Statistical Mechanics

Contents:

Preface  

Chapter 1: Thermodynamics • Introduction • Thermodynamic Equilibrium • Thermodynamic Process • Reversible and Irreversible Processes • Equation of State • First Law of Thermodynamics • Second Law of Thermodynamics • Third Law of Thermodynamics • Entropy and Disorder • Statistical Interpretation of Entropy • Thermodynamic Potential • Maxwell's Thermodynamic Relations • Specific Heats • Method of Jacobians • Thermodynamic and Mechanical Equilibrium • Glimpses • Review Questions • Problems • Short Answer Questions • Multiple Choice Questions

Chapter 2: Fundamentals of Statistical Mechanics • Introduction • Macroscopic and Microscopic States • Phase Space • Density of States in Phase Space • Ensemble • Ensemble Average • Liouville's Theorem • Equation of Motion and Liouville Theorem • Energy Distribution in a Classical Ensemble • Equal a Priori Probability • Ergodic Hypothesis • Statistical Equilibrium • Average Energy of Particle • Equipartition Theorem • Quantum Mechanical Ensemble Theory: Density Matrix • Normalization Condition • Time Derivative • Fluctuations • Glimpses • Review Questions • Problems • Short Answer Questions • Multiple Choice Questions

Chapter 3: Microcanonical Ensemble • Introduction • Microcanonical Distribution • Microcanonical Average • Entropy (S) • Entropy in Statistical Mechanics • Derivation of S = k log W • Entropy of a Perfect Gas in a Microcanonical Ensemble • Gibbs Paradox • Removal of Gibb's Paradox • Thermodynamic Quantities in Microcanonical Ensemble • Sackur?Tetrode Equation • Nerst's Heat Theorem: Third Law of Thermodynamics • Glimpses • Review Questions • Problems • Short Answer Questions • Multiple Choice Questions

Chapter 4: Canonical Ensemble • Introduction • Canonical Distribution • Canonical Average • Canonical Ensemble Partition Function • Importance of the Canonical Ensemble Partition Function • Maxwell Velocity Distribution • Maxwell Absolute Velocity Distribution • Maxwell Energy Distribution • Most Probable Velocity • Mean Kinetic Energy () • Thermodynamic Function • Classical System in a Canonical Ensemble • Ideal Gas • Gibbs Paradox • Resolution of Gibbs Paradox • Microcanonical Versus Canonical Ensembles • Partition Function of Diatomic Gases • Glimpses • Review Questions • Problems • Short Answer Questions • Multiple Choice Questions

Chapter 5: Grand Canonical Ensemble • Introduction • Grand Canonical Distribution • Grand Canonical Average • Grand Canonical Partition Function • Quantum Statistics • Thermodynamic Functions in Grand Canonical Ensemble • Classical System • Ideal Gas in Grand Canonical Ensemble • Density and Energy Fluctuations • Comparison of Various Ensembles • Glimpses • Review Questions • Problems • Short Answer Questions • Multiple Choice Questions

Chapter 6: Three Distribution Laws: Maxwell-Boltzmann (MB), Fermi-Dirac (FD) and Bose-Einstein (BE) • Introduction • Maxwell-Boltzmann (MB) Distribution • Heat Capacity of an Ideal Gas • Maxwell Speed Distribution • Condition for Applicabilities of MB Distribution • Fermi-Dirac (FD) Distribution • Bose-Einstein (BE) Distribution • Comparison between MB, BE and FD Distributions • Glimpses • Review Questions • Problems • Short Answer Questions • Multiple Choice Questions

Chapter 7: Maxwell-Boltzmann System • Introduction • Maxwell-Boltzmann (MB) Distribution • MB Energy Distribution Function (f(E_i)) • MB Energy Distribution Law • Partition Function (Z) • Most Probable Energy (E_p) • Total Number of Particles in the MB Gas • Average Energy (E) of the Particles • MB Velocity Distribution Law • Total Number of Particles for MB Velocity Distribution Law • Most Probable Velocity (V_p) • Average Velocity (<v> or p/v) • Root Mean Square Velocity (v_rms) • Thermodynamical Quantities for the MB Distribution • Maxwell Ideal Gas with Internal Motions • Monoatomic Ideal MB Gas with Internal Motions • Diatomic Ideal MB Gas • Paramagnetic Ideal Gas • Free Electron Gas • Limitations of Classical Statistics • Glimpses • Review Questions • Problems • Short Answer Questions • Multiple Choice Questions

Chapter 8: Fundamentals of Quantum Statistics • Introduction • Quantal Model of Matter and Statistical Operator • Basic Posulates of Quantum Statistical Mechanics • Microcanonical Distribution in Quantum Statistics • Symmetry of Wave Functions • Effect of Symmetry on Counting • Maxwell-Boltzmann (MB) Statistics • Fermi-Dirac (FD) Statistics • Bose-Einstein (BE) Statistics • Comparison of Three Statistics • Density Matrix • Glimpses • Review Questions • Problems • Short Answer Questions • Multiple Choice Questions

