Lectures in Classical Thermodynamics with an Introduction to Statistical Mechanics

Description

This textbook facilitates students’ ability to apply fundamental principles and concepts in classical thermodynamics to solve challenging problems relevant to industry and everyday life. It also introduces the reader to the fundamentals of statistical mechanics, including understanding how the microscopic properties of atoms and molecules, and their associated intermolecular interactions, can be accounted for to calculate various average properties of macroscopic systems. The author emphasizes application of the fundamental principles outlined above to the calculation of a variety of thermodynamic properties, to the estimation of conversion efficiencies for work production by heat interactions, and to the solution of practical thermodynamic problems related to the behavior of non-ideal pure fluids and fluid mixtures, including phase equilibria and chemical reaction equilibria. The book contains detailed solutions to many challenging sample problems in classical thermodynamics and statistical mechanics that will help the reader crystallize the material taught. Class-tested and perfected over 30 years of use by nine-time Best Teaching Award recipient Professor Daniel Blankschtein of the Department of Chemical Engineering at MIT, the book is ideal for students of Chemical and Mechanical Engineering, Chemistry, and Materials Science, who will benefit greatly from in-depth discussions and pedagogical explanations of key concepts. Distills critical concepts, methods, and applications from leading full-length textbooks, along with the author’s own deep understanding of the material taught, into a concise yet rigorous graduate and advanced undergraduate text; Enriches the standard curriculum with succinct, problem-based learning strategies derived from the content of 50 lectures given over the years in the Department of Chemical Engineering at MIT; Reinforces concepts covered with detailed solutions to illuminating and challenging homework problems. Contents Lecture 1: Introduction to the Book 1.1 Motivation and Scope of the Book 1.2 Organization of the Book 1.3 Acknowledgments Part I: Fundamental Principles and Properties of Pure Fluids Lecture 2: Useful Definitions, Postulates, Nomenclature, and Sample Problems 2.1 Introduction 2.2 Useful Definitions 2.3 Postulates I and II (Adapted from Appendix A in T&M) 2.4 Sample Problem 2.1 2.4.1 Solution 2.5 Sample Problem 2.2 2.5.1 Solution 2.6 Nomenclature Lecture 3: The First Law of Thermodynamics for Closed Systems: Derivation and Sample Problems 3.1 Introduction 3.2 Work Interactions 3.3 Sample Problem 3.1 3.3.1 Solution 3.4 Specific Types of Work Interactions 3.5 Sample Problem 3.2 3.5.1 Solution 3.6 Sample Problem 3.3 3.6.1 Solution 3.7 Postulate III (Adapted from Appendix A in T&M) 3.8 Energy Decomposition 3.9 Heat Interactions 3.10 The First Law of Thermodynamics for Closed Systems Lecture 4: The First Law of Thermodynamics for Closed Systems: Thermal Equilibrium, the Ideal Gas, and Sample Problem 4.1 Introduction 4.2 Thermal Equilibrium and the Directionality of Heat Interactions 4.3 Postulate IV (Adapted from Appendix A in T&M) 4.4 Ideal Gas Properties 4.4.1 Equation of State (EOS) 4.4.2 Internal Energy 4.4.3 Enthalpy 4.4.4 Other Useful Relationships 4.5 Sample Problem 4.1: Problem 3.1 in T&M 4.5.1 Solution Lecture 5: The First Law of Thermodynamics for Closed Systems: Sample Problem 4.1, Continued 5.1 Introduction 5.2 Sample Problem 4.1: Problem 3.1 in T&M, Continued 5.3 Solution 1: System III-Atmosphere (a) 5.4 Solution 2: System I-Gas (g) 5.5 Food for Thought Lecture 6: The First Law of Thermodynamics for Open Systems: Derivation and Sample Problem 6.1 Introduction 6.2 The First Law of Thermodynamics for Open Systems 6.2.1 Notation 6.2.2 Derivation 6.3 Sample Problem 6.1: Problem 3.9 in T&M 6.3.1 Solution Strategy 6.3.2 Well-Mixed Gas Model System 6.3.3 Pressurization Step: Well-Mixed Gas Model System 6.3.4 Layered or Stratified Gas Model System 6.3.5 Pressurization Step: Stratified Gas Model System 6.3.6 Emptying Step: Well-Mixed Gas Model System Lecture 7: The Second Law of Thermodynamics: Fundamental Concepts and Sample Problem 7.1 Introduction 7.2 Natural Processes 7.3 Statement (1) of the Second Law of Thermodynamics 7.4 Sample Problem 7.1 7.4.1 Solution 7.5 Statement (1a) of the Second Law of Thermodynamics 7.6 Heat Engine 7.7 Efficiency of a Heat Engine 7.8 Reversible Process Lecture 8: Heat Engine, Carnot Efficiency, and Sample Problem 8.1 Introduction 8.2 Heat Engine 8.3 Theorem of Carnot 8.4 Corollary to Theorem of Carnot 8.5 Sample Problem 8.1 8.5.1 Solution 8.6 Theorem of Clausius Lecture 9: Entropy and Reversibility 9.1 Introduction 9.2 Entropy 9.3 Reversible Process 9.4 Irreversible Process Lecture 10: The Second Law of Thermodynamics, Maximum Work, and Sample Problems 10.1 Introduction 10.2 A More General Statement of the Second Law of Thermodynamics 10.3 Heat Interactions Along Reversible and Irreversible Paths (Closed System) 10.4 Work Interactions Along Reversible and Irreversible Paths (Closed System) 10.5 Sample Problem 10.1 10.5.1 Solution 10.6 Sample Problem 10.2 10.6.1 Solution 10.7 Criterion of Equilibrium Based on the Entropy 10.8 Sample Problem 10.3 10.8.1 Solution Lecture 11: The Combined First and Second Law of Thermodynamics, Availability, and Sample Problems 11.1 Introduction 11.2 Closed, Single-Phase, Simple System 11.3 Open, Single-Phase, Simple System 11.4 Sample Problem 11.1 11.4.1 Solution 11.5 Sample Problem 11.2 11.5.1 Solution Lecture 12: Flow Work and Sample Problems 12.1 Introduction 12.2 Sample Problem 12.1 12.2.1 Solution 12.3 Sample Problem 12.2: Problem 4.3 in T&M 12.3.1 Solution: Assumptions Lecture 13: Fundamental Equations and Sample Problems 13.1 Introduction 13.2 Thermodynamic Relations for Simple Systems 13.3 Fundamental Equation 13.4 The Theorem of Euler in the Context of Thermodynamics (Adapted from Appendix C in T&M) 13.5 Sample Problem 13.1 13.5.1 Solution 13.6 Sample Problem 13.2 13.6.1 Solution 13.7 Variable Transformations and New Fundamental Equations 13.8 Sample Problem 13.3 13.8.1 Solution 13.9 Sample Problem 13.4 13.9.1 Solution Lecture 14: Manipulation of Partial Derivatives and Sample Problems 14.1 Introduction 14.2 Two Additional Restrictions on the Internal Energy Fundamental Equation 14.3 Corollary to Postulate I 14.4 Reconstruction of the Internal Energy Fundamental Equation 14.5 Manipulation of Partial Derivatives of Thermodynamic Functions 14.6 Internal Energy and Entropy Fundamental Equations 14.7 Useful Rules to Calculate Partial Derivatives of Thermodynamic Functions 14.7.1 The Triple Product Rule 14.7.2 The Add Another Variable Rule 14.7.3 The Derivative Inversion Rule 14.7.4 Maxwell´s Reciprocity Rule 14.8 Sample Problem 14.1 14.8.1 Solution 14.9 Jacobian Transformations 14.9.1 Properties of Jacobians 14.10 Sample Problem 14.2 14.10.1 Solution Lecture 15: Properties of Pure Materials and Gibbs Free Energy Formulation 15.1 Introduction 15.2 Gibbs Free Energy Fundamental Equation 15.3 Derivation of the Gibbs-Duhem Equation 15.4 Relating the Gibbs Free Energy to