Fundamentals Of Statistical Thermodynamics

By Prof. Nand Kishore | IIT Bombay

Learners enrolled: 397 | Exam registration: 14

ABOUT THE COURSE:

Statistical thermodynamics will establish a link between bulk properties based on classical thermodynamics (which students are presumed to have learnt) with microscopic properties of individual molecules. All the essential thermodynamic quantities and laws will be expressed in terms of relevant partition functions. The knowledge thus gained from the contents of this course will enable students to understand that thermodynamic quantities can also be obtained from spectroscopic measurements.

INTENDED AUDIENCE: BS (Chemistry); M Sc (Chemistry)

PREREQUISITES: Previous knowledge of Chemical Thermodynamics is preferred

INDUSTRY SUPPORT: Chemical and Pharmaceutical Industries

Summary

Course Status :	Completed
Course Type :	Core
Language for course content :	English
Duration :	12 weeks
Category :	Chemistry Minor 3 in Chemical
Credit Points :	3
Level :	Undergraduate/Postgraduate
Start Date :	24 Jul 2023
End Date :	13 Oct 2023
Enrollment Ends :	07 Aug 2023
Exam Registration Ends :	18 Aug 2023
Exam Date :	28 Oct 2023 IST

Note: This exam date is subject to change based on seat availability. You can check final exam date on your hall ticket.

Page Visits

Course layout

Weeks 1 and 2 :

A recap of concepts of chemical thermodynamics and need to study statistical thermodynamics.
Introducing the concepts of statistical thermodynamics, configurations and weights, Boltzmann distribution.
Introducing the molecular partition function, discussion on various terms therein, interpretation of partition function and discussion on its applications.
Connecting partition function with population of molecules in energy states and deriving expression for translational partition function for a molecule free to move in one dimension: discussion on physical meaning of all the terms in translational partition function.
Deriving partition function for translational motion of particle in 2 and 3-dimensions; applications; tutorial problems based on population of states and partition function.

Weeks 3 and 4 :

Internal energy in terms of molecular partition function; establishing relationship between β and temperature; associated numerical problems/applications
Discussion on statistical entropy and derivation of Boltzmann formula S = klnW
Relationship of entropy with partition function and its applications
Introducing concepts of ensembles (microcanonical, canonical and grand canonical): dominating configurations, canonical distribution and discussion on canonical partition function
Obtaining thermodynamic information in partition function: internal energy and entropy

Weeks 5 and 6 :

Further discussion on entropy; Recovering molecular partition function from canonical partition function: establishing relationship between them for distinguishable and indistinguishable molecules and corresponding numerical problems/applications
Discussion on partition function for a monoatomic perfect gas, derivation of Sackur-Tetrode equation and discussion on concept/terms involved therein
Numerical problems based on Sackur-Tetrode equation and comparison of the result with those based on concept of classical thermodynamics
Thermodynamic functions in terms of canonical partition function: Heltmotz energy, pressure; associated numerical problems/applications
Enthalpy in terms of canonical partition function; associated applications and obtaining ideal gas equation from the use of the canonical partition function

Weeks 7 and 8 :

Gibbs energy in terms of canonical partition function and associated applications/problems
Rotational contribution (for linear and non-linear rotor) to partition function and associated numerical problems/applications
Vibrational and electronic contributions to partition function; Overview of different contributions to overall partition function, associated numerical problems/applications
Overview of different contributions to overall partition function, associated numerical problems/applications continued
Mean energies (translational, rotational and vibrational) in terms of partition function and associated numerical problems/applications

Weeks 9 and 10 :

Heat capacities in terms of translational, rotational, vibrational contributions and effect of dissociation (with numerical problems/applications)
Residual entropy (discussion in terms of statistical and chemical thermodynamics with suitable examples)
Deriving equilibrium constant in terms of partition function and associated numerical problems/applications
Introduction to gas imperfection; Equations of state; Introduction to virial coefficients
Configuration integral; Mayer f-function; hard sphere potential; Virial Coefficients

Weeks 11 and 12 :

Derivation of equations of state with examples
Radial Distribution Functions and their applications in selected systems
Interpretation of thermodynamic quantities by Lattice Models
Fermi-Dirac and Bose-Einstein statistics
Overall summary on different topics covered in statistical thermodynamics and future perspectives

Books and references

1. Physical Chemistry by P. Atkins and J de Paula

2. Molecular Thermodynamics by D. A. McQuarrie and J. D. Simon

3. Molecular Driving Forces: Statistical Thermodynamics in Chemistry and Biology by K. A. Dill and S. Bromberg.

Instructor bio

Prof. Nand Kishore

IIT Bombay

Prof. Nand Kishore is currently Professor at the Department of Chemistry, Indian Institute of Technology Bombay, Mumbai. He was head of the Department from December 2008 to December 2011. After completing his PhD (Chemistry) from Indian Institute of Technology Delhi in 1989, he received postdoctoral training at Yale University, U.S.A. (1989-1991) and at the National Institute of Standards and Technology, U.S.A. (1991-1992). He joined as faculty at IIT Bombay in 1992. He has been Guest Research Scientist several times at the National Institute of Standards and Technology, U.S.A. afterwards. His research interests include understanding physical chemistry underlying the biologically important systems. His research group has contributed to the thermodynamic characterization of protein folding intermediates, drug-protein interactions, protein-solvent interactions, prevention of aggregation/fibrillation of proteins and drug delivery systems by using a combination of calorimetric and spectroscopic techniques. He has published about 145 papers in international journals of repute in the areas of Physical Chemistry, Biophysical Chemistry and Biochemistry. He is also the Editor of the Journal of Chemical Thermodynamics published by Elsevier. He has delivered several plenary and invited lectures in national and international conferences. He is Fellow of the National Academy of Sciences, India. He was President of the Indian Chemical society, Mumbai Branch from 2010 to 2012. He has received The Rev. Fr. L. M. Yedanapally Memorial Award for the Year 2011 for contribution to research in Physical chemistry by Indian Chemical Society.

Course certificate

The course is free to enroll and learn from. But if you want a certificate, you have to register and write the proctored exam conducted by us in person at any of the designated exam centres.

The exam is optional for a fee of Rs 1000/- (Rupees one thousand only).

Date and Time of Exams: 28 October 2023 Morning session 9am to 12 noon; Afternoon Session 2pm to 5pm.

Registration url: Announcements will be made when the registration form is open for registrations.

The online registration form has to be filled and the certification exam fee needs to be paid. More details will be made available when the exam registration form is published. If there are any changes, it will be mentioned then.

Please check the form for more details on the cities where the exams will be held, the conditions you agree to when you fill the form etc.

CRITERIA TO GET A CERTIFICATE

Average assignment score = 25% of average of best 8 assignments out of the total 12 assignments given in the course.
Exam score = 75% of the proctored certification exam score out of 100

Final score = Average assignment score + Exam score

YOU WILL BE ELIGIBLE FOR A CERTIFICATE ONLY IF AVERAGE ASSIGNMENT SCORE >=10/25 AND EXAM SCORE >= 30/75. If one of the 2 criteria is not met, you will not get the certificate even if the Final score >= 40/100.

Certificate will have your name, photograph and the score in the final exam with the breakup.It will have the logos of NPTEL and IIT Bombay .It will be e-verifiable at nptel.ac.in/noc.

Only the e-certificate will be made available. Hard copies will not be dispatched.

Once again, thanks for your interest in our online courses and certification. Happy learning.

- NPTEL team

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