Statistical Mechanics
Teacher
Dr. Nibedita Nayak
Category
Core Courses
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Course Name : Statistical Mechanics
Code(Credit) : CUTM1496(3-2-1)
Course Objectives
- To expose the students to the relationship between macroscopic (bulk) thermodynamic properties of materials and the underlying microscopic (single particle) picture
- To the development of the concept of the Blackbody Radiation and the development of quantum theory of energy/ radiation.
- To expose the students to the temperature dependent (energy-) distribution functions in Classical Mechanical and Quantum Mechanical domains
- To illustrate the application of theoretical concepts of energy and entropy to real systems like pure & doped bulk materials.
Course Outcomes
| COs | Course outcome | Mapping COs with POs (High-3, Medium-2, Low-1) |
| CO1 | Get understanding of the conceptual relationship between bulk picture of Thermodynamics and particle picture of Statistical Mechanics. | PO1-3, PO2-3, PO9-1 |
| CO2 | Understand the basic concepts in the derivations of distribution functions like the Maxwell-Boltzmann Distribution of velocities in Ideal Gas systems, Boltzmann Distribution, Bose-Einstein and Fermi-Dirac Distributions in Quantum Mechanical systems | PO2-3, PO9-1 |
| CO3 | Computation of various statistical properties of various classical systems like Noble Gases, Real Gases, Bulk Materials and quantum systems like photon gas, electron gas etc. | PO4-1, PO5-2, PO9-1 |
Course Syllabus
Module I
Classical Statistics-1: Macrostate & microstate, Elementary concept of ensemble, Phase space, Entropy and thermodynamic probability, Maxwell-Boltzmann distribution law, Partition function, Thermodynamic functions of an ideal gas.
Practice-1
Plot Maxwell-Boltzmann distribution functions with energy at different temperatures. (Using Scilab / Python)
Practice-2
Under Maxwell-Boltzmann Statistics compute Most Probable Speed, Mean Speed and RMS Speed and compare their ratios with theoretical values; (Using Scilab / Python).
Module II
Classical Statistics-2: Classical entropy expression, Gibbs paradox, Sackur Tetrode equation, Law of equipartition of energy (with proof) – applications to specific heat and its limitations.
Practice-3
Plot specific heat of solids according to Dulong-Petit law for high temperature and low temperature and compare them for these two cases.
Practice-4
Plot specific heat of solids according to Einstein distribution function for high temperature and low temperature and compare
Practice-5
Plot specific heat of solids according to Debye distribution function for high temperature and low temperature and compare them for these two cases.
Module III
Classical Theory of Radiation-1: Properties of thermal radiation, Black body radiation, Pure temperature dependence, Kirchhoff’s law, Stefan-Boltzmann law: thermodynamic proof.
Module IV
Classical Theory of Radiation-2: Radiation pressure, Wien’s displacement law, Wien’s distribution law, Saha’s ionisation formula, Rayleigh-Jean’s law, Ultraviolet catastrophe.
Practice-6
Plot Wien’s distribution Law
Practice-7
Plot Rayleigh-Jeans Law
Module V
Quantum Theory of Radiation: Spectral distribution of black body radiation, Planck’s quantum postulates, Planck’s law of black body radiation: experimental verification, Deduction of (1) Wien’s distribution law, (2) Rayleigh-Jeans law, (3) Stefan-Boltzmann law, (4) Wien’s displacement law from Planck’s law.
Practice-8
Plot Planck’s law for black body radiation and compare it with Raleigh-Jeans law at high temperature and low temperature
Module VI
Bose-Einstein Statistics: B-E distribution law, Thermodynamic functions of a strongly degenerate Bose gas, Bose Einstein condensation, properties of liquid He (qualitative description), Radiation as a photon gas and thermodynamic functions of photon gas.
Practice-9
Implications of Planck's Blackbody Radiation formula: Wien's Displacement Law & Stefan-Boltzmann law: Numerical Simulation; (Using Scilab / Python).
Practice-10
Plot Bose-Einstein distribution and Maxwell-Boltzmann Distribution functions with energy at different temperatures. (Using Scilab / Python)
Module VII
Fermi-Dirac Statistics: Fermi-Dirac distribution law, Thermodynamic functions of a completely and strongly degenerate fermi gas, Fermi energy, Electron gas in a metal.
Practice-11
To Plot Fermi-Dirac Distribution and compare with Bose-Einstein distribution and Maxwell-Boltzmann Distribution functions with energy at different temperatures. (Using Scilab / Python)
Text Book:
Statistical Mechanics by R.K. Pathria, Butterworth Heinemann: 2nd Ed., 1996, Oxford University Press.
Reference Books:
- Statistical Physics, Berkeley Physics Course, F. Reif, 2008, Tata McGraw-Hill
- Statistical and Thermal Physics, S. Lokanathan and R.S. Gambhir. 1991, Prentice Hall
- Thermodynamics, Kinetic Theory and Statistical Thermodynamics, Francis W. Sears and Gerhard L. Salinger, 1986, Narosa.
- Modern Thermodynamics with Statistical Mechanics, Carl S. Helrich, 2009, Springer
- An Introduction to Statistical Mechanics & Thermodynamics, R.H. Swendsen, 2012, Oxford Univ. Press
Session 3
Phase space, Entropy and thermodynamic probability.
