ ) d V ( V - b ) V3 V-b 12* Zrr = RTcr _ _ o _ 3^ _JL 21b2 R 8a = = 0.375 Chapter Nine AH = 117,400 J, AS = 59.63 J/K 9.2 yM„=1.08 9.3 (a) The average value o f a is 4396 ± J which indicates that, with respect to the behavior o f G x\ the solution is regular, (b) G\ c = 1583 J and Gm„ = 703 (c) AGM= - 9.370 J (d) p Mn = 0.0118 atm and p Fe = 3.68 X 10"5 atm 9.4 73,380 J 9.5 a = -4578 J, a Sn= 0.418 9.6* AGB= RTaB= -57637 9.1 aB(XB= 0.5) = e x p | - | ^ j=0.5 AGb = RTaB=-1609 b 9.8 The tem perature is increased by 2.37 degrees (K) 9.10 In ycd = 0.425 X i , + 0.30X}„, aCd = 0.577 9.11 oAu= 0.695, oNi= 0.85 9.14 a ' < a' 9.15* aB = 0.824 Chapter Ten 10.1 T= 1317 K, A'CaFi = 0.53 10.2 (a) - 11,140 J, (b) zero 10.3 (a) 2418 K, (b) XAI,0, = 0.62, (c) 2444 K, (d) XAi,o, = 0.38 - 814 J 10.5 a, = 38,096 J, Tcr = 2291 K 10.6 (a) A//„,Ge from liquidus = 21,527 J, (b) A//°.Gc from solidus = 33,111 J ANSWERS TO SELECTED PROBLEMS 683 10.7 The maximum solubility of CaO in MgO is XCa0 = 0.066, and the maxi mum solubility of MgO in CaO is XM„0 = 0.15 Chapter Eleven XCOz = XHi= 0.182, XH,0 = 0.0677, Xco = 0.568 43,800 J C 2/H2 = 1.276 1771 К P T = 0.192 atm, T = 792 К (a) p N = 5.94 x 10-6 atm, (b) P T = 3.18 x 10~9 atm 13.3 atm, ДЯЬзк =-50,900 J, АЯ„3K =-1107 J/K PC15/PC13 = 0.371 At P T = i atm, p Hl = 1.05xl0~8 atm, Po2 =0.0756 atm At P T = 10 atm, pH, =3.31xl0"8 atm, p , =0.756 atm 11.10 11.1 11.2 11.3 11.4 11.5 11.6 11.7 11.8 11.9 •’('и, = = 0.165, XH1 = 0.669, T = 906 К 11.11* „ PCO ~ К4 A p J - P c o : = - j - (K p+l) {K} + 1) Chapter Twelve 12.1 12.2 12.3 12.4 12.5 T - 565 K TmNl = 1731 K, AH’mM = 17,490 J ASn, Ni = 10.1 J/K (a) T = 462 K, (b) T = 421 K pH,0 = 1.32X10"3 atm, and the oxidation reaction is exothermic Equilibrium would produce a gas containing 11.4% HC1, 46.6% H2, and 42% Ar Therefore equilibrium is not attained 12.6 The FeO disappears 12.7 p Mf = 2.42 X KH atm 12.8 (a) T - 1173 K, (b) p c o, =0.055 atm, (c) Pco, = 1-23 atm 12.9 P = atm(pSo, = 7.99x I0“‘atm, pso, =0.612 atm, pih =0.306 atm) 12.10 99.1% of the sulfur is removed, and p s in the effluent gas is 6.3 x 10 11 atm 12.11 AC" =282,000- 1237’ J 12.12 0.76 moles of CH4 are consumed per mole of Fe produced 12.13 Eq (i) for solid Mg, Eq (ii) for gaseous Mg, Eq (iii) for liquid Mg, TmMg 930 K, 7/ Mg = 1372 K ANSWERS TO SELECTED PROBLEMS 684 12.14 54.92 g of Zn are oxidized to form ZnO and 29.78 g of Zn are evaporated, which leaves 115.3 g of metallic Zn in the crucible 12.15 4.76 moles of CaC03 are decomposed per mole of CH4 burned 12.16 XHg = 0.0152, X02 = 0.0071 12.17 PT = 1.651 atm, p co = 1.009 atm, pCOl =0.642 atm Chapter Thirteen 13.1 13.2 13.3 13.4 13.5 13.6 13.7 aCu = 0.159 tfMg = 6.4 x 10-4 aPb0 = 0.5 XCu = 0.018 Increasing T decreases the extent to which Cu is removed ac = 0.5 P h2 =0.92 atm aFcQ= 9.9 X 10-5 (a) P h2 ! p c o = 2.15, (b) ac = 0.194, (c) PT = 5.16 atm, (d) the total pressure does not influence p Q 13.8 With C = and P = 3,77 = 2, which are used by specifying T = 1000 K and [XMn] = 0.001 (XFcQ) = 1.22 x 10“3, Po2 = 3 x l0 '27 atm 13.9 For 2A + B = A2B, AG,°,73 K =-24,370 J ; for A + 2B = A2B, AG,°273 k =-23,1901.