Other Thermodynamic Functions 15.5 First-Order and Second-Order Partial Derivatives of the Gibbs Free Energy 15.6 Determining Which Data Set Has the Same Thermodynamic Information Content as the Gibbs Free Energy Fundamental Equation Lecture 16: Evaluation of Thermodynamic Data of Pure Materials and Sample Problems 16.1 Introduction 16.2 Summary of Changes in Entropy, Internal Energy, and Enthalpy 16.2.1 Using T and P as the Two Independent Intensive Variables 16.2.2 Using T and V as the Two Independent Intensive Variables 16.2.3 The Ideal Gas Limit 16.2.4 Relation between CP and CV 16.3 Sample Problem 16.1 16.3.1 Solution 16.4 Sample Problem 16.2 16.4.1 Solution 16.5 Evaluation of Changes in the Thermodynamic Properties of Pure Materials 16.5.1 Calculation of the Entropy Change 16.5.2 Strategy I 16.5.3 Strategy II 16.5.4 Strategy III Lecture 17: Equations of State of a Pure Material, Binodal, Spinodal, Critical Point, and Sample Problem 17.1 Introduction 17.2 Equations of State of a Pure Material 17.3 Examples of Equations of State (EOS) 17.3.1 The Ideal Gas EOS 17.3.2 The van der Waals EOS 17.4 Sample Problem 17.1 17.4.1 Solution 17.5 Pressure-Explicit Form of the Isotherm P = f (V, T) of a Pure Material 17.6 Stable, Metastable, and Unstable Equilibrium 17.7 Mechanical Analogy of Stable, Metastable, and Unstable Equilibrium States 17.8 Mathematical Conditions for Stability, Metastability, and Instability 17.9 Mathematical Conditions for the Spinodal and the Critical Point Lecture 18: The Principle of Corresponding States and Sample Problems 18.1 Introduction 18.2 Examples of Additional Equations of State (EOS) 18.2.1 The Redlich-Kwong (RK) EOS 18.2.2 Sample Problem 18.1 18.2.2.1 Solution 18.2.3 Sample Problem 18.2 18.2.3.1 Solution 18.2.4 The Peng-Robinson (PR) EOS 18.2.5 The Virial EOS 18.2.6 Sample Problem 18.3 18.2.6.1 Solution 18.3 The Principle of Corresponding States 18.3.1 The Compressibility Factor 18.3.2 Sample Problem 18.4 18.3.2.1 Solution Lecture 19: Departure Functions and Sample Problems 19.1 Introduction 19.2 Sample Problem 19.1 19.2.1 Solution 19.3 Departure Functions 19.4 Calculation of the Entropy Departure Function, DS (T, P) 19.5 Calculation of the Helmholtz Free Energy Departure Function, DA(T, V) 19.6 Calculation of the Entropy Departure Function, DS (T, V) 19.7 Sample Problem 19.2 19.7.1 Solution 19.8 Important Remark Lecture 20: Review of Part I and Sample Problem 20.1 Introduction 20.2 Basic Concepts, Definitions, and Postulates 20.3 Ideal Gas 20.4 The First Law of Thermodynamics for Closed Systems 20.5 The First Law of Thermodynamics for Open, Simple Systems 20.6 The First Law of Thermodynamics for Steady-State Flow Systems 20.7 Carnot Engine 20.8 Entropy of a Closed System 20.9 The Second Law of Thermodynamics 20.10 The Combined First and Second Law of Thermodynamics for Closed Systems 20.11 Entropy Balance for Open Systems 20.12 Maximum Work, Availability 20.13 Fundamental Equations 20.14 Manipulation of Partial Derivatives 20.15 Manipulation of Partial Derivatives Using Jacobian Transformations 20.16 Maxwell´s Reciprocity Rules 20.17 Important Thermodynamic Relations for Pure Materials 20.18 Gibbs-Duhem Equation for a Pure Material 20.19 Equations of State (EOS) 20.20 Stability Criteria for a Pure Material 20.21 Sample Problem 20.1 20.21.1 Solution Part II: Mixtures: Models and Applications to Phase and Chemical Reaction Equilibria Lecture 21: Extensive and Intensive Mixture Properties and Partial Molar Properties 21.1 Introduction 21.2 Extensive and Intensive Differentials of Mixtures 21.3 Choose Set 1: {T, P, N1, , Nn} and Analyze B = B (T, P, N1, , Nn) 21.4 Important Remarks 21.5 Choose Set 2: {T, P, x1, , xn-1, N} and Analyze B = B (T, P, x1, , xn-1, N) 21.6 Choose Set 1: {T, P, N1, , Nn} and Analyze B = B (T, P, N1, , Nn) 21.7 Choose Set 2: {T, P, x1, , xn-1, N} and Analyze B = B (T, P, x1, , xn-1, N) Lecture 22: Generalized Gibbs-Duhem Relations for Mixtures, Calculation of Partial Molar Properties, and Sample Problem 22.1 Introduction 22.2 Partial Molar Properties 22.3 Useful Relations Between Partial Molar Properties 22.4 How Do We Calculate Cases 1, 2, and 3 22.5 Sample Problem 22.1 22.5.1 Solution 22.6 Generalized Gibbs-Duhem Relations for Mixtures Lecture 23: Mixture Equations of State, Mixture Departure Functions, Ideal Gas Mixtures, Ideal Solutions, and Sample Problem 23.1 Introduction 23.2 Sample Problem 23.1 23.2.1 Solution 23.3 Equations of State for Gas Mixtures 23.3.1 Ideal Gas (IG) Mixture EOS 23.3.2 van der Waals (vdW) Mixture EOS 23.3.3 Peng-Robinson (PR) Mixture EOS 23.3.4 Virial Mixture EOS 23.4 Calculation of Changes in the Thermodynamic Properties of Gas Mixtures 23.4.1 Mixture Attenuated State Approach 23.4.2 Mixture Departure Function Approach 23.5 Ideal Gas Mixtures and Ideal Solutions 23.5.1 One Component (Pure, n = 1) Ideal Gas 23.5.2 Ideal Gas Mixture: For Component i 23.5.3 Ideal Solution: For Component i Lecture 24: Mixing Functions, Excess Functions, and Sample Problems 24.1 Introduction 24.2 Sample Problem 24.1 24.2.1 Solution 24.3 Sample Problem 24.2 24.3.1 Solution 24.4 Sample Problem 24.3 24.4.1 Solution 24.5 Other Useful Relations for an Ideal Solution 24.6 Summary of Results for an Ideal Solution 24.7 Mixing Functions 24.7.1 The Mixing B and Reference States 24.7.2 Pure Component Reference State for Component j 24.7.3 Useful Relations for Mixing Functions 24.8 Mixing Functions: Mixing of Three Liquids at Constant T and P 24.9 Ideal Solution Mixing Functions 24.10 Excess Functions Lecture 25: Ideal Solution, Regular Solution, and Athermal Solution Behaviors, and Fugacity and Fugacity Coefficient 25.1 Introduction 25.2 Ideal Solution Behavior 25.3 Regular Solution Behavior 25.4 Athermal Solution Behavior 25.5 Fugacity and Fugacity Coefficient 25.5.1 Variations of with Pressure 25.5.2 Variations of with Temperature 25.6 Other Relations Involving Fugacities 25.7 Calculation of Fugacity 25.8 The Lewis and Randall Rule Lecture 26: Activity, Activity Coefficient, and Sample Problems 26.1 Introduction 26.2 Activity and Activity Coefficient 26.3 Pure Component Reference State 26.4 Calculation of Activity 26.5 Sample Problem 26.1 26.5.1 Solution 26.6 Sample Problem 26.2 26.6.1 Solution Lecture 27: Criteria of Phase Equilibria, and the Gibbs Phase Rule 27.1 Introduction 27.2 Use of Other Reference States 27.3 Phase Equilibria: Introduction 27.4 Criteria of Phase Equilibria 27.4.1 Thermal Equilibrium 27.4.2 Mechanical Equilibrium 27.4.3 Diffusional Equilibrium 27.5 The Gibbs Phase Rule Lecture 28: Application of the Gibbs Phase Rule, Azeotrope, and Sample Problem 28.1 Introduction 28.2 The Gibbs Phase Rule for a Pure Substance 28.3 Sample Problem 28.1 28.3.1 Solution Lecture 29: Differential Approach to Phase Equilibria, Pressure-Temperature-Composition Relations, Clausius-Clapeyron Equation... 