ABOUT THE COURSE: This course introduces the fundamentals and applications of Statistical Thermodynamics from an engineering sciences point of view with particular emphasis on spectroscopy, and laser based diagnostics techniques applied to thermal sciences. The course begins with an introduction to the fundamentals of statistical thermodynamics. Then the course delves into the study of Quantum Mechanics and Spectroscopy to understand the relevant fundamentals before diving into applications involving laser based diagnostics. The course covers several applications like laser induced fluorescence techniques used for meausrement of species concentration and temperature.INTENDED AUDIENCE: UG, PG, PHDPREREQUISITES: Calculus, Basics of Probability Theory and Statistics, Fundamentals of ThermodynamicsINDUSTRY SUPPORT: General Electric, Siemens, Pratt and Whittney, HPCL, GTRE
Overview
Syllabus
Week 1:
1. Introduction1.1 The Statistical Foundation of Classical Thermodynamics1.2 A Classification Scheme for Statistical Thermodynamics1.3 Why Statistical Thermodynamics?
2. Probability and Statistics2.1 Probability: Definitions and Basic Concepts2.2 Permutations and Combinations2.3 Probability Distributions: Discrete and Continuous2.4 The Binomial Distribution2.5 The Poisson Distribution2.6 The Gaussian Distribution2.7 Combinatorial Analysis for Statistical Thermodynamics 2.7.1 Distinguishable Objects 2.7.2 Indistinguishable Objects
Week 2, 3:
3. The Statistics of Independent Particles3.1 Essential Concepts from Quantum Mechanics3.2 The Ensemble Method of Statistical Thermodynamics3.3 The Two Basic Postulates of Statistical Thermodynamics 3.3.1 The M–B Method: System Constraints and Particle Distribution 3.3.2 The M–B Method: Microstates and Macrostates3.4 The Most Probable Macrostate3.5 Bose–Einstein and Fermi–Dirac Statistics 3.5.1 Bose–Einstein Statistics 3.5.2 Fermi-Dirac Statistics 3.5.3 The Most Probable Particle Distribution3.6 Entropy and the Equilibrium Particle Distribution 3.6.1 The Boltzmann Relation for Entropy 3.6.2 Identification of Lagrange Multipliers 3.6.3 The Equilibrium Particle Distribution
Week 4:
4. Thermodynamic Properties in the Dilute Limit4.1 The Dilute Limit4.2 Corrected Maxwell–Boltzmann Statistics4.3 The Molecular Partition Function 4.3.1 The Influence of Temperature 4.3.2 Criterion for Dilute Limit4.4 Internal Energy and Entropy in the Dilute Limit4.5 Additional Thermodynamic Properties in the Dilute Limit4.6 The Zero of Energy and Thermodynamic Properties4.7 Intensive Thermodynamic Properties for the Ideal Gas
Week 5, 6:
5. Basics of Quantum Mechanics5.1 Historical Survey of Quantum Mechanics5.2 The Bohr Model for the Spectrum of Atomic Hydrogen5.3 The de Broglie Hypothesis5.4 A Heuristic Introduction to the Schrödinger Equation5.5 The Postulates of Quantum Mechanics5.6 The Steady-State Schrödinger Equation 5.6.1 Single-Particle Analysis 5.6.2 Multiparticle Analysis5.7 The Particle in a Box5.8 The Uncertainty Principle5.9 Indistinguishability and Symmetry5.10 The Pauli Exclusion Principle5.11 The Correspondence Principle6. Quantum Analysis of Internal Energy Modes6.1 Schrödinger Wave Equation for Two-Particle System 6.1.1 Conversion to Center-of-Mass Coordinates 6.1.2 Separation of External from Internal Modes6.2 The Internal Motion for a Two-Particle System6.3 The Rotational Energy Mode for a Diatomic Molecule6.4 The Vibrational Energy Mode for a Diatomic Molecule6.5 The Electronic Energy Mode for Atomic Hydrogen6.6 The Electronic Energy Mode for Multielectron Species 6.6.1 Electron Configuration for Multielectron Atoms 6.6.2 Spectroscopic Term Symbols for Multielectron Atoms 6.6.3 Electronic Energy Levels and Degeneracies for Atoms 6.6.4 Electronic Energy Levels and Degeneracies for Diatomic Molecules6.7 Combined Energy Modes for Atoms and Diatomic Molecules6.8 Selection Rules for Atoms and Molecules
