THERMODYNAMICS AND STATISTICAL MECHANICS

By JOSHUA THOMPSON

CONTENTS LECTURE INTRODUCTION TO THE BOOK MOTIVATION AND SCOPE OF THE BOOK ORGANIZATION OF THE BOOK ACKNOWLEDGMENTS PART I FUNDAMENTAL PRINCIPLES AND PROPERTIES OF PURE FLUIDS LECTURE USEFUL DE?NITIONS, POSTULATES, NOMENCLATURE, AND SAMPLE PROBLEMS INTRODUCTION USEFUL DE?NITIONS POSTULATES I AND II (ADAPTED FROM APPENDIX A IN T&M) SAMPLE PROBLEM 2 1 SOLUTION SAMPLE PROBLEM 2 2 NOMENCLATURE LECTURE THE FIRST LAW OF THERMODYNAMICS FOR CLOSED SYSTEMS: DERIVATION AND SAMPLE PROBLEMS WORK INTERACTIONS SAMPLE PROBLEM 3 1 SPECI?C TYPES OF WORK INTERACTIONS SAMPLE PROBLEM 3 2 SAMPLE PROBLEM 3 3 POSTULATE III (ADAPTED FROM APPENDIX A IN T&M) ENERGY DECOMPOSITION HEAT INTERACTIONS THE FIRST LAW OF THERMODYNAMICS FOR CLOSED SYSTEMS THE FIRST LAW OF THERMODYNAMICS FOR CLOSED SYSTEMS: THERMAL EQUILIBRIUM, THE IDEAL GAS, AND SAMPLE PROBLEM THERMAL EQUILIBRIUM AND THE DIRECTIONALITY OF HEAT INTERACTIONS POSTULATE IV (ADAPTED FROM APPENDIX A IN T&M) IDEAL GAS PROPERTIES EQUATION OF STATE (EOS) INTERNAL ENERGY ENTHALPY OTHER USEFUL RELATIONSHIPS SAMPLE PROBLEM 4 1: PROBLEM 3 1 IN T&M THE FIRST LAW OF THERMODYNAMICS FOR CLOSED SYSTEMS: SAMPLE PROBLEM 4 1, CONTINUED SAMPLE PROBLEM 4 1: PROBLEM 3 1 IN T&M, CONTINUED SOLUTION 1: SYSTEM III-ATMOSPHERE (A) SOLUTION 2: SYSTEM I-GAS (G) FOOD FOR THOUGHT THE FIRST LAW OF THERMODYNAMICS FOR OPEN SYSTEMS: DERIVATION AND SAMPLE PROBLEM THE FIRST LAW OF THERMODYNAMICS FOR OPEN SYSTEMS NOTATION DERIVATION SAMPLE PROBLEM 6 1: PROBLEM 3 9 IN T&M SOLUTION STRATEGY WELL-MIXED GAS MODEL SYSTEM PRESSURIZATION STEP: WELL-MIXED GAS MODEL SYSTEM LAYERED OR STRATI?ED GAS MODEL SYSTEM PRESSURIZATION STEP: STRATI?ED GAS MODEL SYSTEM EMPTYING STEP: WELL-MIXED GAS MODEL SYSTEM THE SECOND LAW OF THERMODYNAMICS: FUNDAMENTAL CONCEPTS AND SAMPLE PROBLEM NATURAL PROCESSES STATEMENT (1) OF THE SECOND LAW OF THERMODYNAMICS SAMPLE PROBLEM 7 1 STATEMENT (1A) OF THE SECOND LAW OF THERMODYNAMICS HEAT ENGINE EF?CIENCY OF A HEAT ENGINE REVERSIBLE PROCESS HEAT ENGINE, CARNOT EF?CIENCY, AND SAMPLE PROBLEM THEOREM OF CARNOT COROLLARY TO THEOREM OF CARNOT SAMPLE PROBLEM 8 1 THEOREM OF CLAUSIUS ENTROPY AND REVERSIBILITY ENTROPY IRREVERSIBLE PROCESS THE SECOND LAW OF THERMODYNAMICS, MAXIMUM WORK, AND SAMPLE PROBLEMS A MORE GENERAL STATEMENT OF THE SECOND LAW OF THERMODYNAMICS HEAT INTERACTIONS ALONG REVERSIBLE AND IRREVERSIBLE PATHS (CLOSED SYSTEM) WORK INTERACTIONS ALONG REVERSIBLE AND IRREVERSIBLE PATHS (CLOSED SYSTEM) SAMPLE PROBLEM 10 1 SAMPLE PROBLEM 10 2 CRITERION OF EQUILIBRIUM BASED ON THE ENTROPY SAMPLE PROBLEM 10 3 THE COMBINED FIRST AND SECOND