PHYS 251

Statistical Mechanics I

Course Description

PHYS 251 is the first course in a series of graduate-level courses in Statistical Mechanics. In this course, students will learn how to incorporate statistical concepts in determining the thermodynamic properties and behavior of physical systems. The course starts with discussions on the microcanonical, canonical, and grand canonical ensembles. Applications on how to use these ensembles to understand isolated systems or systems that are in contact with a heat bath are then investigated. Along the way, the partition function is introduced which would allow us to calculate the thermodynamic variables of systems in equilibrium with a heat bath. The course ends with discussions on applying the ensemble approach to determining the properties of solids, paramagnets, and the classical ideal gas.

Course Learning Outcomes

After completing this course, you should be able to:

• calculate the properties of thermodynamic systems from either microcanonical, canonical, or grand canonical treatment, depending on their states;

• determine the partition function and other statistical values of thermodynamic systems in equilibrium; and

• analyze the properties and behavior of thermodynamic systems such as the classical ideal gas, paramagnetic solid, and heat engines.

Course Outline

  1. The First Law of Thermodynamics

    • Macroscopic physics

    • Temperature

    • The First Law

  2. The Second Law of Thermodynamics I

    • Direction of natural processes

    • Statistical weight of a macrostate

    • Equilibrium of an isolated system

    • Schottky Defect

    • Equilibrium of a system in a heat bath

  3. Paramagnetism

    • Paramagnetic solid in a heat bath

    • Heat capacity and entropy of a paramagnet

    • Isolated paramagnetic solid

    • Negative temperature

  4. The Second Law of Thermodynamics II

    • Infinitesimal changes

    • Clausius Inequality

    • Helmholtz Free Energy

    • Third Law of Thermodynamics

  5. Thermodynamic systems

    • Heat engines and refrigerators

    • The difference of heat capacities

    • Entropy of Mixing of perfect gases

  6. The heat capacity of solids

    • Einstein's Theory

    • Debye's Theory

  7. The perfect classical gas

    • Partition function of the perfect classical gas

    • Equation of state

    • Heat capacity and entropy of the perfect classical gas

Mode of Delivery

The course will follow the schedule stated in this Syllabus. All course materials, i.e., this Syllabus, the Lecture Activities, lecture slides, and supplementary materials, are going to be available in the course's Canvas Learning Management System (LMS). Online lectures are going to be held twice a week via Zoom meetings. Students can also post questions and start a discussion in the Discussions page of the Canvas LMS.

References

The main reference for this course is:

• F. Mandl, Statistical Physics, 2nd Edition, Wiley, 1988.

Supplementary references are:

• D.V. Schroeder, An Introduction to Thermal Physics, Addison Wesley Longman, 2000.

• F. Reif, Fundamentals of Statistical and Thermal Physics, Waveland Press, 2008.

Lecture Slides

• Lecture Slides 1 • Lecture Slides 11

• Lecture Slides 2 • Lecture Slides 12

• Lecture Slides 3 • Lecture Slides 13

• Lecture Slides 4 • Lecture Slides 14

• Lecture Slides 5 • Lecture Slides 15

• Lecture Slides 6 • Lecture Slides 16

• Lecture Slides 7 • Lecture Slides 17

• Lecture Slides 8 • Lecture Slides 18

• Lecture Slides 9

• Lecture Slides 10

About the Instructor

Name: Eduardo C. Cuansing Jr., Ph.D.

Email Address: eccuansing at up.edu.ph

Homepage: https://sites.google.com/up.edu.ph/eduardo-c-cuansing/home

Eduardo C. Cuansing Jr., Ph.D., is a Professor at the Institute of Mathematical Sciences and Physics (IMSP). He earned his B.S. Physics from the University of the Philippines Diliman and his Ph.D. Physics from Purdue University. He was a postdoctoral researcher at the University of Pittsburgh and the National University of Singapore. He was also previously a faculty member at the University of the Philippines Diliman, De La Salle University, and the Ateneo de Manila University. He currently heads the Quantum Transport and Quantum Thermodynamics (QT2) research group. His research is in theoretical and computational physics, in specific areas such as quantum transport, nonequilibrium physics, quantum thermodynamics, and phase transitions and critical phenomena. He was previously the President of the Samahang Pisika ng Pilipinas (Physics Society of the Philippines) in 2021. He is currently the Vice Chair of Division IX (Physics) at the National Research Council of the Philippines (NRCP) and a member of the General Council of the Asia Pacific Center for Theoretical Physics (APCTP).