** 13.10 (a) 10-\ (b) 8.07 x 10"4, (c) 7.14 x 10-\ (d) 0.65 13.11 AG° =-567,500 J 13.12 Po2 =5.17x1 O'10 atm; hM(l wtc,inFc) = 7.2 x 10 6; C = 3, P = 4, therefore - which is fixed by specifying T - 1600°C 13.13 ^ = 2211 K, Tmin = 1515 K , 13.14 p Mg = 0.053 atm 13.15 c/Mp0(min) = 0.027 13.16 p co = 0.739 atm, Pco^ =0.0117 atm, p 7n = 0.763 atm 13.17 aM2o> =0.129 13.18 (a) wt% AI = 0.00042, wt% O = 0.0039; (b) wt% A1 = 0.00054, wt% O = 0.0035 13.19 Tmax= 1108 K 13.20 P = 6917 atm 13.21 Wustite 0.904 < p co < 3.196 atm, cementite 7.43 < p co < 8.14 atm 13.22 Tmax = 1026 K 13.23 aZl = 0.154 13.24 |wt% OJ = 1.9, /:(1273 K) = 2.0 13.25 The formation of a manganese silicate melt as the deoxidation product decreases the activity of Si02 to a value less than unity and thus shifts the equilibrium [Si] + 2[0] = (Si02) to the right For any given value of [wt% Si], the extent of deoxidation is maximized when the product of deox idation is an MnO-saturated silicate melt in which aSl02 has its minimum value of 0.02 685 ANSWERS TO SELECTED PROBLEMS Chapter Fourteen 14.1 Pb(5) + 2AgCl(„ = 2Ag(„ + PbCl,(s), AG° = -94,560 J, AS° = -35.5 J/K 14.2 (a) -103,400 J, (b) 27.98 J/K, (c) 8338 J/mole of Pb, (d) a Hg = 0.71 46,620£ 63,440 In p0l (atm) = — + - 15.48 T T 14.3 Ac,, = -0.093 J/K (a) aM = 0.673, (b) =-2150 J >(c) A =3329 J (a) 1.62 x 10-6, (b) 0.5, (c) 0.266 wt%, (d) 0.602 wt% pH = 6.33, C S = -0.126 volts, [Pb4+] = 3.1 x 10"62 moles/liter, HPbOi = 10'y moles/liter, pbO,' =2.5x1 O'47 moles/liter, [PbO}- ] = x = 10"221 moles/ liter 14.8 2.20 volts, 1.17 volts 14.9 +6897 J, -4513 J 14.4 14.5 14.6 14.7 Chapter Fifteen 15.1* a S xs = a 2( T - T c ) b C r 7- C f =a 2C 15.2* b G n c First order 686 ANSWERS TO SELECTED PROBLEMS d AH = T0J — < since C < {ie\ e Exothermic 15.4* a T ^ /l-2 = y a |/a c o s j : V b c d a ,/a zero “ Ya, la j / Index Absolute potential, 571 Activity quotient, 469 Adiabatic boundaries, Adiabatic expansion, 40 o f ideal gas, 6 -6 Adiabatic process, 38 Activation energy, 268 A l - C - O - N system , and phase equilibria in, -5 Allotropy, 162, 212 Alloy, 15, 115, 288, 329, 47 -4 7 , 516, 519, ,6 /Amorphous solid, 630 A nodic oxidation reaction, 574, 602 Anolyte, 573 Atom ic order parameter, 3 -3 Auxiliary functions, 122 Barrier, to nucléation, 3 -6 Berthollet, Claude Louis, 523 Berthollides, 523 Binary system s containing com pounds The G a-G aP system , 510-512 The M g -S i system , 512-515 phase diagrams of, -3 Blast furnace, 436 Boltzm ann, Ludwig Eduard, 96 Boltzmann distribution, 104-107 Boltzmann equation, 110-111 Bond energy, 101, 271, -2 8 Boudouard, Octave Leopold, 436 Boudouard reaction, 436 Boundaries, Boyle, Robert, B oyle’s law, 9, 11 Capillarity, and local equilibrium, -6 C arbon-oxygen reactions 443 Carnot, N icolas Leonard Sadi, 68 Carnot cycle, 69, 71, 72, 74 Cathodic reduction reaction, 574 602 Catholytc, 573 Cell reaction 569 Charge neutrality 568 Charles, Jacques-Alexandre-Cesar Charles’ law 9, 11 Chem ical affinity, 381 423 Chem ical potential, 131-134 9 -2 0 Chem ical reaction 122, 131 Chem ical work, 134 Chlorination, 433 Clapeyron, B enoit Paul E m ile, 206 Clapeyron equation, 206 Classical therm odynam ics, 93, 111 Closed system s, - Coefficient o f thermal expansion, 10 Com m on tangent, 324, 341, 348, 352, 358, 361 Com pressibility factor, 239, 240 Concentration cell, 577 -5 Condensation, -2 Condensed and gaseous phases and carbon oxides, -4 and chlorination o f iron, 3 -4 description 414-419 effect o f phase transformations, -4 3 Ellingham diagrams, 2 -4 and Gibbs tree energy change with temperature, -4 2 graphical representation of, 4 -4 overview, 413 Condensed-phase reactions, 413 Condensed solution binary system s containing com pounds, 50 -5 criteria for, -4 7 and dilute solute, 537 -5 and Gibbs equilibrium phase rule, -4 graphical