Statistical Thermodynamics Lecture 3, and the Sackur-Tetrode equation centenary

My third statistical thermodynamics lecture took place last Thursday afternoon. The timetable didn’t help; it was the second lecture in a double slot, and I think that a subject as conceptually and mathematically difficult as statistical thermodynamics can only be digested in limited chunks! But in spite of that, it seemed to go OK.

As for what was covered, I started with calculation of the Gibbs energy for monatomic and diatomic gases. The problem with this, as I commented last year, is that it doesn’t give a value which can be experimentally verified (you would have to calculate the values for each species in a reaction and then obtain the change in Gibbs energy to be able to do this). But nevertheless, it’s very useful to be able to do this type of calculation.

Moving on, I covered the relationship between equilibria and the Boltzmann distribution. This is really interesting, especially where it ties in with the role of entropy in the thermodynamics of reactions. I use a pictorial approach, taking inspiration from Atkins & de Paula, Elements of Physical Chemistry. This leads to the relationship between the  equilibrium constant and the partition functions of the reactants and products. I agree with Profs. Atkins and de Paula that this is a quite extraordinary equation, relating macroscopic and microscopic thermodynamics. I illustrate the use of this equation for an ionisation reaction, as is done in several of the textbooks.

In closing, I should mention (as I did in a tweet last week), that the Sackur-Tetrode equation is 100 years old this year. This is another amazing equation, which enables entropies to be calculated with impressive accuracy, using only some constants and atomic masses. It was derived independently by Sackur and Tetrode, with Hugo Tetrode being a scientist from the Netherlands who carried out some very important work but died at the age of 35. His profile was such that he was once visited by Einstein and Ehrenfest, but they were turned away by his housekeeper! In my tweet I gave a link to a paper about the derivation of the equation.

My next teaching challenge, starting later this week, is four lectures on ballistics for our final year forensics students. Quite a contrast in topic!


5 thoughts on “Statistical Thermodynamics Lecture 3, and the Sackur-Tetrode equation centenary”

  1. I start with the internal energy, then consider heat capacities, and then entropy and residual entropy. For some reason I don’t include enthalpy (I’ll have to look into why!). I don’t teach it in terms of ensembles. As I mentioned in the posts, I am faced with the problem of only a few lectures and a class with varied mathematical experience!

    If you want to look at my lecture slides, they are available at: (ST lectures 1-3)

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