# PHSI421 Statistical Mechanics

Advanced thermodynamics; equilibrium theory of many-particle systems; quantum ideal gas: Bose-Einstein condensation and free electrons; interacting systems and phase transitions.

Paper title Statistical Mechanics PHSI421 Physics 0.0833 10 points First Semester \$628.08 \$2,573.97
Limited to
BSc(Hons), PGDipSci, MSc
Contact
philip.brydon@otago.ac.nz
Teaching staff
Dr Philip Brydon
Textbooks
Schroeder, Daniel V. An Introduction to Thermal Physics. Addison Wesley Longman
Global perspective, Interdisciplinary perspective, Lifelong learning, Scholarship, Communication, Critical thinking, Information literacy, Self-motivation, Teamwork.
Learning Outcomes
After completing this paper students are expected to:
• Understand the statistical basis for describing thermodynamic equilibrium. Be familiar with the concepts of statistical ensembles, microscopic and macroscopic properties.
• Be able to define and apply the microcanonical, canonical and grand canonical ensembles appropriately. Define and use free energies, be able to derive their thermodynamic identities and extract thermodynamic partial derivative relations.
• Derive thermodynamic properties from a microscopic description of standard systems, e.g. ideal paramagnet, Einstein solid, ideal gas.
• Be able to apply the equipartition theorem, and understand its regime of validity.
• Be able to explain the effect indistinguishability has on statistical properties and how it is dealt with in the various ensembles. Demonstrate how to count/enumerate many-particle states of indistinguishable particles. Derive and apply the quantum distribution functions.
• Be able to apply the appropriate quantum statistical method to calculate the thermal properties of the standard quantum systems: an ideal Fermi gas, photons in a cavity, and an ideal Bose gas. Derive and apply the appropriate density of states for these systems.
• Understand general concepts of phase transitions in interacting systems with a detailed understanding of the van der Waals gas and the Ising model. Be able to apply the meanfield treatment to the Ising model and extract critical exponents.

## Timetable

### First Semester

Location
Dunedin
Teaching method
This paper is taught On Campus
Learning management system
None

Advanced thermodynamics; equilibrium theory of many-particle systems; quantum ideal gas: Bose-Einstein condensation and free electrons; interacting systems and phase transitions.

Paper title Statistical Mechanics PHSI421 Physics 0.0833 10 points First Semester \$640.66 \$2,676.93
Limited to
BSc(Hons), PGDipSci, MSc
Contact
philip.brydon@otago.ac.nz
Teaching staff
Dr Philip Brydon
Textbooks
An introduction to thermal physics, Daniel V. Schroeder, Addison Wesley Longman
Global perspective, Interdisciplinary perspective, Lifelong learning, Scholarship, Communication, Critical thinking, Information literacy, Self-motivation, Teamwork.
Learning Outcomes
After completing this paper students are expected to have achieved the following major learning objectives:
• Define and use free energies, be able to derive their thermodynamic identities, and extract information from thermodynamic partial derivative relations
• Understand the thermodynamics of systems undergoing a phase transition, with a detailed knowledge of the phase diagram of the van der Waals model
• Be able to define and apply the microcanonical, canonical and grand canonical ensembles appropriately and understand the statistical basis for thermodynamic equilibrium
• Derive thermodynamic properties from a microscopic description of standard systems (e.g. ideal paramagnet, Einstein solid, ideal gas)
• Be able to apply the equipartition theorem and understand its regime of validity
• Be able to explain the effect indistinguishability has on the statistical properties of matter; derive and apply the quantum distribution functions
• Apply the appropriate quantum statistical method to calculate the thermal properties of the standard quantum systems: an ideal Fermi gas, photons in a cavity, and an ideal Bose gas; derive and apply the appropriate density of states for these systems
• Solve the Ising model using the mean-field approximation

## Timetable

### First Semester

Location
Dunedin
Teaching method
This paper is taught On Campus
Learning management system
None