CarnotCycle on the Gibbs-Helmholtz Equation
I’m a touch late discussing this and can only plead that it has been December after all. Over on the CarnotCycle blog — which is focused on thermodynamics in a way I rather admire — was recently a discussion of the Gibbs-Helmholtz Equation, which turns up in thermodynamics classes, and goes a bit better than the class I remember by showing a couple examples of actually using it to understand how chemistry works. Well, it’s so easy in a class like this to get busy working with symbols and forget that thermodynamics is a supremely practical science .
The Gibbs-Helmholtz Equation — named for Josiah Willard Gibbs and for Hermann von Helmholtz, both of whom developed it independently (Helmholtz first) — comes in a couple of different forms, which CarnotCycle describes. All these different forms are meant to describe whether a particular change in a system is likely to happen. CarnotCycle’s discussion gives a couple of examples of actually working out the numbers, including for the Haber process, which I don’t remember reading about in calculative detail before. So I wanted to recommend it as a bit of practical mathematics or physics.
 I think it was Stephen Brush pointed out many of the earliest papers in thermodynamics appeared in railroad industry journals, because the problems of efficiently getting power from engines, and of how materials change when they get below freezing, are critically important to turning railroads from experimental contraptions into a productive industry. The observation might not be original to him. The observation also might have been Wolfgang Schivelbusch’s instead.