615.651.81 - Statistical Mechanics and Thermodynamics

Expanded Course Description

Prerequisites

Some knowledge of classical mechanics and quantum mechanics will be very helpful in the statistical mechanics portion of the course.

Course Structure

The course materials are divided into 14 modules which can be accessed by clicking Course Modules on the left menu. A module will have several sections including the module-at-a-glance, readings, video lectures and related content, discussions, and quizzes. Students should regularly check the Calendar and Announcements for assignment due dates. Modules begin on Wednesdays and complete on Tuesdays.

Course Topics

• Fundamentals of Classical Thermodynamics
• Applications to Simple Systems
• Applications to Multi-Component Systems
• Fundamental Postulates of Statistical Mechanics and Derivation of the Laws of Thermodynamics
• Phase Space and Concept of an Ensemble
• Microcanonical Ensemble and its Applications
• Canonical Ensemble
• Applications of Canonical Ensemble I: Specific Heat Solids at Low Temperature
• Applications of Canonical Ensemble II: Magnetic Systems, High Temperature Limit, and Thermal Ionization of an Ideal Gas
• Grand Canonical Ensemble and its Application to Quantum Statistics
• Applications of Bose-Einstein Statistics
• Thermodynamics of an Ideal Fermi Gas with Application to Electron Theory of Metals and White Dwarf Stars

Course Goals

The broad objective of the course is to provide the student with detailed understanding of the way in which statistical mechanics not only provides a clear derivation of the empirical laws of thermodynamics but also a framework for explicit computation of many thermal properties of bulk matter from microscopic models. By the end of the course the student should be able to apply thermodynamic principle to simple systems and calculate and analyze various thermodynamic properties of specific idealized classical and quantum systems using standard techniques such as the partition function.

Course Learning Outcomes (CLOs)

• Explain the physical concepts and the laws of classical thermodynamics and derive relations connecting various thermodynamic properties of a single- component system.
• Apply thermodynamic relations to compute thermal properties of specific single component systems.
• Apply thermodynamic concepts to explain physical behavior of multi-component and multi-phase systems.
• Explain the postulates of statistical mechanics and derive the formal structure of thermodynamics from them.
• Explain and develop the ensemble theory for a Hamiltonian dynamical system.
• Apply the microcanonical ensemble to derive the complete thermodynamics of an ideal gas and a system of harmonic oscillators.
• Derive the complete formal structure of thermodynamics from the canonical ensemble.
• Employ the partition function to compute thermodynamic properties of specific systems in thermal equilibrium with a heat reservoir.
• Describe the thermodynamics of an equilibrium system exchanging both particles and energy with a reservoir in terms of the grand partition function.
• Apply the general theory of grand canonical ensemble and the grand partition function to derive the thermodynamics of a system of non-interacting indistinguishable particles obeying Bose-Einstein, Fermi-Dirac and classical Maxwell-Boltzmann statistics.
• Apply quantum statistical mechanics to derive thermodynamic properties of non- interacting quantum systems including ideal quantum gases and black body radiation.
• Apply thermodynamics of quantum systems to explain a variety of exotic phenomena involving ideal quantum gases.

Textbooks

There is a not a required textbook. Each week you will have a required reading from the lecture notes for this course. This is a PDF that has a section for each module/week. 

Other Materials & Online Resources

In addition, optional readings are listed from the following textbooks:

• Fermi, E., Thermodynamics, Dover Publications, New York, 1956.
• Pippard, A.B., The Elements of Classical Thermodynamics, Cambridge University Press, Cambridge, U.K., 1961.
• Zemansky, M.W., Heat and Thermodynamics, McGraw Hill, 1968.
• Pathria, R.K., and Beale, P.D., Statistical Mechanics, 3rd edition, Butterworth- Heinemann, 2011. ISBN: 978-0-12-382188.

Readings from the above textbooks are available as EReserves, linked as epublications directly from the course site.

Required Software

Webcam, microphone (if provided with computer, this is usually adequate along with adequate lighting and no background sound interference). MS Office Suite (Word, Excel) An equation editor will be extremely helpful in completing the assignments in MS Word format. Another superior option is to produce the solution as a TeX document. Final submissions should be in the form of a PDF document.

Student Coursework Requirements

It is expected that each module will take approximately 10-12 hours per week to complete. Here is an approximate breakdown: reading the assigned sections of the texts (approximately 5 hours per week) as well as some videos from guest speakers (2- 3 hours) and instructional videos, listening to the audio annotated slide presentations (approximately 1 hour per week), and writing assignments (approximately 2–3 hours per week).

This course will consist of five basic student requirements:

1. Weekly problem assignments (25% of final grade)
   Weekly problem sets provide an opportunity to apply the material presented each week. Assignments are due at the end of the week they are assigned.

2. Discussion board assignments (10% of final grade)
   Weekly discussion board assignments are meant to help you to think about the mathematical concepts you will be learning. Try to respond to each discussion prompt as well as respond to at least two other students’ post. While not mandatory, participation is strongly recommended.