representation of 516 -5 overview, -4 and phase stability diagrams, —503 solubility o f gases in m etals, -5 standard state of 7 -4 Configurational entropy, 81, 02-104 Congruent solidification 630 Congruent temperature, 325 Conservation o f energy, 23 Constant-pressure processes, 30-31 Constant-temperature heat reservoir, 59 Constant-volume processes -3 Continuous transition, see Higher-order transition Conversion o f energy, 3, Corresponding states, 160 Covalent character, 567 Critical nucleus, 625 Critical point, 238 Cyclic process, 28 Dalton's law, -2 Daniell, John Frederick, 569 Daniell cell, 569, 572 687 INDEX 688 Debye, Peter Joseph W illiam , 159 Debye m odel, 185 Degree, o f m ixed-up-ness, 95 Dependent thermodynamic variables, Diathermal boundaries, 3, D iffusion less transformation, 627 Dilute solute, and reaction equilibria, 537-547 Dissipation o f energy, 59 Dulong, Pierre Louis, 156 Dulong and Petit’s law, 156, 159, 186 Dynam ic equilibrium, 267, 382 Efficiency o f engine, 68 Einstein crystal, see Einstein solid Einstein model, 159 Einstein solid, 157 Electric potential, -5 , 572 Electrochem ical reaction, 568 Electrochem ical series, 596 Electrochem istry and aquèous solution, -5 chem ical and electrical driving forces, : -5 concentration cell, 577 -5 EMF concentration on, 574-575 temperature coefficient of, -5 formation cells, -5 7 Gibbs free energy o f formation o f ions and standard reduction potentials, 591-601 overview, -5 in Pourbaix diagrams, 601-611 for aluminum, -6 equilibrium between two dissolved substances, -6 equilibrium between two solids, -6 equilibrium with single dissolved substance, -6 solubility o f alumina in aqueous solutions, 609-611 thermal energy (heat) effects, -5 Electrolysis 573, 609 Electrolyte 569-571, 57 -5 Electromotive force (EM F) concentration on, 574-575 temperature coefficient of, -5 Ellingham , Harold Johann Thomas, 422 diagrams, 2 -4 EMF see Electrom otive force (EM F) Endothermic process, 171, 287 Energy equation (internal energy), 142-143 Enthalpy, 30, 123 and constant-pressure processes, 30-31 energy equation, 143 o f freezing, 36 as function o f temperature and com position, 162-176 and ideal solutions, 281 -2 o f melting, 94 o f m ixing ideal gases, -2 Entropy aspects of, 94 and atomic scale disorder, -9 and Boltzmann distribution, 104-107 configurational, 81 o f differing atoms in a crystal, -1 o f m agnetic spins, 102-104 and criterion for equilibrium, -7 heat flow and production of, 111-113 ideal solutions, -2 and identical particles, -9 and microstate, -9 as “m ixed-up-ness,” 94, 95 o f m ixing ideal gases, 236 overview, 93 and quantification o f irreversibility, 59—61 and temperature effect, 108-109 thermal equilibrium and Boltzmann equation, 110-111 and working o f heat engine, -7 Equilibrium constant, 386, 390 Equilibrium phase diagram, 13, 324 Equilibrium shape, -6 Equilibrium state, -5 , 61, 78 Eutectic phase diagrams, 7-329 Eutectoid phase diagrams, 27-329 Exact differentials, Exact differential equations, 7-658 Excess free energy, 622 Exchange energy, 103 Exothermic process, 164, -2 8 Extensive thermodynamic variable, 13, 17, 232, 273 Eutectic phase diagram, 7-329 Eutectoid phase diagram, 27-329 Evaporation, -2 , 270 Face-centered cubic (FCC), 628 Faraday, M ichael, 569 Faraday’s constant, 569 FCC see Face-centered cubic (FCC) First Law o f Therm odynam ics constant-pressure processes, 30-31 constant-volume processes, -3 electrical work on dielectric material, 42 