What you should learn from lectures & covered chapters for Final
Last revised: April 25, 2017.Chapter 1:
- Concepts of micro- and macrostates and of macrostate multiplicity.
- Binary spin model.
- Fluctuations around equilibrium.
- Saddle point approximation.
Chapter 2:
- Multiplicity for combined systems.
- Concepts of entropy and temperature.
- Law of increase of entropy and other laws thermodynamics, including their microscopic interpretation.
Chapter 3:
- Helmholtz free energy.
- Boltzmann factor and calculation of partition function.
- Concept of pressure.
- Partition function for a system of N weakly interacting particles, starting from summation over states in a box and replacing summation by integration. Similar procedures are employed later for photons and phonons.
Chapter 4:
- Planck distribution and its derivation.
- Stefan-Boltzmann law of radiation from dimensional arguments.
- Kirchhoff law of radiation.
- Similarities and differences between gases of phonons and photons.
Chapter 5:
- Gibbs free energy.
- Concept of chemical potential and absolute activity.
- Gibbs factor and calculation of Gibbs sum. Grand potential.
- Internal and total chemical potential.
Chapter 6:
- Differences between bosons and fermions.
- Conditions under which quantum statistics is important and other which not.
- Derivation of distribution functions for fermions, bosons and classical particles.
- Distribution functions for fermions bosons and classical particles.
- Behavior of chemical potential with temperature for fermions, bosons and classical particles, at fixed particle number.
- Pressure, energy and heat capacity for classical ideal gas.
- Concept of internal Gibbs sum. Active degrees of freedom and adiabatic index.
- Isothermal, adiabatic and sudden expansions.
Chapter 7:
- Zero temperature Fermi gas: calculation of Fermi energy and of Fermi momentum for given density and of average energy and momentum, in terms of Fermi energy and Fermi momentum.
- Concept of density of states.
- Bosons: behavior of chemical potential near zero temperature, concept of Einstein condensation temperature and behavior of particle numbers in the ground and in excited states below Einstein temperature.
Chapter 8:
- How to calculate work done by a system and heat delivered to a system for a specified cycle or portion of such a cycle. How to tell change in internal energy if the working substance is an ideal gas.
- How to tell whether a heat machine is an engine or a refrigerator.
- How to tell whether a heat machine is reversible, irreversible or impossible.
- Carnot efficiencies for an engine and a refrigerator.
- Concept of enthalpy.
Chapter 9:
- G=N*mu for a single-component system.
- Notation for reactions and different ways of writing down a condition for equilibrium with respect to a reaction, including the law of mass action.
- How to calculate the quotient for a reaction and use it to tell whether the reaction will progress forward or backward as the system strives towards equilibrium.
- How to calculate an equilibrium constant using equilibrium constants for other reactions.
- How to tell enthalpy for a reaction using enthalpies for constituents and/or other reactions. Relation of the enthalpy to heat under conditions of constant pressure and temperature.
Chapter 10:
- Meaning of a phase diagram: concepts of coexistence line, triple point and critical point.
- Clausius-Clapeyron equation and its uses.
- Van der Waals equation of state.
- How to find the location of a critical point given an equation of state.
- Maxwell construction.
- Essentials of mean-field theory of ferromagnetism.
- Types of phase transitions and Landau explanation thereof.
Chapter 14:
- Concept of distribution function in space and velocity.
- Maxwell velocity distribution and different associated characteristic velocities.
- Collision cross section, mean free path and mean free flight time.
- Extensive and intensive transport laws.
- Concepts of diffusion, charge conduction, heat conduction and viscosity.