The Plight of Boltzmann+ Four Laws

By the time the first lecture of Week 7 had finished, we had discussed all four laws of thermodynamics, in mathematical and verbal forms, established the probabilistic nature of entropy and worked through ten types of entropy calculations. In fact, nearly all of the framework has now been constructed for Chapter 6, in which everything comes to fruition as we discuss spontaneity and equilibrium.

Backtracking, last Friday we explored the work of [my idol] Ludwig Boltzmann, who beat his head against the scientific establishment as he spearheaded the development of statistical mechanics. Bypassing all the entropy is disorder nonsense, here we can see the physical underpinnings of entropy are probabilistic and that entropy is a measure of the number of accessible microstates to a system [which may arise as translational, rotational, vibrational, electronic, nuclear, configurational, etc]. In other words, entropy is a metric related to the number of ways that energy can be dispersed (into these microstates). Now that you have been equipped with this interpretation of absolute entropy, you can successfully point-and-laugh at all those who persist in utilizing the now-debunked disorder interpretation.

On Monday, we finished [finally] our set of ten processes:

01. cyclic process
02. reversible adiabatic
03. reversible isothermal
04. reversible phase change (at constant T, P)
05. reversible change of state [ideal gas]
06. irreversible change of state [ideal gas]
07. change of state [general] (two versions: T,V and T,P)
08. mixing of ideal gases A and B (also ideal solutions)
09. irreversible phase change (at constant T, P)
10. chemical reactions

These 10 processes cover nearly every situation of interest in chemistry.

Finally we elucidated the Third Law of Thermodynamics, that S → 0 as T → 0. As indicated in class, this is a restatement of what we saw in the Carnot engine, that absolute zero cannot be attained (although we've gotten way way down there, to 450 pK, where matter acts truly bizarre because of the dominance of quantum over thermal effects).

The absolute entropy of real matter, incidentally, usually approaches a nonzero S₀, the residual entropy, which is a loose measurement of the strength of low-temperature intermolecular forces.

I hope it is clear by now that the Laws of Thermodynamics, in essence, establish a logical code from which nearly all energy transfer (and, hence, all phenomena) can be described. Turning this framework into usable results is not always easy, however.

Interestingly, a Fourth Law of Thermodynamics is often proposed, the Onsager reciprocal relations which we will not cover until pchem 2.

And now, the Four Laws of Thermodynamics, translated for Sanitation Engineers:

0th: There is shit.
1st: You can't get rid of it.
2nd: It gets deeper.
3rd: A nice empty trashcan is wishful thinking.