Chapter 9: Ideal Fermi-Dirac Gas • Fermi-Dirac (FD) Distribution • Degeneracy • Weakly Degenerate FD Gas • Very Weakly Degenerate Gas • Weakly Degenerate Gas • Fermi-Dirac Velocity Distribution • Strongly or Completely Degenerate FD Gas at T = 0 • Strongly Degenerate Fermi-Dirac Gas at T > 0 • Electrons in Metals • Thermionic Emission and Photoelectric Emission • Spin Paramagnetism • Landau Diamagnetism • Equation of State of High Density • White Dwarf Stars • Neutron Stars • Nuclear Matter • Superconductivity • Glimpses • Review Questions • Problems • Short Answer Questions • Multiple Choice Questions

Chapter 10: Bose-Einstein (BE) Gas • Introduction • Bose-Einstein Energy Distribution • Bose Einstein Gas at Temperature T • Bose-Einstein Gas at High Temperature (T = T_B) • Bose-Einstein Gas at Low Temperature, T < T_B: Degenerate Bose Gas • Black-Body Radiation • Phonons in solids: Debye Model of Solids • Liquid Helium • Two fl uid Model • Landau Theory of Liquid He-II: Spectrum of Phonos and Rotons • Feyman Theory of Liquid He-II • ³He • ⁴He Mixtures • Superfluidity of ³He • Glimpses • Review Questions • Problems • Short Answer Questions • Multiple Choice Questions

Chapter 11: Imperfect (Real) Gases: Interacting Systems • Introduction • Cluster Expansion for a Classical Gas • van der Waals Equation for Real Gases • Explanation of the Discrepancy between Theory and Experiments • Some other Equations of State • Glimpses • Review Questions • Problems • Short Answer Questions • Multiple Choice Questions

Chapter 12: Phase Transition and Critical Phenomena • Introduction • First Order Phase Transitions • Clausius-Clapeyron Equation • Liquid Vapour Phase Transition • Solid-Liquid Phase Transition • Second Order Phase Transition • Landau Theory of Second Order Phase Transition • Critical Exponents • Ising Model • Formulation of Ising Model • One-Dimensional Ising Model • Two-Dimensional Ising Model • Three-dimensional Ising Model • Renormalization • One-Dimensional Ising Chain • Two-Dimensional Ising Chain • Critical Phenomena • Scaling Hypothesis • Glimpses • Review Questions • Problems • Short Answer Questions • Multiple Choice Questions

Chapter 13: Kinetic Physics: Non-Equilibrium States • Introduction • Boltzmann Transport Equation • Boltzmann H-theorem • Maxwell • Boltzmann Distribution • Equilibrium Distribution for a Dilute Gas in an External Force • Validity of Boltzmann Transport Equation • Mean Free Path • Transport Properties of a Gas • Viscosity • Thermal Conductivity • Diffusion • Glimpses • Review Questions • Problems • Short Answer Questions • Multiple Choice Questions

Chapter 14: Dynamical Theory of Gases: Fluctuations • Introduction • Thermodynamic Fluctuations • Brownian Motion • Einstein's Theory of Brownian Motion • Langevin Theory of the Brownian Motion • Wiener-Khintchine Theorem: Power Spectrum of Fluctuations: Fourier Analysis of Fluctuation Nyquist Formula and Fluctuation-Dissipation Theorem • Fokker • Planck Equation • Diffusion • Brownian Motion • Irreversible Transport Phenomena and Onsager Principle • Thermoelectric Phenomena • Peltier Effect • Seebeck Effect • Thomson Effect • Systems Far from Equilibrium • Glimpses • Review Questions • Problems • Short Answer Questions • Multiple Choice Questions

Appendix A: Semiconductor Statistics

Appendix B: Certain Mathematical Functions

Appendix C: Stirling Formula

Appendix D: Lagrange Method

Appendix E: Useful Mathematical Results

Appendix F: Probability

Appendix G: Volume of a Hypersphere

Appendix H: Units and Physical Constants

Bibliography

Index

About the Authors:

Prof. Dr S.L. Kakani, M.Sc. (Phys.), Ph.D., former Executive Director, Institute of Technology and Management, Bhilwara, is an internationally renowned physicist and has had a distinguished career spanning more than four decades of teaching, research and administration. He has authored several standard books. His two research monographs on superconductivity have been published by NOVA Science, New York, and recently four of his books have also been published by Anshan Ltd., UK. He has authored a large number of research papers in the fields of superconductivity, nanomaterials, condensed matter physics, material science, etc. He has supervised Ph.D. theses in the field of superconductivity and thin films.

Prof. Kakani served as the Chairman, BOS and Research Board, MDS University, Ajmer. He is visiting Professor at several prestigious institutions. He has received several national and international awards and honours for his outstanding academic contributions and achievements. He is a life member of IAPT, Vigyan Parishad and High-Tc Update.

Dr C. Hemrajani, Head (Retd.), Physics Department, MLV Government PG College, Bhilwara. A Ph.D. from MDS University, Ajmer, he is the co-author of several UG and PG textbooks. He has put in thirty-six years of service teaching Physics right from UG to PC.