# Basic Statistical Mechanics

By Prof. Biman Bagchi   |   IIT Bombay
Learners enrolled: 1274
In order to understand natural phenomena like phase transitions or nucleation or many biological reactions like protein folding, enzyme kinetics, we need to understand how many particles interact and behave together in certain specified manner. For example, ice melts at 00 C and water boils at 1000 C, at low temperature the rain drops form in the upper atmosphere. Enzyme beta-galactosidase allows the breaking of the C-O bond that leads to the digestion of lactose .These are complex processes which involve many particles to behave in a collective fashion. This could happen because of the interaction among particles. However, these cannot be solved by Newton’s equations, because we cannot solve Newton’s equations even for three particles interacting system. So the forefathers of this field, Maxwell, Boltzmann and Gibbs introduced probabilistic approach and combined it with mechanics to form the ‘Statistical Mechanics.’ This a branch of theoretical science that parallels Quantum Mechanics and these two together form the main tools at our disposal to understand why things happen and how they happen. The present course will address the basic postulates of Statistical Mechanics and then will show how starting from the basic postulates one builds a formidable framework which can be used to explain phenomena mentioned above.

INTENDED AUDIENCE
Chemistry, Physics, Material Science, Chemical Engineering
PREREQUISITES Thermodynamics, Basic Algebra and Calculus
INDUSTRIES  SUPPORT     : Pharmaceutical and fuel cell companies will recognize this course very useful.
Summary
 Course Status : Completed Course Type : Elective Duration : 12 weeks Category : Chemistry Credit Points : 3 Level : Undergraduate/Postgraduate Start Date : 14 Sep 2020 End Date : 04 Dec 2020 Enrollment Ends : 25 Sep 2020 Exam Date : 20 Dec 2020 IST

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

### Course layout

Week 1: Preliminaries: Objectives of Statistical Mechanics (SM), probability and statistics
Week 2: Probability and Statistics, Fundamental concepts of SM
Week 3:  Phase Space and Trajectories, postulates
Week 4: Postulates of Statistical Mechanics, Microcanonical ensemble
Week 5: Microcanonical Ensemble, Canonical Ensembles
Week 6: Canonical Ensemble, Grand Canonical Ensemble, isothermal-isobaric ensemble
Week 7:  Fluctuation and Response Functions, ideal monatomic gas
Week 8: Ideal Monatomic Gas: Microscopic Expression of Translational Entropy, ideal gas of diatomic molecules
Week 9: Ideal Gas of Diatomic molecules: Microscopic Expression of Rotational and Vibrational Entropy and Specific Heat
Week 10:Non-ideal gas, Cluster Expansion and Mayer’s Theory
Week 11: Mayer’s Theory for Interacting Systems: Phase Transition
Week 12:Landau Theory of Phase Transitions: Order Parameter Expansion and Free Energy Diagrams, Nucleation
.

### Books and references

1. B. Bagchi, Statistical Mechanics for Chemistry and Materials Science (Francis-Taylor, CRC Press, 2018).
2. D. A. McQuarrie, Statistical Mecanics (Harper and Row Publishers, 1976).
3. D. Chandler, Introduction to Modern Statistical Mechanics (Oxford University Press, 1987).
4. B. Bagchi, Molecular Relaxation in Liquids (Oxford University Press, 2012).

### Prof. Biman Bagchi

IIT Bombay
Prof. Biman Bagchi is internationally known in the area of physical and biophysical chemist, particularly in the study of phase transition and nucleation, solvation dynamics, mode-coupling theory of electrolyte transport, dynamics of biological macromolecules, protein folding, enzyme kinetics, supercooled liquids and protein hydration layer. He has been working on these areas for more than 35 years, and received a large number of awards. He has published around 470 papers in reputed journals with h-index 73 and has authored 22 major review articles. Besides several scientific articles, he has authored three books: (i) Molecular Relaxation in Liquids, (ii) Water in Biological and Chemical Processes: From Structure and Dynamics to Function and (iii) Statistical Mechanics for Chemistry and Materials Science

### 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: 20 December 2020, 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.