3. Midterm Exams (20% of final grade each/total 40%)
   There are two midterm exams, in modules 5 and 11. Each is cumulative for the content in that period; i.e. the first midterm exam covers content from modules 1- 4; the second midterm exam covers content form modules 5 through 10. These exams are considered take-home exams because you have the entire week to complete them; however, no collaboration is permitted.

4. Final Exam (25% of final grade)
   The final exam is in module 14. It covers material from the entire semester. It is a take-home exam. You have the entire week to complete it; however, no collaboration is allowed.

Grading Policy

Assignments are due according to the dates posted in the Blackboard course site. Students may check these due dates in the Course Calendar or the Assignments in the corresponding modules. Grades will post no later than one week after assignment due dates. A grade of A indicates achievement of consistent excellence and distinction throughout the course—that is, conspicuous excellence in all aspects of assignments and discussion in every week. A grade of B indicates work that meets all course requirements on a level appropriate for graduate academic work. These criteria apply to both undergraduates and graduate students taking the course.

The following grades are used for this course: A+, A, A– (excellent), B+, B, B– (good), C (unsatisfactory), F (failure), I (incomplete). A grade of F indicates the student’s failure to complete or comprehend the course work.

A course for which an unsatisfactory grade (C or F) has been received may be retaken. The original grade is replaced with an R. If the failed course includes laboratory, both the lecture and laboratory work must be retaken unless the instructor indicates otherwise. A grade of W is issued to those who have dropped the course after the refund period but before the drop deadline. The transcript is part of the student’s permanent record at the university. No grade may be changed except to correct an error, to replace an incomplete with a grade, or to replace a grade with an R.

The Whiting School assumes that students possess acceptable written command of the English language. It is proper for faculty to consider writing quality when assigning grades.

For incomplete grades, please see the Graduate Programs catalogue for the Whiting School of Engineering.

The course grading scale is the following:

Academic Policies

Deadlines for Adding, Dropping and Withdrawing from Courses

Students may add a course up to one week after the start of the term for that particular course. Students may drop courses according to the drop deadlines outlined in the EP academic calendar (https://ep.jhu.edu/student-services/academic-calendar/). Between the 6th week of the class and prior to the final withdrawal deadline, a student may withdraw from a course with a W on their academic record. A record of the course will remain on the academic record with a W appearing in the grade column to indicate that the student registered and withdrew from the course.

Academic Misconduct Policy

All students are required to read, know, and comply with the Johns Hopkins University Krieger School of Arts and Sciences (KSAS) / Whiting School of Engineering (WSE) Procedures for Handling Allegations of Misconduct by Full-Time and Part-Time Graduate Students.

This policy prohibits academic misconduct, including but not limited to the following: cheating or facilitating cheating; plagiarism; reuse of assignments; unauthorized collaboration; alteration of graded assignments; and unfair competition. Course materials (old assignments, texts, or examinations, etc.) should not be shared unless authorized by the course instructor. Any questions related to this policy should be directed to EP’s academic integrity officer at ep-academic-integrity@jhu.edu.

Students with Disabilities - Accommodations and Accessibility

Johns Hopkins University values diversity and inclusion. We are committed to providing welcoming, equitable, and accessible educational experiences for all students. Students with disabilities (including those with psychological conditions, medical conditions and temporary disabilities) can request accommodations for this course by providing an Accommodation Letter issued by Student Disability Services (SDS). Please request accommodations for this course as early as possible to provide time for effective communication and arrangements.

For further information or to start the process of requesting accommodations, please contact Student Disability Services at Engineering for Professionals, ep-disability-svcs@jhu.edu.

Student Conduct Code

The fundamental purpose of the JHU regulation of student conduct is to promote and to protect the health, safety, welfare, property, and rights of all members of the University community as well as to promote the orderly operation of the University and to safeguard its property and facilities. As members of the University community, students accept certain responsibilities which support the educational mission and create an environment in which all students are afforded the same opportunity to succeed academically. 

For a full description of the code please visit the following website: https://studentaffairs.jhu.edu/policies-guidelines/student-code/

Classroom Climate

JHU is committed to creating a classroom environment that values the diversity of experiences and perspectives that all students bring. Everyone has the right to be treated with dignity and respect. Fostering an inclusive climate is important. Research and experience show that students who interact with peers who are different from themselves learn new things and experience tangible educational outcomes. At no time in this learning process should someone be singled out or treated unequally on the basis of any seen or unseen part of their identity. 
 
If you have concerns in this course about harassment, discrimination, or any unequal treatment, or if you seek accommodations or resources, please reach out to the course instructor directly. Reporting will never impact your course grade. You may also share concerns with your program chair, the Assistant Dean for Diversity and Inclusion, or the Office of Institutional Equity. In handling reports, people will protect your privacy as much as possible, but faculty and staff are required to officially report information for some cases (e.g. sexual harassment).

Course Auditing

When a student enrolls in an EP course with “audit” status, the student must reach an understanding with the instructor as to what is required to earn the “audit.” If the student does not meet those expectations, the instructor must notify the EP Registration Team [EP-Registration@exchange.johnshopkins.edu] in order for the student to be retroactively dropped or withdrawn from the course (depending on when the "audit" was requested and in accordance with EP registration deadlines). All lecture content will remain accessible to auditing students, but access to all other course material is left to the discretion of the instructor.