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.

1.1 The Statistical Foundation of Classical Thermodynamics

1.2 A Classification Scheme for Statistical Thermodynamics

1.3 Why Statistical Thermodynamics?

2.1 Probability: Definitions and Basic Concepts

2.2 Permutations and Combinations

2.3 Probability Distributions: Discrete and Continuous

2.4 The Binomial Distribution

2.5 The Poisson Distribution

2.6 The Gaussian Distribution

2.7 Combinatorial Analysis for Statistical Thermodynamics

2.7.1 Distinguishable Objects

2.7.2 Indistinguishable Objects

3.1 Essential Concepts from Quantum Mechanics

3.2 The Ensemble Method of Statistical Thermodynamics

3.3 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 Macrostates

3.4 The Most Probable Macrostate

3.5 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 Distribution

3.6 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

4.1 The Dilute Limit

4.2 Corrected Maxwell–Boltzmann Statistics

4.3 The Molecular Partition Function

4.3.1 The Influence of Temperature

4.3.2 Criterion for Dilute Limit

4.4 Internal Energy and Entropy in the Dilute Limit

4.5 Additional Thermodynamic Properties in the Dilute Limit

4.6 The Zero of Energy and Thermodynamic Properties

4.7 Intensive Thermodynamic Properties for the Ideal Gas

5.1 Historical Survey of Quantum Mechanics

5.2 The Bohr Model for the Spectrum of Atomic Hydrogen

5.3 The de Broglie Hypothesis

5.4 A Heuristic Introduction to the Schrödinger Equation

5.5 The Postulates of Quantum Mechanics

5.6 The Steady-State Schrödinger Equation

5.6.1 Single-Particle Analysis

5.6.2 Multiparticle Analysis

5.7 The Particle in a Box

5.8 The Uncertainty Principle

5.9 Indistinguishability and Symmetry

5.10 The Pauli Exclusion Principle

5.11 The Correspondence Principle

6.1 Schrödinger Wave Equation for Two-Particle System

6.1.1 Conversion to Center-of-Mass Coordinates

6.1.2 Separation of External from Internal Modes

6.2 The Internal Motion for a Two-Particle System

6.3 The Rotational Energy Mode for a Diatomic Molecule

6.4 The Vibrational Energy Mode for a Diatomic Molecule

6.5 The Electronic Energy Mode for Atomic Hydrogen

6.6 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 Molecules

6.7 Combined Energy Modes for Atoms and Diatomic Molecules

6.8 Selection Rules for Atoms and Molecules

7.1 Rotational Spectroscopy Using the Rigid-Rotor Model

7.2 Vibrational Spectroscopy Using the Harmonic-Oscillator Model

7.3 Rovibrational Spectroscopy: The Simplex Model

7.4 The Complex Model for Combined Rotation and Vibration

7.5 Rovibrational Spectroscopy: The Complex Model

7.6 Electronic Spectroscopy

7.7 Energy-Mode Parameters for Diatomic Molecules

8.1 Energy and Degeneracy

8.2 Separation of Energy Modes

8.3 The Molecular Internal Energy

8.4 The Partition Function and Thermodynamic Properties

8.5 Energy-Mode Contributions in Classical Mechanics

8.5.1 The Phase Integral

8.5.2 The Equipartition Principle

8.5.3 Mode Contributions

9.1 The monoatomic gas

9.1.1 Translation Mode

9.1.2 Electronic Mode

9.2 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 Mode

9.3 Rigorous and Semirigorous Models for the Diatomic Gas

9.4 The Polyatomic Gas

9.4.1 Rotational Contribution

9.4.2 Vibrational Contribution

9.4.3 Property Calculations for Polyatomic Molecules

10.1 Equilibrium Particle Distribution for the Ideal Gas Mixture

10.2 Thermodynamic Properties of the Ideal Gas Mixture

10.3 The Reacting Ideal Gas Mixture

10.3.1 Equilibrium Particle Distribution for Reactive Ideal Gas Mixture

10.3.2 Equilibrium Constant: Introduction and Development

10.4 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

11.1 Mode Temperatures

11.2 Radiative Transitions

11.2.1 Spectral Transfer of Radiation

11.2.2 The Einstein Coefficients

11.2.3 Line Broadening

11.3 Absorption Spectroscopy

11.4 Emission Spectroscopy

11.4.1 Emissive Diagnostics

11.4.2 The problem of Self-Absorption

11.5 Fluorescence Spectroscopy

11.6 Sodium D-Line Reversal

11.7 Advanced Diagnostic Techniques

Reference book:

Statistical Thermodynamics

Fundamentals and Applications by Laurendeau

Statistical Thermodynamics

Fundamentals and Applications by Laurendeau

Dr. Saptarshi Basu is currently an Associate Professor in the Department of Mechanical Engineering at Indian Institute of Science.Prof. Basu leads large scale initiatives in the area of combustion, multi-phase flow and heat transfer. He is a project leader in the National Center for Combustion Research and Development and SERIIUS (Solar Energy Research Institute for India and the United States).Before joining IISc, Dr. Saptarshi Basu was an Assistant Professor in the Department of Mechanical, Materials and Aerospace Engineering at University of Central Florida from August 2007-May 2010.Dr. Saptarshi Basu received his M.S. and Ph. D. degrees in Mechanical Engineering from University of Connecticut in 2004 and 2007 respectively. His current research interests include combustion instability, flame-vortex interaction, sprays, droplet combustion, colloids, droplet/spray vaporization, acoustic levitation of functional droplets, droplet dynamics in high temperature plasmas, water transport characteristics in fuel cells, thermal storage and general areas of heat transfer.He has expertise in optical diagnostics particularly laser induced fluorescence, particle image velocimetry, tunable diode laser absorption spectroscopy, IR-thermography, rayleigh scattering and laser induced incandescence. He has authored over 180 technical publications in journals and conferences . Prof. Basu is a member of ASME, AIAA, ISHMT and Combustion Institute.Prof. Saptarshi Basu has been awarded the prestigious Swarnajayanti Fellowship in Engineering Sciences, 2013-2014; Department of Science and Technology, Government of India. Prof. Saptarshi Basu has been awarded the K.N Seetharamu Medal and Prize, 2015; Indian Society of Heat and Mass Transfer, [Awarded to 1 researcher in heat and mass transfer biennially all over India]. Prof. Basu is a Fellow of the Indian National Academy of Engineering.

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