Module Information

Following a brief recap of some of the basic ideas of thermodynamics, including the zeroth and first laws of thermodynamics, this module presents the concept of entropy and its statistical significance, thermodynamic engines and refrigerators, the Carnot cycle and the second and third laws of thermodynamics. Thermodynamic potentials and the Maxwell relations are introduced, with real gases and phase transitions also considered. The concepts and techniques of statistical mechanics are introduced and are used to link the microscopic behaviour of matter with thermodynamic parameters.

INTRODUCTION (RECAP)
1. Ideal gas, state variables, changes of state.
2. Thermal equilibrium, zeroth law of thermodynamics, temperature scales.
3. Work, Heat and Internal Energy, first law of thermodynamics.
4. Heat Capacity, Enthalpy.

ENTROPY
1. Entropy and its statistical definition.
2. Reversible and irreversible processes.
3. Heat engines, refrigerators and heat pumps.
4. The second law of thermodynamics: Kelvin-Planck, Clausius statements.
5. Carnot cycle, thermodynamic temperature scale.
6. The third law of thermodynamics and absolute entropy.

THERMODYNAMIC POTENTIALS AND MAXWELL RELATIONS
1. Gibbs and Helmholtz free energies.
2. The Maxwell relations.
3. Phase equilibria.
4. Clausius-Clapeyron relation.

REAL GASES
1. The van der Waals equation of state, critical temperature, the Dieterici equation of state.
2. Virial expansion, Boyle temperature, condensation of gases.
3. Joule-Kelvin expansion.

PHASE TRANSITIONS
1. Thermodynamic definition, phase rule, and mixing of real solutions.
2. Calculation of thermodynamic potentials and partition function.
3. Dynamics of phase transitions, fluctuations of density, nucleation and diffusion.

STATISTICAL MECHANICS
1. Basic ideas: Assembly. Macrostates and Microstates. Distinguishable and Indistinguishable identical particles. Quasi-independent. Distribution. Entropy and number of microstates.
2. Distinguishable particles: Distributions of a macrostate. Most probable distribution. Boltzmann distribution. Partition function. Partition function and thermodynamic functions.
3. Indistinguishable particles: Fermi-Dirac distribution function. Bose-Einstein distribution function. Dilute gas. Density of states. Maxwell-Boltzmann distribution function. Partition function for a Maxwell-Boltzmann gas. Partition function and thermodynamic functions. Maxwell-Boltzmann speed distribution. Introduction to: Fermi-Dirac gases, Fermi energy, Fermi temperature and Bose-Einstein condensation.