Though it’s the summer months I’m happy to say the Carnot Cycle thermodynamics blog is still posting. He had been writing about Jacobus Henricus van ‘t Hoff, first recipient of the Nobel Prize in Chemistry. In the 1880s van ‘t Hoff was studying the osmosis. In April’s essay Carnot Cycle described the problem, and how van ‘t Hoff passed up a correct formula describing osmotic pressure in favor of an attractive but wrong alternative.
In this month’s essay Carnot Cycle continues the topic. It particularly goes over just how van ‘t Hoff got to his mistaken idea. It’s not that he started out wrong. He began from a good start and derived a mistaken formula. The derivation involved a string of assumptions and simplifications and approximations, of the kind that must be made to go from starting principles to a specific problem. He was guided by an idea of what the answer ought to look like, though, and that led him astray. The blog describes what he did and why it would look reasonable in the circumstance. It’s worth reading to see what actual mathematics, the kind that doesn’t have known answers, is like.