Session 7
Practice-1 (2 hours)
Plot Maxwell-Boltzmann Distribution function vs. speed at different temperatures. (Using Scilab or Python)
Session 8
Practice-2 (2 hours)
Under Maxwell-Boltzmann Statistics compute Most Probable Speed, Mean Speed and RMS Speed and compare their ratios with theoretical values; (Using Scilab / Python).
Session 12
Law of equipartition of energy (with proof) .
Session 13
Applications of equipartition of energy to specific heat and its Limitations .
Session 14
Flip class-1
Application of law of equipartition energy in specific heat of a gas. Meyer's relation.
Session 15
Practice-3 (2 hours)
Plot specific heat of solids according to Dulong-Petit law for high temperature and low temperature and compare them for these two cases. (Using Scilab / Python)
Session 16
Practice-4 (2 hours)
Plot specific heat of solids according to Einstein distribution function for high temperature and low temperature and compare. (Using Scilab / Python)
Session 17
Practice-5 (2 hours)
Plot specific heat of solids according to Debye distribution function for high temperature and low temperature and compare them for these two cases. (Using Scilab / Python)
Session 19
Black body radiation. Pure temperature dependence
Session 20
Group Quiz-1
Properties of Thermal Radiation, Blackbody radiation, Pure Temperature Dependence of Blackbody Radiation
Session 23
Flip class-2
Stefan Boltzmann law practical application .
Session 24
Radiation pressure, Effects of solar radiation pressure on satellite orbits
Session 25
Wien’s displacement law, Wien’s distribution law
Session 26
Group Quiz-2
Radiation Pressure, Effects of Radiation Pressure, Wien Distribution Law, Wien's Displacement Law
Wien’s displacement law, Wien’s distribution law
Session 27
Session 28
Saha Ionization Formula-2
Session 29
Flip class -3
Rayleigh - Jeans Law and Ultraviolet Catastrophe
Session 30
Practice-6 (2 hours)
Plot Wien’s distribution law. (Using Scilab / Python)
Session 31
Practice-7 (2 hours)
Plot Rayleigh-Jeans law. (Using Scilab / Python).
Session 32
Planck's Quantum Postulates, Derivation of Planck's Law of Blackbody Radiation
Session 33
Planck's Blackbody Radiation Law - Experimental Verification, Spectral Distribution of Blackbody Radiation
Session 34
Practice-8
Plot Planck’s law for Black Body radiation and compare it with Raleigh-Jeans Law at high temperature and low temperature. (Using Scilab / Python).
Session 35
Deduction of Wien’s distribution law from Planck’s law.
Session 36
Deduction of Rayleigh-Jeans Law from Planck’s law
Session 37
Flip class-4
Deduction of Stefan-Boltzmann law and Wien’s Displacement law from Planck’s law.
Session 38
Practice-9 (2 hours)
Implications of Planck's Blackbody Radiation formula: Wien's Displacement Law & Stefan-Boltzmann law: Numerical Simulation; (Using Scilab / Python).
Session 39
Bose-Einstein Distribution Law - I (Derivation)
Session 40
Bose-Einstein Distribution Law - II
.
Session 41
Thermodynamic functions of a strongly degenerate Bose gas - I (Derivation)
Session 42
Thermodynamic functions of a strongly degenerate Bose gas - II (Derivation to be continued)
Session 43
Flip class-5 (2 hours)
Bose-Einstein Condensation, Properties of Liquid helium
Session 44
Practice-10 (2 hours)
Plot Bose-Einstein distribution and Maxwell-Boltzmann Distribution functions with energy at different temperatures. (Using Scilab / Python)
Session 45
Group Quiz -3
Bose- Einstein Statistics, Its Implications and Applications
Session 46
Fermi-Dirac Distribution Law - I (Derivation)
Session 47
Fermi-Dirac Distribution Law - II (Derivation to be continued)
Session 48
Thermodynamic functions of a completely and strongly Degenerate Fermi Gas - I (Derivation)
Session 49
Thermodynamic functions of a completely and strongly Degenerate Fermi Gas - II (Derivation to be continued), Definition of Fermi Energy, Fermi Momentum etc.
Session 50
Flip class-6 (2 hours)
Electron gas in a metal, Application of Fermi-Dirac distribution to semiconductors, difference between Maxwell Boltzman , Bose Einstein and Fermi Dirac statistics and their uses.
Session 51
Practice-11 (2 hours)
To Plot Fermi-Dirac Distribution and compare with Bose-Einstein distribution and Maxwell-Boltzmann Distribution functions with energy at different temperatures. (Using Scilab / Python)
Session 52
Group Quiz-4
Fermi-Dirac Statistics, Its Implications and Applications
Our Main Teachers
Dr. Nibedita Nayak is working as an Assistant Professor in the Department of Physics, School of Applied Sciences, Bhubaneswar Campus of Centurion University of Technology and Management, Odisha. She completed her Ph.D from Berhampur University in 2018. She is working on computational tools and new material development. She has more than six years of […]
Dr. Subrata Sarangi has a Masters’ Degree in Physics from IIT, Kanpur and a Ph.D in Nuclear Structure Theory from Physical Research Laboratory, Ahmedabad. He has 25 years’ experience in teaching at UG, PG and PhD levels. He has published over 20 peer reviewed research articles in areas of Atomic Nuclei, Nuclear Matter, Materials Sciences […]