29.1 Introduction 29.2 Sample Problem 29.1 29.2.1 Solution 29.3 Simplifications of Eqs. (29.21) and (29.22) Lecture 30: Pure Liquid in Equilibrium with Its Pure Vapor, Integral Approach to Phase Equilibria, Composition Models, and Sam... 30.1 Introduction 30.2 From Lecture 29 30.3 Pure Liquid in Equilibrium with Its Pure Vapor 30.4 Integral Approach to Phase Equilibria 30.4.1 Sample Problem 30.1 30.4.2 Solution Strategy 30.4.3 Calculation of Vapor Mixture Fugacities 30.4.4 Calculation of Liquid Mixture Fugacities 30.4.5 Calculation of Pure Component i Liquid Fugacity 30.4.6 Simplifications of Eq. (30.29) 30.4.7 Models for the Excess Gibbs Free Energy of Mixing of n = 2 Mixtures 30.4.8 Models for the Excess Gibbs Free Energy of Mixing of n > 2 Mixtures Lecture 31: Chemical Reaction Equilibria: Stoichiometric Formulation and Sample Problem 31.1 Introduction 31.2 Contrasting the Calculation of Changes in Thermodynamic Properties With and Without Chemical Reactions 31.2.1 Case I: Closed Binary System of Inert Components 1 and 2 31.2.2 Case II: Closed Binary System of Components 1 and 2 Undergoing a Dissociation Reaction 31.3 Stoichiometric Formulation 31.4 Important Remark 31.5 Sample Problem 31.1 31.5.1 Solution Lecture 32: Criterion of Chemical Reaction Equilibria, Standard States, and Equilibrium Constants for Gas-Phase Chemical React... 32.1 Introduction 32.2 Derivation of the Criterion of Chemical Reaction Equilibria 32.3 Derivation of the Equilibrium Constant for Chemical Reaction r 32.4 Derivation of the Equilibrium Constant for a Single Chemical Reaction 32.5 Discussion of Standard States for Gas-Phase, Liquid-Phase, and Solid-Phase Chemical Reactions 32.6 Comments on the Standard-State Pressure 32.7 Decomposition of the Equilibrium Constant into Contributions from the Fugacity Coefficients, the Gas Mixture Mole Fractio... Lecture 33: Equilibrium Constants for Condensed-Phase Chemical Reactions, Response of Chemical Reactions to Temperature, and L... 33.1 Introduction 33.2 Derivation of the Equilibrium Constant for a Condensed-Phase Chemical Reaction 33.3 Determination of the Standard Molar Gibbs Free Energy of Reaction 33.4 Response of Chemical Reactions to Changes in Temperature and Pressure 33.5 How Does a Chemical Reaction Respond to Temperature? 33.6 Le Chatelier´s Principle Lecture 34: Response of Chemical Reactions to Pressure, and Sample Problems 34.1 Introduction 34.2 How Does a Chemical Reaction Respond to Pressure? 34.3 Sample Problem 34.1 34.3.1 Solution 34.4 Sample Problem 34.2 34.4.1 Solution Lecture 35: The Gibbs Phase Rule for Chemically-Reacting Systems and Sample Problem 35.1 Introduction 35.2 Sample Problem 35.1 35.2.1 Solution Strategy 35.2.2 Selection of Standard States 35.2.3 Remarks 35.2.4 Evaluation of Fugacities 35.2.5 Calculation of the Equilibrium Constant 35.2.6 Comment on the Standard-State Pressure Lecture 36: Effect of Chemical Reaction Equilibria on Changes in Thermodynamic Properties and Sample Problem 36.1 Introduction 36.2 Sample Problem 36.1: Production of Sulfuric Acid by the Contact Process 36.3 Solution Strategy 36.4 Evaluation of K(T) 36.5 Derivation of the Second Equation Relating T and xi Lecture 37: Review of Part II and Sample Problem 37.1 Introduction 37.2 Partial Molar Properties 37.3 Generalized Gibbs-Duhem Relations for Mixtures 37.4 Gibbs-Helmholtz Relation 37.5 Mixing Functions 37.6 Ideal Gas Mixtures 37.7 Ideal Solutions 37.8 Excess Functions 37.9 Fugacity 37.10 Variation of Fugacity with Temperature and Pressure 37.11 Generalized Gibbs-Duhem Relation for Fugacities 37.12 Fugacity Coefficient 37.13 Lewis and Randall Rule 37.14 Activity 37.15 Activity Coefficient 37.16 Variation of Activity Coefficient with Temperature and Pressure 37.17 Generalized Gibbs-Duhem Relation for Activity Coefficients 37.18 Conditions for Thermodynamic Phase Equilibria 37.19 Gibbs Phase Rule 37.20 Differential Approach to Phase Equilibria 