heat and work, -2 heat capacity, 31-37 internal energy and, -2 689 INDEX m agnetic work on param agnetic material, -4 overview, 23 reversible adiabatic processes, -3 reversible isotherm al process, -4 and Second Law, 79-81 work to create or extend surface, -4 First-order phase transition, 203 Flory, P J., 309 F lory-H u ggin s M odel -3 Forbidden energy bands, 96 Formation cells, -5 7 Fugacity, 252, 253 Fundamental equation, 129-130 133 irhe G a -G a P system , 510 -5 G alvanic cell, 569, -5 Gas constant, 12 G aseous reaction, 389 Gas mixture and equilibrium constant as com prom ise between enthalpy and entropy, -3 description, -3 8 in H20 - H and C O :-C O m ixtures, 399-401 overview , 381 -3 pressure effect on, 390-391 in S 2( x ) - S M - 2(g), -3 9 temperature effect on 8 -3 Gibbs, Josiah W illard, 94 G ib b s-D u h em equation ideal solutions, -2 H enry’s and Raoult’s laws, -2 total molar Gibbs free energy o f m ixing -2 Gibbs equilibrium phase rule 208, -4 Gibbs free energy, 128-129 constant-pressure molar heat capacities, -6 as function o f temperature and pressure, -2 m agnetic field on P-T diagram, 217-218 o f m ixing ideal gases, -2 molar entropies of various substances, 653 molar heat constant-pressure capacities, 051-652 o f formation, 653 of melting and transformation 655 and pressure at constant temperature, -2 saturated vapor pressures 654 and saturated vapor pressures 654 so lid -so lid equilibria 212-217 and temperature at constant pressure 0 -2 vapor and condensed phase equilibrium between, 210-211 graphical representation, 212 Gibbs free energy com position liquid and solid standard states, 331-338 overview, 21-322 and phase diagram s, -3 o f binary system s, -3 eutectic and eutectoid, -3 lens diagram, -3 low-temperature regions in, -3 peritectic and peritectoid, 329-331 unequal enthalpies o f m ixing, -3 o f regular solutions, 338-341 criteria for phase stability in, -3 and thermodynam ic activity, 2 -3 , -3 Gibbs free energy o f formation and ideal solutions xhan ge in, 27 -2 molar, -2 7 partial molar, -2 7 tangential intercepts, 278 o f ions and standard reduction potentials 591-601 G ib bs-H elm h oltz equation, 145-146 G ibbs-K on ovalov rule 326 G ib b s-W u lff construction, 632 Graphical representation, o f phase equilibria in A l - C - O - N system , -5 in M g -A l-O system , -5 Heat How and entropy production, 111-113 m echanical equivalent of, 24 and work, -2 Heat capacity, 31-37 constant-pressure molar, 1-652 empirical representation of 162 over v ievv, 155-156 theoretical calculation of 156-161 Heat engine, -7 H elm holtz free energy, 123-127, 663 H enry’s law 267-271, -2 Hess' law o f constant heat sum m ation, 31 H eterogeneous nucleation 632 H eterogeneous system 14 Higher-order phase transition, 203 H om ogeneous nucleation 632 H om ogeneous system , 14 Horizontal in fleet ion point, 343 Huggins M L., 309 Hypereutectic reaction 328 Hypoeutectic reaction, 328 690 Ideal gases adiabatic expansion of, 6 -6 enthalpy o f m ixing, -2 entropy o f m ixing, 236 equations o f state, -2 free expansion of, - Gibbs free energy o f m ixing, -2 isothermal expansion of, -6 m ixtures o f Dalton's law o f partial pressures, 1-232 mole fraction, 231 partial molar quantities, -2 nonideal gases equations o f state for, 250-251 thermodynam ic treatment of, 251-259 overview, 229 P-V-T relationships, 2 -2 reversible isothermal com pression, -6 and van der Waals fluid, -2 Ideal solutions chafige in volume, -2 enthalpy o