LAW OF THERMODYNAMICS, AVAILABILITY, AND SAMPLE PROBLEMS CLOSED, SINGLE-PHASE, SIMPLE SYSTEM OPEN, SINGLE-PHASE, SIMPLE SYSTEM SAMPLE PROBLEM 11 1 SAMPLE PROBLEM 11 2 FLOW WORK AND SAMPLE PROBLEMS SAMPLE PROBLEM 12 1 SAMPLE PROBLEM 12 2: PROBLEM 4 3 IN T&M SOLUTION: ASSUMPTIONS FUNDAMENTAL EQUATIONS AND SAMPLE PROBLEMS THERMODYNAMIC RELATIONS FOR SIMPLE SYSTEMS FUNDAMENTAL EQUATION THE THEOREM OF EULER IN THE CONTEXT OF THERMODYNAMICS (ADAPTED FROM APPENDIX C IN T&M) SAMPLE PROBLEM 13 1 SAMPLE PROBLEM 13 2 VARIABLE TRANSFORMATIONS AND NEW FUNDAMENTAL EQUATIONS SAMPLE PROBLEM 13 3 SAMPLE PROBLEM 13 4 MANIPULATION OF PARTIAL DERIVATIVES AND SAMPLE PROBLEMS TWO ADDITIONAL RESTRICTIONS ON THE INTERNAL ENERGY FUNDAMENTAL EQUATION COROLLARY TO POSTULATE I RECONSTRUCTION OF THE INTERNAL ENERGY FUNDAMENTAL EQUATION MANIPULATION OF PARTIAL DERIVATIVES OF THERMODYNAMIC FUNCTIONS INTERNAL ENERGY AND ENTROPY FUNDAMENTAL EQUATIONS USEFUL RULES TO CALCULATE PARTIAL DERIVATIVES OF THERMODYNAMIC FUNCTIONS THE TRIPLE PRODUCT RULE THE ADD ANOTHER VARIABLE RULE THE DERIVATIVE INVERSION RULE MAXWELL’S RECIPROCITY RULE SAMPLE PROBLEM 14 1 JACOBIAN TRANSFORMATIONS PROPERTIES OF JACOBIANS SAMPLE PROBLEM 14 2 PROPERTIES OF PURE MATERIALS AND GIBBS FREE ENERGY FORMULATION GIBBS FREE ENERGY FUNDAMENTAL EQUATION DERIVATION OF THE GIBBS-DUHEM EQUATION RELATING THE GIBBS FREE ENERGY TO OTHER THERMODYNAMIC FUNCTIONS FIRST-ORDER AND SECOND-ORDER PARTIAL DERIVATIVES OF THE GIBBS FREE ENERGY DETERMINING WHICH DATA SET HAS THE SAME THERMODYNAMIC INFORMATION CONTENT AS THE GIBBS FREE ENERGY FUNDAMENTAL EQUATION EVALUATION OF THERMODYNAMIC DATA OF PURE MATERIALS AND SAMPLE PROBLEMS SUMMARY OF CHANGES IN ENTROPY, INTERNAL ENERGY, AND ENTHALPY USING T AND P AS THE TWO INDEPENDENT INTENSIVE VARIABLES USING T AND V AS THE TWO INDEPENDENT INTENSIVE VARIABLES THE IDEAL GAS LIMIT RELATION BETWEEN CP AND CV SAMPLE PROBLEM 16 1 SAMPLE PROBLEM 16 2 EVALUATION OF CHANGES IN THE THERMODYNAMIC PROPERTIES OF PURE MATERIALS CALCULATION OF THE ENTROPY CHANGE STRATEGY I STRATEGY II STRATEGY III EQUATIONS OF STATE OF A PURE MATERIAL, BINODAL, SPINODAL, CRITICAL POINT, AND SAMPLE PROBLEM EQUATIONS OF STATE OF A PURE MATERIAL EXAMPLES OF EQUATIONS OF STATE (EOS) THE IDEAL GAS EOS THE VAN DER WAALS EOS SAMPLE PROBLEM 17 1 PRESSURE-EXPLICIT FORM OF THE ISOTHERM P ¼ F (V, T) OF A PURE MATERIAL STABLE, METASTABLE, AND UNSTABLE EQUILIBRIUM MECHANICAL ANALOGY OF STABLE, METASTABLE, AND UNSTABLE EQUILIBRIUM STATES MATHEMATICAL CONDITIONS FOR STABILITY, METASTABILITY, AND INSTABILITY MATHEMATICAL CONDITIONS FOR THE SPINODAL AND THE CRITICAL POINT THE PRINCIPLE