Course Planner and Assignments

Covered material and homework assignments are updated weekly.  Students should check the assigned homework before beginning to work on a problem set. 

 

Unit 0: Lectures 1-2 (Aug. 23th - 25th)

 

Material covered

Course description.

Review of important math tools.

 

What to study

Review elementary calculus with emphasis on functions of two variables, partial derivatives, simple integrals, Taylor series.

 

Homework Assignment #1, due Aug. 30th

Problems Math1, Math2, Math3, Math4.

 

 

Unit 1: Lectures 3-5 (Aug. 25th - Sept. 1st)

 

Material covered

Properties of gases:

Ideal gas equation of state.

Van der Waals equation.

Pressure-volume diagrams, critical point.

Law of corresponding states.

Virial coefficients.

Simple models (hard spheres, square well potential, hard sphere potential with attractive tail, Lennard-Jones potential.

The origin of intermolecular forces.  The Born-Oppenheimer approximation and potential energy curves.

 

What to study

Study Chapter 16 but omit Redlich-Kwong equation and Peng-Robinson equation.

 

Homework assignment #2, due Sept. 6th

McQuarrie & Simon problems 16-3, 16-39, 16-43, 16-58, 16-59.

 

Further thinking

Why does the hard sphere model predict temperature-independent second Virial coefficient?  How does the square well model correct that deficiency? 

 

 

Unit 2: Lectures 6-13 (Sept. 6th-22nd)

 

Material covered

The Canonical Ensemble: Boltzmann factor and partition functions:

Concept of statistical ensemble. Binomial and multinomial distributions.

The method of Lagrange multipliers.  The Boltzmann factor.

Partition function.

Internal energy.

Heat capacity at constant volume.

Contributions to molecular partition function, internal energy and heat capacity from translational, electronic, vibrational and rotational degrees of freedom.

The equipartition principle.

 

What to study

Study Chapters 17 and 18, except section 17-5, plus lecture notes on ensembles and on the equipartition principle.

 

Homework assignment #3, due Sept. 20th

McQuarrie & Simon problems 17-32, 17-36, 17-37, 18-8, 18-11.

 

Homework assignment #4, due Sept. 27th

Fill in the small steps (mostly evaluation of derivatives) left out in class to obtain the internal energy and heat capacity for rotational and vibrational motion of a diatomic molecule, given the expressions obtained for the corresponding partition functions, in the rigid rotor/harmonic oscillator approximation.  Also work out Problem StatMech1.

 

Further thinking

Why is it correct to say that a vibrational mode makes negligible contribution to the heat capacity at temperatures much lower than its vibrational temperature (or frequency, expressed in temperature units)? To answer it, recall the definition of heat capacity as the change of internal energy corresponding to a small change of temperature. Will a small increase of temperature change the internal energy of that vibrational mode significantly under these conditions? How does the argument change if the temperature is comparable to or higher than the vibrational temperature of the given mode?

 

Unit 3: Lectures 15-20 (Sept. 27th - Oct. 6th)

 

Material covered

The first law of thermodynamics:

Mechanical work.

Reversible processes.

Exact and inexact differentials.

State functions.

Internal energy function.

First law.

Reversible isothermal, isobaric and adiabatic expansions.

Free expansion.

Enthalpy

Heat capacity at constant pressure.

 

What to study

Study Chapter 19 except section 19-6.

 

Homework assignment #5, due Oct . 11th

McQuarrie & Simon problems 19-2, 19-4, 19-5, 19-6, 19-13.

 

 

Unit 4: Lectures 19-22 (Oct. 9th-16th)

 

Material covered

The second law of thermodynamics:

The entropy function.

Entropy of an ideal gas.

The Clausius principle.

Spontaneous processes and the second law.

Caratheodory's principle.

The Carnot cycle. The Otto cycle and the internal combustion engine.

Enthalpy changes and phase transitions.

Statistical mechanical definition of entropy.

Microscopic interpretation of heat, work, and entropy changes.

 

What to study

Study Chapter 20 plus sections 17-5 and 19-6.

 

Homework assignment #6, due Oct . 18th

McQuarrie & Simon problems 20-6, 20-8, 20-9, 20-13.

 

Further thinking

Can you turn the Carnot engine into a cooling device? Is it possible to cool your kitchen on a hot summer day by opening the door of your refrigerator?

 

 

Unit 5: Lecture 23 (Oct. 18th)

 

Material covered

The third law of thermodynamics.

Entropy at low temperatures.

The third law.

Discontinuity of entropy across phase transitions.

 

What to study

Study Chapter 21.

 

Homework assignment #7, due Oct . 25th

McQuarrie & Simon problems 20-14, 20-15, 20-32, 21-2, 21-6.

 

 

Unit 6: Lectures 24-26 (Oct. 20th-25th)

 

Material covered

Important tools and relations.

Helmholtz and Gibbs free energies.

Legendre transforms.

Maxwell's relations.

Pfaffian forms.

 

What to study

Study Chapter 22 except section 22-8.

 

Homework assignment #8, due Nov. 1st

McQuarrie & Simon problems 22-8, 22-10 without the Redlich-Kwong part, 22-11, 22-14, 22-18.

 

 

Unit 7: Lectures 27-29 (Oct. 27th - Nov. 1st)

 

Material covered

Phase equilibria:

Phase diagrams, phase coexistence, phase transitions.

Chemical work and chemical potential.

General conditions of equilibrium. Thermal and mechanical equilibrium. Equilibrium with respect to matter flow.

The Clausius-Clapeyron equation.

Statistical mechanical calculation of chemical potential.

 

What to study

Study Chapter 23.

 

Homework assignment #9, due Nov. 8th

McQuarrie & Simon problems 22-23, 23-1, 23-2, 23-20, 23-27. To avoid arriving at an inconsistency, please disregard the last sentence about densities in problem 23-2.

 

Second hour exam

 

 

Unit 8: Lectures 30-34 (Nov. 6th-15th)

 

Material covered

Solutions:

Euler relations.

The Gibbs-Duhem equation.

Phase equilibrium in multi-component systems.

Raoult's law and ideal solutions.

Vapor pressure and chemical potentials in binary liquid-liquid solutions.

Osmotic pressure.

What to study

Study Chapter 24 except sections 24-8 and 24-9. Also study section 25-4.

 

Homework assignment #10, due Nov. 29th

Problems Thermo1, Thermo2, Thermo3.  Also, McQuarrie and Simon problems 24-5, 24-18.

 

 

Unit 9: Lecture 35 (Nov. 17th)

 

Material covered

The kinetic theory of gases.

Distribution of velocity components. Root-mean-square velocity.

The Maxwell-Boltzmann distribution.

Average speed and most probable speed.

Temperature effects on chemical reactions.

 

What to study

Study Chapter 27.

 

 

Unit 10: Lectures 36-40 (Nov. 27th - Dec. 6th)

 

Material covered

Special topics in thermodynamics and chemical kinetics.

Chemical reaction rates. Reaction order, rate laws. Arrhenius plots. Classical transition state theory. Barrier recrossing.  Tunneling effects in chemistry.  Stability conditions for entropy and thermodynamic potentials. Fluctuations and phase transitions.

Superfluidity and Bose-Einstein condensation.

 

Special Presentation

The Ising Model -- A special presentation by Lukasz Koscielski

 

What to study

Study your lecture notes and the material in the Powerpoint file.