Thermodynamics and Statistical Mechanics

Aim

After completing the course, the student must:

• be able to construct idealized models of microscopic systems and calculate equilibrium properties under different conditions, e.g. at a given temperature, chemical potential, energy, or volume;
• be able give an account, in a well-structured and logically coherent manner, of the reasoning and derivations behind central concepts in statistical mechanics and thermodynamics, as well as the relationships between the theory's central concepts
• be able to use results from statistical mechanics and thermodynamics in problem solving in areas such as energy technology (for example, efficient energy use), materials science and chemistry.

Content

• Entropy and the statistical definitions of temperature, pressure, and chemical potential, and their connection to the thermodynamic identity; the second law of thermodynamics.
• Energy; the first law of thermodynamics; heat and work; heat capacity; enthalpy.
• Different model systems: binary model system, the Einstein solid, and the ideal gas.
• Reversibility and different thermodynamic processes: adiabatic, isochoric, isentropic, isothermal, isobaric.
• Heat engines: efficiency measures for a heat engine, refrigerator, and heat pump. The Carnot cycle.
• Helmholtz and Gibbs free energy; entropy, pressure, volume, and chemical potential written as partial derivatives of the Helmholtz or Gibbs free energy.
• The thermodynamics of chemical reactions and the law of mass action.
• Phase transformations and the Clausius–Clapeyron equation.
• Reasoning leading to the Boltzmann factor, the Gibbs factor, and the associated partition function and grand partition function, respectively.
• Connection between the partition function and the Helmholtz free energy.
• Calculation of a system’s expected energy and expected particle number from the dependence of the different partition functions on temperature and chemical potential, respectively.
• Calculation of the partition function for a classical ideal gas.
• The concepts of total, external, and internal chemical potential.
• Particles’ internal structure described in terms of an internal partition function for a classical ideal gas.
• Occupation numbers for fermions and bosons.
• The free-electron model for metals.
• The thermal energy distribution in a photon gas: blackbody radiation, and briefly the Earth’s energy balance and the greenhouse effect.