OF CORRESPONDING STATES AND SAMPLE PROBLEMS EXAMPLES OF ADDITIONAL EQUATIONS OF STATE (EOS) THE REDLICH-KWONG (RK) EOS SAMPLE PROBLEM 18 1 SAMPLE PROBLEM 18 2 THE PENG-ROBINSON (PR) EOS THE VIRIAL EOS SAMPLE PROBLEM 18 3 THE PRINCIPLE OF CORRESPONDING STATES THE COMPRESSIBILITY FACTOR SAMPLE PROBLEM 18 4 DEPARTURE FUNCTIONS AND SAMPLE PROBLEMS SAMPLE PROBLEM 19 1 DEPARTURE FUNCTIONS CALCULATION OF THE ENTROPY DEPARTURE FUNCTION, DS (T, P) CALCULATION OF THE HELMHOLTZ FREE ENERGY DEPARTURE FUNCTION, DA(T, V) CALCULATION OF THE ENTROPY DEPARTURE FUNCTION, DS (T, V) SAMPLE PROBLEM 19 2 IMPORTANT REMARK REVIEW OF PART I AND SAMPLE PROBLEM BASIC CONCEPTS, DE?NITIONS, AND POSTULATES IDEAL GAS THE FIRST LAW OF THERMODYNAMICS FOR OPEN, SIMPLE SYSTEMS THE FIRST LAW OF THERMODYNAMICS FOR STEADY-STATE FLOW SYSTEMS CARNOT ENGINE ENTROPY OF A CLOSED SYSTEM THE SECOND LAW OF THERMODYNAMICS THE COMBINED FIRST AND SECOND LAW OF THERMODYNAMICS FOR CLOSED SYSTEMS ENTROPY BALANCE FOR OPEN SYSTEMS MAXIMUM WORK, AVAILABILITY FUNDAMENTAL EQUATIONS MANIPULATION OF PARTIAL DERIVATIVES MANIPULATION OF PARTIAL DERIVATIVES USING JACOBIAN TRANSFORMATIONS MAXWELL’S RECIPROCITY RULES IMPORTANT THERMODYNAMIC RELATIONS FOR PURE MATERIALS GIBBS-DUHEM EQUATION FOR A PURE MATERIAL EQUATIONS OF STATE (EOS) STABILITY CRITERIA FOR A PURE MATERIAL SAMPLE PROBLEM 20 1 PART II MIXTURES: MODELS AND APPLICATIONS TO PHASE AND CHEMICAL REACTION EQUILIBRIA LECTURE EXTENSIVE AND INTENSIVE MIXTURE PROPERTIES AND PARTIAL MOLAR PROPERTIES EXTENSIVE AND INTENSIVE DIFFERENTIALS OF MIXTURES CHOOSE SET 1: {T, P, N1, , NN} AND ANALYZE B ¼ B (T, P, N1, , NN) IMPORTANT REMARKS CHOOSE SET 2: {T, P, X1, , XN-1, N} AND ANALYZE B ¼ B (T, P, X1, , XN-1, N) GENERALIZED GIBBS-DUHEM RELATIONS FOR MIXTURES, CALCULATION OF PARTIAL MOLAR PROPERTIES, AND SAMPLE PROBLEM PARTIAL MOLAR PROPERTIES USEFUL RELATIONS BETWEEN PARTIAL MOLAR PROPERTIES HOW DO WE CALCULATE BI? CASES 1, 2, AND 3 SAMPLE PROBLEM 22 1 GENERALIZED GIBBS-DUHEM RELATIONS FOR MIXTURES MIXTURE EQUATIONS OF STATE, MIXTURE DEPARTURE FUNCTIONS, IDEAL GAS MIXTURES, IDEAL SOLUTIONS, AND SAMPLE PROBLEM SAMPLE PROBLEM 23 1 EQUATIONS OF STATE FOR GAS MIXTURES IDEAL GAS (IG) MIXTURE EOS VAN DER WAALS (VDW) MIXTURE EOS PENG-ROBINSON (PR) MIXTURE EOS VIRIAL MIXTURE EOS CALCULATION OF CHANGES IN THE THERMODYNAMIC PROPERTIES OF GAS MIXTURES MIXTURE ATTENUATED STATE APPROACH MIXTURE DEPARTURE FUNCTION APPROACH IDEAL GAS MIXTURES AND IDEAL SOLUTIONS ONE COMPONENT (PURE, N ¼ 1) IDEAL GAS IDEAL GAS MIXTURE: FOR COMPONENT I IDEAL SOLUTION: FOR COMPONENT I MIXING FUNCTIONS, EXCESS FUNCTIONS, AND SAMPLE PROBLEMS SAMPLE PROBLEM 