f formation 28 -2 entropy o f formation, -2 G ib bs-D uh em equation, 27 -2 H enry’s and Raoult’s laws, -2 total molar Gibbs free energy o f m ixing, -2 Gibbs free energy o f formation change in, 7 -2 molar, -2 7 partial molar, -2 7 tangential intercepts, 278 and nonideal solutions, -2 8 overview, 267 Raoult’s law and H enry’s law, 267-271 regular solutions, -2 atomic order parameter, 3 -3 Flory-H uggins M odel, -3 second-neighbor interactions, -3 statistical model of, -3 subregular solutions, -3 thermodynamic activity o f component in, 271-273 Impermeable boundaries, Independent thermodynamic variables, Infinite dilution, 478 Interaction parameter, 539 Internal energy, -2 energy equation, 142-143 Intensive thermodynamic variable, 13, 95, 199 Ionic character, 567 Irreversible processes, 57, 59 INDEX Isentropic process, 66 Isolated system s, Isothermal process com pression, 7, -6 expansion, 40, -6 Joule, definition, 24 Joule, James Prescott, 24 Kinetic energy, 23 K irchhoff’s law, 172 Kopp, Em ile, 156 Kopp rule, 156 Landau, Lev Davidovich, 636 theory on phase transformations, 6 -6 4 Landau model, 636, 643 Latent heat o f melting, 202 Law o f corresponding states, 240 Law o f definite proportions, 504 Laws o f Therm odynam ics, 12, 17 Le Chatelier, Henry Louis, 171, 173 Le Chatelier’s principle, 171, 205, 389, 390, 395, 396 Legendre, Adrien-M arie, 659 Legendre transformations, -6 Lens phase diagrams, -3 Liquid junction potential, 575 Liquidus curve, 326, 356, 358 L iquid-vapor equilibrium, 238 Local equilibrium, and capillarity, -6 Log pressure vs 1IT phase diagram, 446 Long-range order parameter (LRO), 303 Low-temperature regions, in phase diagrams, -3 LRO, see Long-range order parameter (LRO) M acroscopic thermodynamic variables, M agnetic work, on paramagnetic material, -42 M agnetization, 143 Martens, Adolf, 628 Martensitic phase transformations, 628 M assive phase transformations, 628 M aximum work, -7 M axwell construction, 247 M axw ell’s relations, 135-145 • energy equation (internal energy), 142-143 enthalpy energy equation, 143 magnetic relation, 143-144 S, V, and M with independent variables T, P, and H , 144-145 S and V as dependent variables, 141-142 T and P as independent variables, 141-142 TdS equation 691 INDEX first, 137-139 second, 139-141 M echanical equivalent o f heat, 24 M elting temperature, 203, 206, 212 M etal-ca rb o n -oxygen equilibria, 443 M etallic glass, 630 M etatectic phase diagram, 331 M g - A l - system , and phase equilibria in, -5 M g -S i system , 512-515 M icroscopic therm odynam ic variables, - M icrostate, and entropy, -9 M ixtures o f ideal gases Dalton’s law o f partial pressures, 31-232 ' mole fraction, 231 partial molar quantities, -2 M olality, -5 8 , 600 Molar enthalpy o f melting 202 Molar free energy o f molting 331 356 Molar heats capacity, 47 constant-pressure capacities, 651-652 o f formation, 653 o f m elting and transformation, 655 Molarity, 587, 600, 601 M ole fraction, 231 M onotectic equilibrium , 361 Natural processes, 58 Nernst equation, 569 Nernst heat theorem, 173 N ern st-P lan ck -Sim on statement, 175 Nonequilibrium state, 58, 61, 78 Nonideal gases equations o f state for, 250-251 thermodynam ic treatment of 251 -2 Nonideal solutions, -2 8 Nonstoichiom etric com pound, 523 O pen-circuit EMF, 572 Open system s, Order parameter, 636 Ostwald ripening, 636 Oxidation, o f pure solid phase, 424 Paramagnet, 104 Partial molar quantities, -2 Partial pressures, 231-232 Particle