37.21 Dependence of Fugacitities on Temperature, Pressure, and Mixture Composition 37.22 Integral Approach to Phase Equilibria 37.23 Pressure-Temperature Relations 37.24 Stoichiometric Formulation for Chemical Reactions 37.25 Equilibrium Constant 37.26 Typical Reference States for Gas, Liquid, and Solid 37.27 Equilibrium Constant for Gases Undergoing a Single Chemical Reaction 37.28 Equilibrium Constants for Liquids and Solids 37.29 Calculation of the Standard Molar Gibbs Free Energy of Reaction 37.30 Variation of the Equilibrium Constant with Temperature and Pressure 37.31 Sample Problem 37.1 37.31.1 Solution Part III: Introduction to Statistical Mechanics Lecture 38: Statistical Mechanics, Canonical Ensemble, Probability and the Boltzmann Factor, and Canonical Partition Function 38.1 Introduction 38.2 Canonical Ensemble and the Boltzmann Factor 38.3 Probability That a System in the Canonical Ensemble Is in Quantum State j with Energy Ej(N, V) 38.4 Physical Interpretation of the Canonical Partition Function Lecture 39: Calculation of Average Thermodynamic Properties Using the Canonical Partition Function and Treatment of Distinguis... 39.1 Introduction 39.2 Calculation of the Average Energy of a Macroscopic System 39.3 Calculation of the Average Heat Capacity at Constant Volume of a Macroscopic System 39.4 Calculation of the Average Pressure of a Macroscopic System 39.5 Canonical Partition Function of a System of Independent and Distinguishable Molecules 39.6 Canonical Partition Function of a System of Independent and Indistinguishable Molecules 39.7 Decomposition of a Molecular Canonical Partition Function into Canonical Partition Functions for Each Degree of Freedom 39.8 Energy States and Energy Levels Lecture 40: Translational, Vibrational, Rotational, and Electronic Contributions to the Partition Function of Monoatomic and D... 40.1 Introduction 40.2 Partition Functions of Ideal Gases 40.3 Translational Partition Function of a Monoatomic Ideal Gas 40.4 Electronic Contribution to the Atomic Partition Function 40.5 Sample Problem 40.1 40.5.1 Solution 40.6 Average Energy of a Monoatomic Ideal Gas 40.7 Average Heat Capacity at Constant Volume of a Monoatomic Ideal Gas 40.8 Average Pressure of a Monoatomic Ideal Gas 40.9 Diatomic Ideal Gas Lecture 41: Thermodynamic Properties of Ideal Gases of Diatomic Molecules Calculated Using Partition Functions and Sample Prob... 41.1 Introduction 41.2 Vibrational Partition Function of a Diatomic Molecule 41.3 Sample Problem 41.1 41.3.1 Solution 41.4 Rotational Partition Function of a Diatomic Molecule 41.5 Average Rotational Energy of an Ideal Gas of Diatomic Molecules 41.6 Average Rotational Heat Capacity at Constant Volume of an Ideal Gas of Diatomic Molecules 41.7 Fraction of Diatomic Molecules in the Jth Rotational Level 41.8 Rotational Partition Functions of Diatomic Molecules Contain a Symmetry Number 41.9 Total Partition Function of a Diatomic Molecule 41.10 Sample Problem 41.2 41.10.1 Solution Lecture 42: Statistical Mechanical Interpretation of Reversible Mechanical Work, Reversible Heat, and the First Law of Thermod... 42.1 Introduction 42.2 Statistical Mechanical Interpretation of Reversible Mechanical Work, Reversible Heat, and the First Law of Thermodynamics 42.3 Micro-Canonical Ensemble and Entropy 42.4 Relating Entropy to the Canonical Partition Function 42.5 Sample Problem 42.1 42.5.1 Solution 42.6 Relating the Statistical Mechanical Relation, S = kBlnW, to the Thermodynamic Relation, Lecture 43: Statistical Mechanical Interpretation of the Third Law of Thermodynamics, Calculation of the Helmholtz Free Energy... 