24 1 SAMPLE PROBLEM 24 2 SAMPLE PROBLEM 24 3 OTHER USEFUL RELATIONS FOR AN IDEAL SOLUTION SUMMARY OF RESULTS FOR AN IDEAL SOLUTION MIXING FUNCTIONS THE MIXING B AND REFERENCE STATES PURE COMPONENT REFERENCE STATE FOR COMPONENT J USEFUL RELATIONS FOR MIXING FUNCTIONS MIXING FUNCTIONS: MIXING OF THREE LIQUIDS AT CONSTANT T AND P IDEAL SOLUTION MIXING FUNCTIONS EXCESS FUNCTIONS IDEAL SOLUTION, REGULAR SOLUTION, AND ATHERMAL SOLUTION BEHAVIORS, AND FUGACITY AND FUGACITY COEF?CIENT IDEAL SOLUTION BEHAVIOR REGULAR SOLUTION BEHAVIOR ATHERMAL SOLUTION BEHAVIOR FUGACITY AND FUGACITY COEF?CIENT VARIATIONS OF BFI AND FI WITH PRESSURE VARIATIONS OF BFI AND FI WITH TEMPERATURE OTHER RELATIONS INVOLVING FUGACITIES CALCULATION OF FUGACITY THE LEWIS AND RANDALL RULE ACTIVITY, ACTIVITY COEF?CIENT, AND SAMPLE PROBLEMS ACTIVITY AND ACTIVITY COEF?CIENT PURE COMPONENT REFERENCE STATE CALCULATION OF ACTIVITY SAMPLE PROBLEM 26 1 SAMPLE PROBLEM 26 2 CRITERIA OF PHASE EQUILIBRIA, AND THE GIBBS PHASE RULE USE OF OTHER REFERENCE STATES PHASE EQUILIBRIA: INTRODUCTION CRITERIA OF PHASE EQUILIBRIA THERMAL EQUILIBRIUM MECHANICAL EQUILIBRIUM DIFFUSIONAL EQUILIBRIUM THE GIBBS PHASE RULE APPLICATION OF THE GIBBS PHASE RULE, AZEOTROPE, AND SAMPLE PROBLEM THE GIBBS PHASE RULE FOR A PURE SUBSTANCE SAMPLE PROBLEM 28 1 DIFFERENTIAL APPROACH TO PHASE EQUILIBRIA, PRESSURE-TEMPERATURE-COMPOSITION RELATIONS, CLAUSIUS-CLAPEYRON EQUATION, AND SAMPLE PROBLEM SAMPLE PROBLEM 29 1 SIMPLI?CATIONS OF EQS (29 21) AND (29 22) PURE LIQUID IN EQUILIBRIUM WITH ITS PURE VAPOR, INTEGRAL APPROACH TO PHASE EQUILIBRIA, COMPOSITION MODELS, AND SAMPLE PROBLEMS FROM LECTURE 29 PURE LIQUID IN EQUILIBRIUM WITH ITS PURE VAPOR INTEGRAL APPROACH TO PHASE EQUILIBRIA SAMPLE PROBLEM 30 1 CALCULATION OF VAPOR MIXTURE FUGACITIES CALCULATION OF LIQUID MIXTURE FUGACITIES CALCULATION OF PURE COMPONENT I LIQUID FUGACITY SIMPLI?CATIONS OF EQ (30 29) MODELS FOR THE EXCESS GIBBS FREE ENERGY OF MIXING OF N ¼ 2 MIXTURES MODELS FOR THE EXCESS GIBBS FREE ENERGY OF MIXING OF N > 2 MIXTURES CHEMICAL REACTION EQUILIBRIA: STOICHIOMETRIC FORMULATION AND SAMPLE PROBLEM CONTRASTING THE CALCULATION OF CHANGES IN THERMODYNAMIC PROPERTIES WITH AND WITHOUT CHEMICAL REACTIONS CASE I: CLOSED BINARY SYSTEM OF INERT COMPONENTS 1 AND 2 CASE II: CLOSED BINARY SYSTEM OF COMPONENTS 1 AND 2 UNDERGOING A DISSOCIATION REACTION STOICHIOMETRIC FORMULATION SAMPLE PROBLEM 31 1 CRITERION OF CHEMICAL REACTION EQUILIBRIA, STANDARD STATES, AND EQUILIBRIUM CONSTANTS FOR GAS-PHASE CHEMICAL REACTIONS DERIVATION OF THE CRITERION OF CHEMICAL REACTION EQUILIBRIA DERIVATION OF THE EQUILIBRIUM CONSTANT FOR CHEMICAL REACTION