Week 7:
7. The Spectroscopy of Diatomic Molecules7.1 Rotational Spectroscopy Using the Rigid-Rotor Model7.2 Vibrational Spectroscopy Using the Harmonic-Oscillator Model7.3 Rovibrational Spectroscopy: The Simplex Model7.4 The Complex Model for Combined Rotation and Vibration7.5 Rovibrational Spectroscopy: The Complex Model7.6 Electronic Spectroscopy7.7 Energy-Mode Parameters for Diatomic Molecules
Week 8:
8. Interlude: From Particle to Assembly8.1 Energy and Degeneracy8.2 Separation of Energy Modes8.3 The Molecular Internal Energy8.4 The Partition Function and Thermodynamic Properties8.5 Energy-Mode Contributions in Classical Mechanics 8.5.1 The Phase Integral 8.5.2 The Equipartition Principle 8.5.3 Mode Contributions
Week 9, 10:
9 Thermodynamic Properties of the Ideal Gas9.1 The monoatomic gas 9.1.1 Translation Mode 9.1.2 Electronic Mode9.2 The Diatomic Gas 9.2.1 Translational and Electronic Modes 9.2.2 The Zero of Energy 9.2.3 Rotational Mode 9.2.4 Quantum Origin of Rotational Symmetry Factor 9.2.5 Vibrational Mode9.3 Rigorous and Semirigorous Models for the Diatomic Gas9.4 The Polyatomic Gas 9.4.1 Rotational Contribution 9.4.2 Vibrational Contribution 9.4.3 Property Calculations for Polyatomic Molecules
10. Statistical Thermodynamics for Ideal Gas Mixtures10.1 Equilibrium Particle Distribution for the Ideal Gas Mixture10.2 Thermodynamic Properties of the Ideal Gas Mixture10.3 The Reacting Ideal Gas Mixture 10.3.1 Equilibrium Particle Distribution for Reactive Ideal Gas Mixture 10.3.2 Equilibrium Constant: Introduction and Development10.4 Equilibrium Constant: General Expression and Specific Examples 10.4.1 Dissociation of a Homonuclear Diatomic 10.4.2 The Homonuclear–Heteronuclear Conversion Reaction 10.4.3 The Ionization Reaction
Week 11, 12:
11. Concentration and Temperature Measurements11.1 Mode Temperatures11.2 Radiative Transitions 11.2.1 Spectral Transfer of Radiation 11.2.2 The Einstein Coefficients 11.2.3 Line Broadening11.3 Absorption Spectroscopy11.4 Emission Spectroscopy 11.4.1 Emissive Diagnostics 11.4.2 The problem of Self-Absorption11.5 Fluorescence Spectroscopy11.6 Sodium D-Line Reversal11.7 Advanced Diagnostic Techniques
1. Introduction1.1 The Statistical Foundation of Classical Thermodynamics1.2 A Classification Scheme for Statistical Thermodynamics1.3 Why Statistical Thermodynamics?
2. Probability and Statistics2.1 Probability: Definitions and Basic Concepts2.2 Permutations and Combinations2.3 Probability Distributions: Discrete and Continuous2.4 The Binomial Distribution2.5 The Poisson Distribution2.6 The Gaussian Distribution2.7 Combinatorial Analysis for Statistical Thermodynamics 2.7.1 Distinguishable Objects 2.7.2 Indistinguishable Objects
Week 2, 3:
3. The Statistics of Independent Particles3.1 Essential Concepts from Quantum Mechanics3.2 The Ensemble Method of Statistical Thermodynamics3.3 The Two Basic Postulates of Statistical Thermodynamics 3.3.1 The M–B Method: System Constraints and Particle Distribution 3.3.2 The M–B Method: Microstates and Macrostates3.4 The Most Probable Macrostate3.5 Bose–Einstein and Fermi–Dirac Statistics 3.5.1 Bose–Einstein Statistics 3.5.2 Fermi-Dirac Statistics 3.5.3 The Most Probable Particle Distribution3.6 Entropy and the Equilibrium Particle Distribution 3.6.1 The Boltzmann Relation for Entropy 3.6.2 Identification of Lagrange Multipliers 3.6.3 The Equilibrium Particle Distribution
Week 4:
4. Thermodynamic Properties in the Dilute Limit4.1 The Dilute Limit4.2 Corrected Maxwell–Boltzmann Statistics4.3 The Molecular Partition Function 4.3.1 The Influence of Temperature 4.3.2 Criterion for Dilute Limit4.4 Internal Energy and Entropy in the Dilute Limit4.5 Additional Thermodynamic Properties in the Dilute Limit4.6 The Zero of Energy and Thermodynamic Properties4.7 Intensive Thermodynamic Properties for the Ideal Gas
Week 5, 6:
5. Basics of Quantum Mechanics5.1 Historical Survey of Quantum Mechanics5.2 The Bohr Model for the Spectrum of Atomic Hydrogen5.3 The de Broglie Hypothesis5.4 A Heuristic Introduction to the Schrödinger Equation5.5 The Postulates of Quantum Mechanics5.6 The Steady-State Schrödinger Equation 5.6.1 Single-Particle Analysis 5.6.2 Multiparticle Analysis5.7 The Particle in a Box5.8 The Uncertainty Principle5.9 Indistinguishability and Symmetry5.10 The Pauli Exclusion Principle5.11 The Correspondence Principle6. Quantum Analysis of Internal Energy Modes6.1 Schrödinger Wave Equation for Two-Particle System 6.1.1 Conversion to Center-of-Mass Coordinates 6.1.2 Separation of External from Internal Modes6.2 The Internal Motion for a Two-Particle System6.3 The Rotational Energy Mode for a Diatomic Molecule6.4 The Vibrational Energy Mode for a Diatomic Molecule6.5 The Electronic Energy Mode for Atomic Hydrogen6.6 The Electronic Energy Mode for Multielectron Species 6.6.1 Electron Configuration for Multielectron Atoms 6.6.2 Spectroscopic Term Symbols for Multielectron Atoms 6.6.3 Electronic Energy Levels and Degeneracies for Atoms 6.6.4 Electronic Energy Levels and Degeneracies for Diatomic Molecules6.7 Combined Energy Modes for Atoms and Diatomic Molecules6.8 Selection Rules for Atoms and Molecules
Week 7:
7. The Spectroscopy of Diatomic Molecules7.1 Rotational Spectroscopy Using the Rigid-Rotor Model7.2 Vibrational Spectroscopy Using the Harmonic-Oscillator Model7.3 Rovibrational Spectroscopy: The Simplex Model7.4 The Complex Model for Combined Rotation and Vibration7.5 Rovibrational Spectroscopy: The Complex Model7.6 Electronic Spectroscopy7.7 Energy-Mode Parameters for Diatomic Molecules
Week 8:
8. Interlude: From Particle to Assembly8.1 Energy and Degeneracy8.2 Separation of Energy Modes8.3 The Molecular Internal Energy8.4 The Partition Function and Thermodynamic Properties8.5 Energy-Mode Contributions in Classical Mechanics 8.5.1 The Phase Integral 8.5.2 The Equipartition Principle 8.5.3 Mode Contributions
Week 9, 10:
9 Thermodynamic Properties of the Ideal Gas9.1 The monoatomic gas 9.1.1 Translation Mode 9.1.2 Electronic Mode9.2 The Diatomic Gas 9.2.1 Translational and Electronic Modes 9.2.2 The Zero of Energy 9.2.3 Rotational Mode 9.2.4 Quantum Origin of Rotational Symmetry Factor 9.2.5 Vibrational Mode9.3 Rigorous and Semirigorous Models for the Diatomic Gas9.4 The Polyatomic Gas 9.4.1 Rotational Contribution 9.4.2 Vibrational Contribution 9.4.3 Property Calculations for Polyatomic Molecules
10. Statistical Thermodynamics for Ideal Gas Mixtures10.1 Equilibrium Particle Distribution for the Ideal Gas Mixture10.2 Thermodynamic Properties of the Ideal Gas Mixture10.3 The Reacting Ideal Gas Mixture 10.3.1 Equilibrium Particle Distribution for Reactive Ideal Gas Mixture 10.3.2 Equilibrium Constant: Introduction and Development10.4 Equilibrium Constant: General Expression and Specific Examples 10.4.1 Dissociation of a Homonuclear Diatomic 10.4.2 The Homonuclear–Heteronuclear Conversion Reaction 10.4.3 The Ionization Reaction
Week 11, 12:
11. Concentration and Temperature Measurements11.1 Mode Temperatures11.2 Radiative Transitions 11.2.1 Spectral Transfer of Radiation 11.2.2 The Einstein Coefficients 11.2.3 Line Broadening11.3 Absorption Spectroscopy11.4 Emission Spectroscopy 11.4.1 Emissive Diagnostics 11.4.2 The problem of Self-Absorption11.5 Fluorescence Spectroscopy11.6 Sodium D-Line Reversal11.7 Advanced Diagnostic Techniques
Taught by
Prof. Saptarshi Basu