43.1 Introduction 43.2 The Third Law of Thermodynamics and Entropy 43.3 Calculation of the Helmholtz Free Energy of a Pure Material Using the Canonical Partition Function 43.4 Sample Problem 43.1 43.4.1 Solution 43.5 Sample Problem 43.2 43.5.1 Solution 43.6 Sample Problem 43.3 43.6.1 Solution Lecture 44: Grand-Canonical Ensemble, Statistical Fluctuations, and Sample Problems 44.1 Introduction 44.2 Grand-Canonical Ensemble 44.3 Statistical Fluctuations 44.4 Sample Problem 44.1 44.4.1 Solution 44.5 Sample Problem 44.2 44.5.1 Solution 44.6 Fluctuations in the Number of Molecules 44.7 Sample Problem 44.3 44.7.1 Solution 44.8 Equivalence of All the Ensembles in the Thermodynamic Limit Lecture 45: Classical Statistical Mechanics and Sample Problem 45.1 Introduction 45.2 Classical Statistical Mechanics 45.3 Classical Molecular Partition Function 45.4 Classical Partition Function of an Atom in an Ideal Gas 45.5 Classical Partition Function of a Rigid Rotor 45.6 Classical Partition Function of a System Consisting of N Independent and Indistinguishable Molecules 45.7 Classical Partition Function of a System Consisting of N Interacting and Indistinguishable Molecules 45.8 Sample Problem 45.1 45.8.1 Solution 45.9 Simultaneous Treatment of Classical and Quantum Mechanical Degrees of Freedom 45.10 Equipartition of Energy Lecture 46: Configurational Integral and Statistical Mechanical Derivation of the Virial Equation of State 46.1 Introduction 46.2 Modeling Gases at Number Densities Approaching Zero 46.3 Modeling Gases at Higher Number Densities 46.4 Derivation of the Virial Equation of State Using the Grand-Canonical Partition Function Lecture 47: Virial Coefficients in the Classical Limit, Statistical Mechanical Derivation of the van der Waals Equation of Sta... 47.1 Introduction 47.2 Virial Coefficients in the Classical Limit 47.3 Spatial Dependence of the Two-Body Interaction Potential Including Its Long-Range Asymptotic Behavior 47.4 Sample Problem 47.1: Calculate the Second Virial Coefficient Corresponding to the Hard-Sphere Interaction Potential 47.4.1 Solution 47.5 Calculating the Second Virial Coefficient Corresponding to an Interaction Potential Consisting of a Hard-Sphere Repulsion... 47.6 Important Remarks About the Behavior of Interaction Potentials 47.7 Derivation of the van der Waals Equation of State Using Statistical Mechanics Lecture 48: Statistical Mechanical Treatment of Chemical Reaction Equilibria and Sample Problem 48.1 Introduction 48.2 Expressing the Equilibrium Constant Using Partition Functions 48.3 Relating the Pressure-Based and the Number Density-Based Equilibrium Constants for Ideal Gas Mixtures 48.4 Sample Problem 48.1 48.4.1 Solution Lecture 49: Statistical Mechanical Treatment of Binary Liquid Mixtures 49.1 Introduction 49.2 Modeling Binary Liquid Mixtures Using a Statistical Mechanical Approach 49.3 Calculating DeltaSmix Using the Micro-Canonical Ensemble 49.4 Range of Validity of the Lattice Description of Binary Liquid Mixtures 49.5 Lattice Theory Calculation 49.6 Calculation of Chemical Potentials 49.7 Molecular Characteristics of Ideal Solutions Lecture 50: Review of Part III and Sample Problem 50.1 Introduction 50.2 Canonical Ensemble 50.3 Average Properties in the Canonical Ensemble 50.4 Calculation of the Canonical Partition Function 50.5 Molecular Partition Functions of Ideal Gases 50.6 Summary of Thermodynamic Functions of Ideal Gases 50.7 Grand-Canonical Ensemble 50.8 Average Properties in the Grand-Canonical Ensemble 50.9 Micro-Canonical Ensemble 50.10 Average Entropy in the