R DERIVATION OF THE EQUILIBRIUM CONSTANT FOR A SINGLE CHEMICAL REACTION DISCUSSION OF STANDARD STATES FOR GAS-PHASE, LIQUID-PHASE, AND SOLID-PHASE CHEMICAL REACTIONS COMMENTS ON THE STANDARD-STATE PRESSURE DECOMPOSITION OF THE EQUILIBRIUM CONSTANT INTO CONTRIBUTIONS FROM THE FUGACITY COEF?CIENTS, THE GAS MIXTURE MOLE FRACTIONS, AND THE PRESSURE EQUILIBRIUM CONSTANTS FOR CONDENSED-PHASE CHEMICAL REACTIONS, RESPONSE OF CHEMICAL REACTIONS TO TEMPERATURE, AND LE CHATELIER’S PRINCIPLE DERIVATION OF THE EQUILIBRIUM CONSTANT FOR A CONDENSED-PHASE CHEMICAL REACTION DETERMINATION OF THE STANDARD MOLAR GIBBS FREE ENERGY OF REACTION RESPONSE OF CHEMICAL REACTIONS TO CHANGES IN TEMPERATURE AND PRESSURE HOW DOES A CHEMICAL REACTION RESPOND TO TEMPERATURE? LE CHATELIER’S PRINCIPLE RESPONSE OF CHEMICAL REACTIONS TO PRESSURE, AND SAMPLE PROBLEMS HOW DOES A CHEMICAL REACTION RESPOND TO PRESSURE? SAMPLE PROBLEM 34 1 SAMPLE PROBLEM 34 2 THE GIBBS PHASE RULE FOR CHEMICALLY-REACTING SYSTEMS AND SAMPLE PROBLEM SAMPLE PROBLEM 35 1 SELECTION OF STANDARD STATES REMARKS EVALUATION OF FUGACITIES CALCULATION OF THE EQUILIBRIUM CONSTANT COMMENT ON THE STANDARD-STATE PRESSURE EFFECT OF CHEMICAL REACTION EQUILIBRIA ON CHANGES IN THERMODYNAMIC PROPERTIES AND SAMPLE PROBLEM SAMPLE PROBLEM 36 1: PRODUCTION OF SULFURIC ACID BY THE CONTACT PROCESS EVALUATION OF K(T) DERIVATION OF THE SECOND EQUATION RELATING T AND ? REVIEW OF PART II AND SAMPLE PROBLEM GIBBS-HELMHOLTZ RELATION IDEAL GAS MIXTURES IDEAL SOLUTIONS FUGACITY VARIATION OF FUGACITY WITH TEMPERATURE AND PRESSURE GENERALIZED GIBBS-DUHEM RELATION FOR FUGACITIES FUGACITY COEF?CIENT LEWIS AND RANDALL RULE ACTIVITY ACTIVITY COEF?CIENT VARIATION OF ACTIVITY COEF?CIENT WITH TEMPERATURE AND PRESSURE GENERALIZED GIBBS-DUHEM RELATION FOR ACTIVITY COEF?CIENTS CONDITIONS FOR THERMODYNAMIC PHASE EQUILIBRIA GIBBS PHASE RULE DIFFERENTIAL APPROACH TO PHASE EQUILIBRIA DEPENDENCE OF FUGACITITIES ON TEMPERATURE, PRESSURE, AND MIXTURE COMPOSITION PRESSURE-TEMPERATURE RELATIONS STOICHIOMETRIC FORMULATION FOR CHEMICAL REACTIONS EQUILIBRIUM CONSTANT TYPICAL REFERENCE STATES FOR GAS, LIQUID, AND SOLID EQUILIBRIUM CONSTANT FOR GASES UNDERGOING A SINGLE CHEMICAL REACTION EQUILIBRIUM CONSTANTS FOR LIQUIDS AND SOLIDS CALCULATION OF THE STANDARD MOLAR GIBBS FREE ENERGY OF REACTION VARIATION OF THE EQUILIBRIUM CONSTANT WITH TEMPERATURE AND PRESSURE SAMPLE PROBLEM 37 1 PART III INTRODUCTION TO STATISTICAL MECHANICS LECTURE STATISTICAL MECHANICS, CANONICAL ENSEMBLE, PROBABILITY AND THE BOLTZMANN FACTOR, AND CANONICAL PARTITION FUNCTION CANONICAL ENSEMBLE AND THE BOLTZMANN FACTOR PROBABILITY THAT A SYSTEM