coarsening, 636 Partition function, 107 Perfect gas, 2 -2 Pcritectic phase diagrams 329-331 Peritectoid phase diagrams 329-331 Permeable boundaries, Perpetual motion, 70 Petit, A lexis T hérèse, 156 Phase, definition, 621 Phase diagram s, -3 o f binary system s, -3 eutectic and eutectoid, -3 lens diagram, -3 low-temperature regions in, -3 peritectic and peritectoid, 329-331 unequal enthalpies o f m ixing, -3 Phase stability diagram s, -5 Phase transformations capillarity and local equilibrium, -6 with change in com position, -6 definition 621 and Landau theory, 6 -6 4 with no change in com position, 2 -6 surface energy equilibrium shape, -6 heterogeneous, -6 hom ogeneous nucléation, 632 T{) curves, 6 -6 formation o f amorphous phases, -6 martensitic transformation, 628 m assive transformations, 628 Planck, Max Karl Ernst Ludwig, 157, 174 Polym orphism , 162,212 Potential energy, 23 Pourbaix diagrams, 601-611 for aluminum, -6 equilibrium with one dissolved substance, -6 between two dissolved substances, -6 between two solids, -6 solubility o f alumina in aqueous solutions, 609-611 Predom inance diagrams, see Phase stability diagrams Pressure, definition, 199 Principle o f Clausius, 70 Principle o f Kelvin and Planck, 70 P-T diagram, m agnetic field on, 217-218 P-V-T relationships, in ideal gases, 2 -2 Q uasi-static process, 61 Raoultian standard state, 477 Raoult’s law 26 -2 , -2 Reactants, and products, 386,-393 Reaction equilibria in condensed and gaseous phases and carbon oxides, -4 692 INDEX and chlorination o f iron, 3 -4 description, 414-419 effect o f phase transformations, -4 3 Ellingham diagrams, 2 -4 and Gibbs free energy change with temperature, -4 2 graphical representation of, 4 -4 overview, 413 in condensed solution binary system s containing com pounds, -5 criteria for, -4 7 and dilute solute, -5 and Gibbs equilibrium phase rule, -4 graphical representation of, 16-532 overview, -4 and phase stability diagrams, -5 solubility o f gases in m etals, 532 -5 standard state of, 7 -4 in gas mixture and equilibrium constant as com prom ise between enthalpy and entropy 391 -3 description, -3 8 in H 20 - H and C 2- C mixtures, 9-401 overview, -3 pressure effect on, 390-391 •inS02te )-s '0 te ;-o 2fe), 394-399 temperature effect on, 8 -3 Reduction, o f oxide, 416-417, 436 Regnault, Henri Victor, 11 Regular ideal solutions, -2 atomic order parameter 3 -3 F lory-H uggins M odel, -3 second-neighbor interactions, -3 Regular solution behavior, -2 model, 3 -3 Regular solutions, o f Gibbs free energy, 338-341 criteria for phase stability in, 341 -3 Reversible adiabatic processes, -3 Reversible and irreversible expansion, -6 ideal gas free expansion of, -6 isothermal expansion of, -6 Reversible isothermal com pression, -6 Reversible isothermal process, 0-41 Reversible processes, 61 Richards, Theodore W illiam , 173 Richardson nomographic scale, 427 Roberts-Austen, W illiam Chandler, 628 Salt bridge, 575 Saturated vapor pressures, and Gibbs free energy, 654 Second Law o f Therm odynam ics adiabatic expansion o f ideal gas, 6 -6 amount o f work, -7 description, -7 entropy and criterion for equilibrium, -7 and First Law, -7 overview, 57 reversible and irreversible expansion, -6 free expansion o f ideal gas, -6 isothermal expansion o f ideal gas, -6 reversible isothermal compression, -6 spontaneous/natural/irreversible processes, -5 entropy and quantification of, 59-61 thermodynamic temperature scale, 71-73 and working o f heat engine, -7 