Chem 458 and Chem 555

Spring 2023.

Instructor: David Harrington.

FAQ

• What is statistical thermodynamics/statistical mechanics? Statistical mechanics tells how macroscopic properties (e.g., thermodynamic functions, dielectric constant, equilibrium constants) can be worked out from molecular-level properties, especially energy levels. Because it is too hard to solve the quantum mechanics for the number of particles we deal with in macroscopic systems, we give up wanting to know everything, and ask only about average properties (and fluctuations about the average). Hence we are interested in statistics and the probabilities that things can happen. In general, we assume that we know the energy levels of molecules already (so we don't worry about how quantum mechanics gives those energy levels). We will have to make some reckless assumptions to make our life easy, and along the way we will get a deeper insight into what temperature and entropy really mean.
• Do I have to know any statistics or probability? No, we will review these ideas before using them.
• Are there lots of equations? There are, but you don't have to memorize them and we'll spend most of our time thinking about their meaning, not deriving them.
• Will I have to plug in lots of numbers into formulas? There will be some of that, especially the first time we work with them, but there is a program provided (see below) to do much of the heavy lifting.
• How much math do I need to know? You should be able to rearrange equations, and differentiate and integrate simple functions, but nothing beyond that. (If you want to use a symbolic program like Maple or Mathematica to help you, you can.) The point is to understand the concepts. In most cases we will use very simple model systems where the math is also simple.
• Sounds boring - will I learn something interesting? Here are some teasers
  • Nanomachines won't look like bigger machines, and they won't take over the world.
  • There is a deep connection between information and entropy - they are more or less the same!
  • Why is the equilibrium constant for H₂ + D₂ = 2HD equal to 4, not 1 (hint: )
  • Who is Maxwell's Demon, and does he exist?
  • How can you unmix two gases?
  • What does annealing have to do with traveling salespersons?

Learning Objectives

At the conclusion of this course, you should:

• understand basic concepts in statistical thermodynamics, such as termperature, entropy and partition functions.
• be able to calculate microstate probabilities, partition functions and thermodynamic properties for simple model systems.
• be able to calculate accurate enthalpies, energies, entropies and heat capacities for most simple gases.
• understand and be able to reconstruct thermodynamic tables for gaseous species.
• understand what entropy really means.
• have an appreciation for some of the philosophical underpinnings of statistical mechanics.

Course Outline

1. Introduction to probabilities and ensembles.
2. Thermodynamic functions from energy levels.
3. Calculation of thermodynamic functions of an ideal gas from spectroscopic data.
4. Statistical mechanics of solids and adsorption; adsorption isotherms.
5. Phase transitions and emergence.
6. Some philosophical issues and paradoxes; relationship between entropy and information; Maxwell's demon.
7. Fluctuations, nanoscale systems, Brownian motors.

StatMech program to calculate thermodynamic functions from spectroscopic data.

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