IN THE CANONICAL ENSEMBLE IS IN QUANTUM STATE J WITH ENERGY EJ(N, V) PHYSICAL INTERPRETATION OF THE CANONICAL PARTITION FUNCTION CALCULATION OF AVERAGE THERMODYNAMIC PROPERTIES USING THE CANONICAL PARTITION FUNCTION AND TREATMENT OF DISTINGUISHABLE AND INDISTINGUISHABLE MOLECULES CALCULATION OF THE AVERAGE ENERGY OF A MACROSCOPIC SYSTEM CALCULATION OF THE AVERAGE HEAT CAPACITY AT CONSTANT VOLUME OF A MACROSCOPIC SYSTEM CALCULATION OF THE AVERAGE PRESSURE OF A MACROSCOPIC SYSTEM CANONICAL PARTITION FUNCTION OF A SYSTEM OF INDEPENDENT AND DISTINGUISHABLE MOLECULES CANONICAL PARTITION FUNCTION OF A SYSTEM OF INDEPENDENT AND INDISTINGUISHABLE MOLECULES DECOMPOSITION OF A MOLECULAR CANONICAL PARTITION FUNCTION INTO CANONICAL PARTITION FUNCTIONS FOR EACH DEGREE OF FREEDOM ENERGY STATES AND ENERGY LEVELS TRANSLATIONAL, VIBRATIONAL, ROTATIONAL, AND ELECTRONIC CONTRIBUTIONS TO THE PARTITION FUNCTION OF MONOATOMIC AND DIATOMIC IDEAL GASES AND SAMPLE PROBLEM PARTITION FUNCTIONS OF IDEAL GASES TRANSLATIONAL PARTITION FUNCTION OF A MONOATOMIC IDEAL GAS ELECTRONIC CONTRIBUTION TO THE ATOMIC PARTITION FUNCTION SAMPLE PROBLEM 40 1 AVERAGE ENERGY OF A MONOATOMIC IDEAL GAS AVERAGE HEAT CAPACITY AT CONSTANT VOLUME OF A MONOATOMIC IDEAL GAS AVERAGE PRESSURE OF A MONOATOMIC IDEAL GAS DIATOMIC IDEAL GAS THERMODYNAMIC PROPERTIES OF IDEAL GASES OF DIATOMIC MOLECULES CALCULATED USING PARTITION FUNCTIONS AND SAMPLE PROBLEMS VIBRATIONAL PARTITION FUNCTION OF A DIATOMIC SAMPLE PROBLEM 41 1 ROTATIONAL PARTITION FUNCTION OF A DIATOMIC MOLECULE AVERAGE ROTATIONAL ENERGY OF AN IDEAL GAS OF DIATOMIC MOLECULES AVERAGE ROTATIONAL HEAT CAPACITY AT CONSTANT VOLUME OF AN IDEAL GAS OF DIATOMIC MOLECULES FRACTION OF DIATOMIC MOLECULES IN THE JTH ROTATIONAL LEVEL ROTATIONAL PARTITION FUNCTIONS OF DIATOMIC MOLECULES CONTAIN A SYMMETRY NUMBER TOTAL PARTITION FUNCTION OF A DIATOMIC MOLECULE SAMPLE PROBLEM 41 2 STATISTICAL MECHANICAL INTERPRETATION OF REVERSIBLE MECHANICAL WORK, REVERSIBLE HEAT, AND THE FIRST LAW OF THERMODYNAMICS, THE MICRO-CANONICAL ENSEMBLE AND ENTROPY, AND SAMPLE PROBLEM STATISTICAL MECHANICAL INTERPRETATION OF REVERSIBLE MECHANICAL WORK, REVERSIBLE HEAT, AND THE FIRST LAW OF THERMODYNAMICS MICRO-CANONICAL ENSEMBLE AND ENTROPY RELATING ENTROPY TO THE CANONICAL PARTITION FUNCTION SAMPLE PROBLEM 42 1 RELATING THE STATISTICAL MECHANICAL RELATION, S ¼ KBLNW, TO THE THERMODYNAMIC RELATION, DS ¼ ?QREV=T STATISTICAL MECHANICAL INTERPRETATION OF THE THIRD LAW OF THERMODYNAMICS, CALCULATION OF THE HELMHOLTZ FREE ENERGY AND CHEMICAL POTENTIALS USING THE CANONICAL PARTITION FUNCTION, AND SAMPLE PROBLEMS THE THIRD LAW OF THERMODYNAMICS