Sem iperm eable boundaries, SHE, see Standard hydrogen electrode (SHE) Sieverts, Adolf, 536, 537 Sieverts’ constant, 536 Sieverts’ law, 536, 540 Simple system s, 41 Simple thermodynamic system s, Single electrode potential, 594 S olid -solid equilibria, 212-217 Solidus curve, 334, 358 Solubility product, -5 9 Spin entropy, 214, 215 Spontaneous processes, -5 Standard EMF, o f cell, 575 Standard Gibbs free energy change, 383, 394, 400 Standard hydrogen electrode (SHE), 594 Standard state, 230 Statistical interpretation o f entropy and atomic scale disorder, -9 and Boltzmann distribution, 104-107 and configurational entropy o f differing atoms in a crystal, -1 o f magnetic spins, 102-104 heat flow and production of, 111-113 and identical particles, -9 and microstate, -9 overview, 93 • and temperature effect, 108-109 thermal equilibrium and Boltzmann equation, 110-111 Statistical thermodynamics, 93, 95, 96 Stoichiometric compound, 504, 530 Stoichiometry, 382, 394, 397 Subregular ideal solutions, -3 Supercritical fluid, 238 693 INDEX Surface energy, and phase transformations equilibrium shape, -6 heterogeneous, -6 hom ogeneous nucleation, 632 T{) curves, 6 -6 formation o f amorphous phases, -6 martensitic transformation, 628 m assive transformations, 628 TdS equation first, 137-139 second, 139-141 Temperature vs com position phase diagram, 322 definition, 199 and entropy, 108-109 instability 641, 642 Thermal energy (heat) effects, -5 Thermal entropy, 94 Thermal equilibrium, and Bolt/m ann equation, 110-111 Therm ochem ical calorie, 24 Therm odynam ic activity o f com ponent in solution, 271-273 and Gibbs free energy com position, 2 -3 , -3 o f nonideal gases, 1-259 Therm odynam ic degree o f freedom , 208 Therm odynam ic field variables, Therm odynam ic potential, see Internal energy Therm odynam ics definition, fundamental equations and chem ical potential, 131-134 for closed system , 129-130 enthalpy, 123 G ib b s-H elm h oltz equation, 145-146 H elm holtz free energy, 123-127, 663 M axw ell’s relations, 135-145 overview, 121-122 thermodynam ic relations, 134-135 Gibbs free energy, 128-129 Therm odynam ic state functions, 15, 658 Therm odynam ic state variable 13, 29, 30 Therm odynam ic temperature scale, -7 Third Law o f Therm odynam ics contradictions to, 175-176 development of, 172-175 experim ental verification of, 177-182 influence o f pressure on, 182-184 Thom son Benjamin, 24 Transition states, 622 Trouton, Frederick Thom as, 180 van dcr Waals lluid -2 van:t Hoff, Jacobus H enricus, 202 van’t H off rule, 202 Vapor and condensed phase equilibrium between, 210-211 graphical representation, 212 Vapor pressure, 15 Vegard, Lars, 280 Vegard's law, 280 Vibrational entropy, 214-215 Virial equation, 251 V-P-T space, Work, and heat, -2 Work function, 125 W ulff, George Yuri Viktorovich, 632 Values of Selected Physical Constants Absolute temperature of the ice point (0°C) = 273.15 K Absolute temperature of the triple point of H O (by definition) = 273.16000 K Faraday s constant f Avogadros number N q = 6.0232 x 1023/gram*mole Boltzmanns constant kB = 1.38054 x 10'23joules/degree 8.61733 x 10"5 evldegree Atmosphere Gas constant = 96,487 coulomb/mole atm = 1.01325 bar - = 101.325 kPa = 760 mm Hg R = 8.3144(6) joules/degree*mole = 82.06 cm3*atm/degree*mole = 1.987 cal/degree*mole Planck constant h = 6.6262 x 10 34 joule*sec Permeability of vacuum {4q = 47rxlO '7 H /m Permittivity of vacuum coulomb2 joule • m e := ^ — = 8.8542 ’2—— j c2/a