Micro-Canonical Ensemble 50.11 Classical Statistical Mechanics 50.12 Calculation of Virial Coefficients 50.13 Statistical Mechanical Treatment of Chemical Reaction Equilibria 50.14 Statistical Mechanical Treatment of Binary Liquid Mixtures 50.15 Useful Constants in Statistical Mechanics 50.16 Useful Relations in Statistical Mechanics 50.17 Sample Problem 50.1 50.17.1 Solution Solved Problems for Part I Problem 1 Problem 3.4 in Tester and Modell Solution to Problem 1 Solution Strategy Solving the Problem Other Possible Solution Strategies Problem 2 Problem 3.8 in Tester and Modell Solution to Problem 2 Solution Strategy Problem 3 Problem 4.11 in Tester and Modell Solution to Problem 3 Solution Strategy Solving the Problem Additional Comments Problem 4 Problem 4.29 in Tester and Modell Solution to Problem 4 Solution Strategy Other Possible Solution Strategies Problem 5 Problems 5.17 + 5.27 in Tester and Modell Solution to Problem 5 Solution to Problem 5.17 Solution Strategy Solution to Problem 5.27 Solution Strategy Problem 6 Problem 5.28 in Tester and Modell Solution to Problem 6 Solution Strategy Other Possible Solution Strategies Problem 7 Problem 8.2 in Tester and Modell Solution to Problem 7 Solution Strategy Problem 8 Problem 8.4 in Tester and Modell Solution to Problem 8 Solution Strategy Problem 9 Problem 8.6 in Tester and Modell Solution to Problem 9 Solution Strategy Problem 10 Adapted from Problem 8.15 in Tester and Modell Solution to Problem 10 Solution Strategy Derivations Attenuated-State Approach Departure Function Approach Solved Problems for Part II Problem 11 Problem 9.24 in Tester and Modell Solution to Problem 11 Solution strategy Problem 12 Problem 9.2 in Tester and Modell Solution to Problem 12 Solution Strategy Problem 13 Problem 9.23 in Tester and Modell Solution to Problem 13 Solution Strategy Selection of System and Boundaries Problem 14 Problem 15.4 in Tester and Modell Solution to Problem 14 Solution Strategy Draw the System and Describe the Boundaries Use the Gibbs Phase Rule Draw a Schematic Phase Diagram Decide Whether the Integral Approach or the Differential Approach Is More Appropriate Solve the Problem N2 Liquid/Solid Equilibrium O2 Liquid/Solid Equilibrium Problem 15 Problem 15.13 in Tester and Modell Solution to Problem 15 Solution Strategy Problem 16 Problem 16.7 in Tester and Modell Solution to Problem 16 Solution Strategy Other Possible Solution Strategies Problem 17 Problem 16.11 in Tester and Modell Solution to Problem 17 Solution Strategy Problem 18 Problem 9.3 in Tester and Modell Solution to Problem 18 Solution Strategy Problem 19 Solution to Problem 19 Solution Strategy Calculation of Phase Equilibria Problem 20 Solution to Problem 20 Solution Strategy Conditions of Phase Equilibria Choosing the Differential Approach to Phase Equilibria Solved Problems for Part III Problem 21 Problem 21.1 Problem 21.2 Problem 21.3 Solution to Problem 21 Solution to Problem 21.1 Solution to Problem 21.2 Solution to Problem 21.3 Problem 22 Problem 22.1 Problem 22.2 Problem 22.3 Solution to Problem 22 Solution to Problem 22.1 Solution to Problem 22.2 Solution to Problem 22.3 Problem 23 Problem 23.1 Problem 23.2 Problem 23.3 Solution to Problem 23 Solution to Problem 23.1 Solution to Problem 23.2 Solution to Problem 23.3 Problem 24 Problem 24.1 Problem 24.2 Problem 24.3 Solution to Problem 24 Solution to Problem 24.1 Solution to Problem 24.2 Solution to Problem 24.3 Problem 25 Problem 25.1 Problem 25.2 (Adapted from D&B) Problem 25.3 Solution to Problem 25 Solution to Problem 25.1 Problem Solution 25.2 Solution to Problem 25.3