AND ENTROPY CALCULATION OF THE HELMHOLTZ FREE ENERGY OF A PURE MATERIAL USING THE CANONICAL PARTITION FUNCTION SAMPLE PROBLEM 43 1 SAMPLE PROBLEM 43 2 SAMPLE PROBLEM 43 3 GRAND-CANONICAL ENSEMBLE, STATISTICAL FLUCTUATIONS, AND SAMPLE PROBLEMS GRAND-CANONICAL ENSEMBLE STATISTICAL FLUCTUATIONS SAMPLE PROBLEM 44 1 SAMPLE PROBLEM 44 2 FLUCTUATIONS IN THE NUMBER OF MOLECULES SAMPLE PROBLEM 44 3 EQUIVALENCE OF ALL THE ENSEMBLES IN THE THERMODYNAMIC LIMIT CLASSICAL STATISTICAL MECHANICS AND SAMPLE PROBLEM CLASSICAL STATISTICAL MECHANICS CLASSICAL MOLECULAR PARTITION FUNCTION CLASSICAL PARTITION FUNCTION OF AN ATOM IN AN IDEAL GAS CLASSICAL PARTITION FUNCTION OF A RIGID ROTOR CLASSICAL PARTITION FUNCTION OF A SYSTEM CONSISTING OF N INDEPENDENT AND INDISTINGUISHABLE MOLECULES CLASSICAL PARTITION FUNCTION OF A SYSTEM CONSISTING OF N INTERACTING AND INDISTINGUISHABLE MOLECULES SAMPLE PROBLEM 45 1 SIMULTANEOUS TREATMENT OF CLASSICAL AND QUANTUM MECHANICAL DEGREES OF FREEDOM EQUIPARTITION OF ENERGY CON?GURATIONAL INTEGRAL AND STATISTICAL MECHANICAL DERIVATION OF THE VIRIAL EQUATION OF STATE MODELING GASES AT NUMBER DENSITIES APPROACHING ZERO MODELING GASES AT HIGHER NUMBER DENSITIES DERIVATION OF THE VIRIAL EQUATION OF STATE USING THE GRAND-CANONICAL PARTITION FUNCTION VIRIAL COEF?CIENTS IN THE CLASSICAL LIMIT, STATISTICAL MECHANICAL DERIVATION OF THE VAN DER WAALS EQUATION OF STATE, AND SAMPLE PROBLEM VIRIAL COEF?CIENTS IN THE CLASSICAL LIMIT SPATIAL DEPENDENCE OF THE TWO-BODY INTERACTION POTENTIAL INCLUDING ITS LONG-RANGE ASYMPTOTIC BEHAVIOR SAMPLE PROBLEM 47 1: CALCULATE THE SECOND VIRIAL COEF?CIENT CORRESPONDING TO THE HARD-SPHERE INTERACTION POTENTIAL CALCULATING THE SECOND VIRIAL COEF?CIENT CORRESPONDING TO AN INTERACTION POTENTIAL CONSISTING OF A HARD-SPHERE REPULSION AND A VAN DER WAALS ATTRACTION IMPORTANT REMARKS ABOUT THE BEHAVIOR OF INTERACTION POTENTIALS DERIVATION OF THE VAN DER WAALS EQUATION OF STATE USING STATISTICAL MECHANICS STATISTICAL MECHANICAL TREATMENT OF CHEMICAL REACTION EQUILIBRIA AND SAMPLE PROBLEM EXPRESSING THE EQUILIBRIUM CONSTANT USING PARTITION FUNCTIONS RELATING THE PRESSURE-BASED AND THE NUMBER DENSITY-BASED EQUILIBRIUM CONSTANTS FOR IDEAL GAS MIXTURES SAMPLE PROBLEM 48 1 STATISTICAL MECHANICAL TREATMENT OF BINARY LIQUID MIXTURES MODELING BINARY LIQUID MIXTURES USING A STATISTICAL MECHANICAL APPROACH CALCULATING ?SMIX USING THE MICRO-CANONICAL ENSEMBLE RANGE OF VALIDITY OF THE LATTICE DESCRIPTION OF BINARY LIQUID MIXTURES LATTICE THEORY CALCULATION CALCULATION OF CHEMICAL POTENTIALS MOLECULAR CHARACTERISTICS OF IDEAL SOLUTIONS REVIEW OF PART III AND SAMPLE PROBLEM CANONICAL ENSEMBLE