I recently returned from vacationing in the UK, and just spent a couple of days in the West End of Glasgow, near Kelvingrove Park. Yes, the same Kelvin of scientific fame! Seeing his statue got me thinking about the second law of thermodynamics—enough that I was inspired to jot a few thoughts down about the second law.
The second law and entropy are two of the hardest topics to write about at a general chemistry level, in my opinion. Not only has there been fierce debate over the years as to the ideal intuitive notions and analogies for these topics, but related derivations with mathematical rigor can be painfully complicated. There’s a gulf here between the theory and practice of chemical thermodynamics that is difficult to navigate.
A while back I tried just to get down on paper a rigorous derivation of the definition of entropy in terms of heat and temperature, using the second law and a hypothetical thermodynamic cycle. While the work was mathematically correct, the writing made me—the author, mind you!—want to tear my eyeballs out recently. That text will never see the light of day in a general chemistry class. At that point, I wondered if I was even capable of dispensing with rigor to write a more intuitive piece. I’ve always found it difficult to write while sacrificing rigor because I still recall craving rigor and theory in the depths of my soul as a student.
The reality, of course, is that all chemists use heuristics, shortcuts, or metaphors when confronted with certain topics. The best chemist writers can navigate rigorous theory and metaphor with finesse, presenting derivations where the mind “wants” them and metaphors elsewhere. Tro is a good example—while he makes no effort to dumb down important equations, he also presents the practical metaphors that chemists most often use.
In the edition I have, he even manages to lay out all three general interpretations of entropy: entropy as disorder, entropy as energy dispersal, and the statistical interpretation. Color me jealous!