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 relate the microscopic properties of individual atoms and molecules to the macroscopic or bulk properties of materials.
  • To explore the different types of distribution functions in order to explain the behaviour of the particles.
  • To study of quantum theory of radiation and explain black body radiations with help of the various theories and models.
  • To explain the thermodynamic behaviour of the atoms and molecules

Learning Outcomes

Upon successful completion of this course, students will be able to:

  • understand the basic properties of thermodynamics and statistical mechanics.
  • understand the black-body radiation and distribution functions.
  • distinguish between classical and quantum radiation

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

Computation of the partition function Z(β) of systems with a finite number of single particle levels (e.g., 2 level, 3 level, etc.) and a finite number of non-interacting particles N under Maxwell-Boltzmann statistics :  Study of how Z(β), average energy <E>, energy fluctuation ΔE and specific heat at constant volume Cv depend upon the temperature and total number of particles N

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

Plot Bose-Einstein distribution functions with energy at different temperatures 

Practice-10

Computation of the partition function Z(β) of systems with a finite number of single particle levels (e.g., 2 level, 3 level, etc.) and a finite number of non-interacting particles N under Bose-Einstein statistics :  Study of how Z(β), average energy <E>, energy fluctuation ΔE and specific heat at constant volume Cv depend upon the temperature and total number of particles N

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

Plot Fermi-Dirac distribution functions with energy at different temperatures 

Practice-12

Computation of the partition function Z(β) of systems with a finite number of single particle levels (e.g., 2 level, 3 level, etc.) and a finite number of non-interacting particles N under Fermi-Dirac statistics :  Study of how Z(β), average energy <E>, energy fluctuation ΔE and specific heat at constant volume Cv depend upon the temperature and total number of particles N .

Text Book:

Statistical Mechanics by R.K. Pathria, Butterworth Heinemann: 2nd Ed., 1996, Oxford University Press. 

e-book

Reference Books:

  1. Statistical Physics, Berkeley Physics Course, F. Reif, 2008, Tata McGraw-Hill
  2. Statistical and Thermal Physics, S. Lokanathan and R.S. Gambhir. 1991, Prentice Hall
  3. Thermodynamics, Kinetic Theory and Statistical Thermodynamics, Francis W. Sears and Gerhard L. Salinger, 1986, Narosa.
  4. Modern Thermodynamics with Statistical Mechanics, Carl S. Helrich, 2009, Springer
  5. An Introduction to Statistical Mechanics & Thermodynamics, R.H. Swendsen, 2012, Oxford Univ. Press

Session 3

Phase space, Entropy and thermodynamic probability.

https://www.youtube.com/watch?v=YM-uykVfq_E&t=14s

Session 5

Session 6

Flip class-1

Thermodynamic functions of an ideal gas

https://www.youtube.com/watch?v=G-L81TfsqKI

Session 7

Practice-1 (2 hours)

Plot Maxwell-Boltzmann distribution functions with energy at different temperatures. (Using Scilab or Python)

.

Session 8

Practice-2 (2 hours)

Under Maxwell-Boltzmann statistics, study of how Z(β), average energy <E>, energy fluctuation ΔE and specific heat at constant volume Cv depend upon the temperature and total number of particles N (Using Scilab / Python).

Session 9

Classical entropy expression

https://www.youtube.com/watch?v=t4zxgJSrnVw

Session 12

Session 13

Applications of equipartition of energy to specific heat and its Limitations .

https://www.youtube.com/watch?v=1u207DoAdzE

Session 14

Flip class-2

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 18

Properties of thermal radiation

https://www.youtube.com/watch?v=5GoZZKcNZiQ

Session 19

Black body radiation. Pure temperature dependence

https://www.youtube.com/watch?v=_0tkbp8yk-w

Session 20

Flip class-3

Applications of black body radiation.

https://www.youtube.com/watch?v=3eOBT6XdBmg

Session 21

Session 22

Stefan-Boltzmann law-Thermodynamic proof.

https://www.youtube.com/watch?v=sUp_WZKZID4

Session 23

Flip class-4

Stefan Boltzmann law practical application .

https://www.youtube.com/watch?v=LidveOARCec

Session 24

Session 25

Flip class-5

Effects of solar radiation pressure on satellite orbits

https://www.youtube.com/watch?v=AVO42b7QLNM

Session 26

Wien’s displacement law, Wien’s distribution law

https://www.youtube.com/watch?v=4piwVbihZz4

Session 28

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

Session 33

Planck’s quantum postulates..

https://www.youtube.com/watch?v=0_YdVo3BS5w

Session 34

Flip class -7

Planck’s Law of black body radiation-experimental verification.

https://www.youtube.com/watch?v=VMAmh_dtef0

Session 35

Deduction of Wien’s distribution law from Planck’s law.

https://www.youtube.com/watch?v=d-CmdePjdKQ

Session 36

Deduction of Rayleigh-Jeans Law from Planck’s law

https://www.youtube.com/watch?v=WL1GrzXhbwA

Session 37

Flip class-8

Deduction of  Stefan-Boltzmann law and Wien’s Displacement law from Planck’s law.

https://www.youtube.com/watch?v=sUp_WZKZID4&t=37s

Session 38

Practice-8 (2 hours)

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 39

Bose-Einstein distribution law.

https://www.youtube.com/watch?v=iLU6NvVgZc4

Session 40

Thermodynamic functions of a strongly degenerate Bose gas.

.

Session 43

Flip class-9 (2 hours)

Radiation as a photon gas, Thermodynamic functions of photon gas.

https://www.youtube.com/watch?v=GPspau1DeRA

ttps://www.youtube.com/watch?v=YSgk78ToKrs

Session 44

Practice-9 (2 hours)

Plot Bose-Einstein distribution functions with energy at different temperatures. (Using Scilab / Python)

.

Session 45

Practice-10 (2 hours)

Under Bose-Einstein statistics :  Study of how Z(β), average energy <E>, energy fluctuation ΔE, specific heat at constant volume Cv, depend upon the temperature and total number of particles N. (Using Scilab / Python).

Session 46

Fermi-Dirac Distribution Law.

https://www.youtube.com/watch?v=VVeNM4SoRcs

Session 47

Thermodynamic functions of a completely and strongly Degenerate Fermi Gas

https://www.youtube.com/watch?v=OMRsmNpgZQ0

Session 49

Session 50

Flip class-10 (2 hours)

Application of Fermi-Dirac distribution to semiconductors, difference between Maxwell Boltzman , Bose Einstein and Fermi Dirac statistics and their uses

https://www.youtube.com/watch?v=jKQCRf3EZRc

https://ecee.colorado.edu/~bart/book/book/chapter2/ch2_5.htm#top

Session 51

Practice-11 (2 hours)

Plot Fermi-Dirac distribution functions with energy at different temperatures. (Using Scilab / Python)

.

Session 52

Practice-12 (2 hours)

Under Fermi-Dirac statistics :  Study of how Z(β), average energy <E>, energy fluctuation ΔE and specific heat at constant volume Cv depend upon the temperature and total number of particles N. (Using Scilab / Python).

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 […]