AVERAGE PROPERTIES IN THE CANONICAL ENSEMBLE CALCULATION OF THE CANONICAL PARTITION FUNCTION MOLECULAR PARTITION FUNCTIONS OF IDEAL GASES SUMMARY OF THERMODYNAMIC FUNCTIONS OF IDEAL GASES AVERAGE PROPERTIES IN THE GRAND-CANONICAL ENSEMBLE MICRO-CANONICAL ENSEMBLE AVERAGE ENTROPY IN THE MICRO-CANONICAL ENSEMBLE CALCULATION OF VIRIAL COEF?CIENTS STATISTICAL MECHANICAL TREATMENT OF CHEMICAL REACTION EQUILIBRIA USEFUL CONSTANTS IN STATISTICAL MECHANICS USEFUL RELATIONS IN STATISTICAL MECHANICS SAMPLE PROBLEM 50 1 SOLVED PROBLEMS FOR PART I SOLVED PROBLEMS FOR PART II SOLVED PROBLEMS FOR PART III STUDENTS, IN 2018, I ?NALLY DECIDED TO WRITE THIS BOOK WHICH IS BASED ON MY LECTURE NOTES, SUPPLEMENTED BY MANY SOLVED SAMPLE PROBLEMS WHICH HELP CRYSTALLIZE THE MATERIAL TAUGHT INCLUDING THIS LECTURE, THE BOOK CONSISTS OF 50 LECTURES AND IS PRIMARILY DESIGNED FOR GRADUATE STUDENTS AND SENIOR UNDERGRADUATE STUDENTS IN CHEMICAL ENGINEERING THE BOOK IS ALSO SUITABLE FOR GRADUATE STUDENTS IN MECHANICAL ENGINEERING, CHEM- ISTRY, AND MATERIALS SCIENCE IT FOCUSES ON DEVELOPING THE ABILITY OF THE READER TO SOLVE A BROAD RANGE OF CHALLENGING PROBLEMS IN CLASSICAL THERMODYNAMICS, BY APPLYING THE FUNDAMENTAL PRINCIPLES AND CONCEPTS TAUGHT TO NEW AND OFTEN UNUSUAL SCENARIOS IN ADDITION, THE BOOK INTRODUCES READERS TO THE FUNDAMENTALS OF STATISTICAL MECHANICS, INCLUDING DEMONSTRATING HOW THE MICROSCOPIC PROPERTIES OF ATOMS AND MOLECULES, AS WELL AS THEIR INTERACTIONS, CAN BE ACCOUNTED FOR TO CALCULATE VARIOUS PRACTICALLY RELEVANT AVERAGE THERMODYNAMIC PROPERTIES OF MACROSCOPIC SYSTEMS AGAIN, SOLVED SAMPLE PROBLEMS ARE PRESENTED TO HELP THE READER BETTER UNDERSTAND THE MATERIAL TAUGHT MY LECTURE NOTES, AND THEREFORE THIS BOOK, ARE INSPIRED BY CONCEPTS, PRINCIPLES, METHODS, AND APPLICATIONS THAT I DISTILLED AND ADAPTED FROM A NUMBER OF BOOKS (SEE BELOW), AS WELL AS BY MY OWN IN-DEPTH UNDERSTANDING OF THE MATERIAL TAUGHT THE BOOK PROVIDES A PEDAGOGICAL PRESENTATION OF THE FUNDAMENTALS OF CLASSICAL THERMO- DYNAMICS, WITH AN INTRODUCTION TO STATISTICAL MECHANICS, INCLUDING APPLYING THESE FUNDAMENTALS TO THE SOLUTION OF ILLUMINATING AND PRACTICALLY RELEVANT SAMPLE PROB- LEMS WHICH ARE DISPERSED THROUGHOUT THE LECTURES ACKNOWLEDGMENTS I AM GRATEFUL TO THE STUDENTS WHO ATTENDED MY 10 40 LECTURES OVER THE YEARS FOR CHALLENGING ME WITH INSIGHTFUL QUESTIONS WHICH HELPED ME IMPROVE THE QUALITY OF MY LECTURES MANY THANKS TO ALL THE TEACHING ASSISTANTS WHO WORKED WITH ME OVER THE YEARS, AND WHO HELPED THE STUDENTS CRYSTALLIZE THE MATERIAL TAUGHT IN CLASS THROUGH FRUITFUL INTERACTIONS DURING OF?CE HOURS AND ONE-ON-ONE MEETINGS, INCLUDING