PHYS5130 Principles of Thermal and Statistical Physics (a course for M.Sc. students)
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PHYS5130 Principles of Thermal and Statistical Physics (a course for M.Sc. students)
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Class Notes [Front Matter]
  • Front Matter [Course coverage, Assessment Scheme, Academic Honesty Policy, etc.]


    • Class Notes [Essential Math Skills]
  • Essential Math Skills I - Partial Differentiation (6 Sept 2020)
  • Essential Math Skills II - The Sterling's Formula for ln N!
  • Essential Math Skills III - Number of Microstates of two subsystems multiply and the Math of 3T (Triple Trio)
  • Essential Math Skills IV - Some Gaussian Integrals
  • Essential Math Skills V - Method of Lagrange Multipliers for Constrained Optimization
  • Essential Math Skills VI - The Gamma Function and Deriving the Stirling Formula


    • Class Notes [Principles of Thermodynamics]
  • Ch. I - The Zeroth Law and Related Ideas
  • Ch. II - The First Law of Thermodynamics [revised and complete]
  • Ch. III - Results of Classical Ideal Gases
  • Ch. IV - The Second Law of Thermodynamics [complete]
  • Ch. V - Entropy (complete)
  • Ch. VI - Thermodynamic Potentials (U, H, F, G) and Maxwell Relations [complete]
  • Ch. VII Part 1 - Selected Topics (Difference in heat capacities, Joule coefficient, Euler's equation, Gibbs-Duhem equation)
  • Ch. VII Part 2 - Selected Topics (Thermodynamics of Phase Transitions and 3rd Law) (revised)
  • Further Reading on Thermodynamics (List of books)


    • Class Notes [Principles of Statistical Mechanics]
  • List of Books on Statistical Mechanics and Statistical Physics
  • Ch. VIII Part 1 - Boltzmann's Formula S = k ln W, macrostate and microstates, all accessible microstates are equally probable, phase space, time average and ensemble average, microcanonical ensemble theory (revised)
  • Ch. XIII Part 2 - Boltzmann Formula makes sense and making sense of Boltzmann Formula, Gibbs Entropy Formula, Formalism for find the Most Probable Distribution
  • Ch. VIII Part 3 - Two systems in Thermal Contact - Equilibrium Conditions and Bridging over to Canonical Ensemble
  • Microcanonical Ensemble - Application A - Heat capacity of solids at low temperatures (Einstein's model) [revised]
  • Microcanonical Ensemble - Application B - Number of Defects thermally generated in Solids
  • Microcanonical Ensemble - Application C - Classical Ideal Gas
  • Ch. IX Part 1 - System in Equilibrium with a Heat Bath and the Partition Function Z(T,V,N)
  • Ch. IX Application A - Two-level Particles and Paramagnetism
  • Ch. IX Application B - Heat Capacity of Solids and the Debye Model
  • Ch. IX Part 2 (partial) - Does it work? Fluctuations, Canonical Ensemble
  • Ch. IX Application C - Classical Gases and Classical Ideal Gas
  • Ch. IX Application D - Maxwell Distribution of Molecular Speeds in a Gas and Gaussian Integrals
  • Ch. IX Application E - The Equipartition Theorem and Heat Capacity of Diatomic Gases


    • Class Notes [Physics of Ideal Fermi Gas and Ideal Bose Gas]
  • Ch. X Part 1 - Non-interacting Particles: Fermi-Dirac and Bose-Einstein Distributions (revised)
  • Ch. X Part 2 - Density of Single-Particle States and Governing Equations for Ideal Quantum Gases
  • Ch. XI Part 1 - Ideal Fermi Gas in 3D - Zero-Temperature Physics is the dominating physics
  • Ch.XI Part 2 - Ideal Fermi Gas in 3D - Low temperature physics
  • Ch.XI Appendices A and B - Detailed calculations of chemical potential and total energy at low temperatures
  • Ch. XI Part 3 - Ideal Fermi Gas in 3D - High temperature behavior plus References
  • Ch. XII Part 1 - Ideal Bose Gas in 3D - Low-temperature Physics and Bose-Einstein Condensation (revised)
  • Ch.XII Part 2 - Cold Atom Gases and Experimental Observation of Bose-Einstein Condensation
  • Ch. XII Part 3 - Ideal Bose Gas in 3D - High-temperature behavior plus References


    • Class Notes [Physics of Ideal Fermi Gas and Ideal Bose Gas]


    Class Notes [Statistical Physics in Interacting Systems]
  • Ch. XIII Part 1 - Weakly Interacting Classical Gas and the Second Virial Coefficient
  • Ch. XIII Part 2 - Weakly Interacting Classical Gas - Van der Waals Equation and Behavior near the Critical Point
  • Ch.XIV Part 1 - Ferromagnetism - Ising Model and Critical Behavior from Simplest Mean-field Theory
  • Ch.XIV Part 2 - From Ising Model to Landau Theory of Continuous Transitions


    • Class Notes [Phase Transitions and Other Topics]


    Class Notes [Back Matter]


    Additional Learning Materials


    Problem Sets (Students should submit homework to Blackboard system)
  • Problem Set 1 (due 19 Sept 2020, T+2 = 21 Sept 2020)
  • Problem Set 2 (due 3 Oct 2020, T+2 = 5 Oct 2020)
  • Problem Set 3 revised (due 17 Oct 2020, T+2 = 19 Oct 2020)
  • Problem Set 4 (due 31 Oct 2020, T+2 = 2 Nov 2020)
  • Problem Set 5 (due 9 Nov 2020, T+2 = 11 Nov 2020)
  • Problem Set 6 (due 23 Nov 2020, T+2 = 25 Nov 2020)
  • Problem Set 7 (due 9 Dec 2020, T+2 = 11 Dec 2020)


    • Solutions to Problem Sets
  • Problem Set 1 Solution
  • Problem Set 2 Solution
  • Problem Set 3 Solution
  • Problem Set 4 Solution (Revised)
  • Problem Set 5 Solution
  • Problem Set 6 Solution (Typo Corrected)
  • Problem Set 7 Solution


    • Other Learning Materials, Further Reading, and Announcements


    Erratum (Corrected typos on pages of class notes)