Statistical Mechanics

Learning Outcomes

Knowledge and Understanding

Having successfully completed this module, you will be able to demonstrate knowledge and understanding of:

• Chemical potential
• Microscopic definition of entropy and temperature
• Canonical ensemble, and applications to some simple physical systems immersed in a heat bath (temperature)
• Microcanonical ensemble (e.g. enumerate microstates for some simple physical systems)
• How Bose-Einstein condensation leads to unique states of matter at low temperatures
• Probabilistic interpretation of entropy, heat and work

Subject Specific Practical Skills

Having successfully completed this module you will be able to:

• Distinguish between Bose and Fermi gases and their ground states
• Employ quantum mechanics for a correct statistical description in terms of Fermi and Bose gases and their applications

• Revision of the basics laws of thermodynamics
• Brief summary of combinatorics and probabilities
• Discussion of basic concepts, notions and postulates of statistical mechanics e.g. microstates vs macrostates, notion of ensemble and postulate of equal a priori probability and ergodicity
• Microcanonical ensemble (isolated system). From where a microscopic definition of entropy and temperature emerges.
• Canonical ensemble (system in a heat reservoir). Uncover the free energy F as the natural thermodynamic potential.
• Discuss the equivalence of microcanonical and canonical ensemble in the thermodynamic limit.
• Applications: paramagnetism, heat capacity of solids (phonons);
• Grand canonical ensemble (systems with a variable numbers of particles); Discussion of the chemical potential;
• Discussion of indistinguishable particles in quantum mechanics and introduce the two types of particles: bosons and fermions
• Applications: Fermi gases; zero point pressure, zero point energy, discuss the free fermion electron model
• Bose gases: Black body radiation, Bose-Einstein condensation

Teaching and learning methods

Lectures and problem classes.

Resources & Reading list

Textbooks

S Blundell and K Blundell Ð (2006). Concepts in Thermal Physics. Oxford University Press.

R,Baierlein. Thermal Physics. Cambridge.

Assessment strategy

Weekly course work will be set and assessed in the normal way, but only the best ‘n-2’ attempts will contribute to the final coursework mark. Here n is the number of course work items issued during that Semester. As an example, if you are set 10 sets of course work across a Semester, the best 8 of those will be counted.

In an instance where a student may miss submitting one or two sets of course work, those sets will not be counted. Students will, however, still be required to submit Self Certification forms on time for all excused absences, as you may ultimately end up missing 3+ sets of course work through illness, for example. The submitted Self Certification forms may be considered as evidence for potential Special Considerations requests.

In the event that a third (or higher) set of course work is missed, students will be required to go through the Special Considerations procedures in order to request mitigation for that set. Please note that documentary evidence will normally be required before these can be considered."

Summative

This is how we’ll formally assess what you have learned in this module.

Referral

This is how we’ll assess you if you don’t meet the criteria to pass this module.

Repeat

An internal repeat is where you take all of your modules again, including any you passed. An external repeat is where you only re-take the modules you failed.

Repeat Information

Repeat type: Internal & External