How Gibbs derived the Phase Rule

Originally posted on carnotcycle:
The Phase Rule formula was first stated by the American mathematical physicist Josiah Willard Gibbs in his monumental masterwork On the Equilibrium of Heterogeneous Substances (1875-1878), in which he almost single-handedly laid the theoretical foundations of chemical thermodynamics. In a paragraph under the heading “On Coexistent Phases of Matter”, Gibbs gives…

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 … Continue reading “CarnotCycle on the Gibbs-Helmholtz Equation”

Gibbs’ Elementary Principles in Statistical Mechanics

I had another discovery from the collection of books at, now that I thought to look for it: Josiah Willard Gibbs’s Elementary Principles in Statistical Mechanics, originally published in 1902 and reprinted 1960 by Dover, which gives you a taste of Gibbs’s writings by its extended title, Developed With Especial Reference To The Rational … Continue reading “Gibbs’ Elementary Principles in Statistical Mechanics”

The End 2016 Mathematics A To Z: Distribution (statistics)

As I’ve done before I’m using one of my essays to set up for another essay. It makes a later essay easier. What I want to talk about is worth some paragraphs on its own. Distribution (statistics) The 19th Century saw the discovery of some unsettling truths about … well, everything, really. If there is … Continue reading “The End 2016 Mathematics A To Z: Distribution (statistics)”

Reading the Comics, September 16, 2015: Celebrity Appearance Edition

I couldn’t go on calling this Back To School Editions. A couple of the comic strips the past week have given me reason to mention people famous in mathematics or physics circles, and one who’s even famous in the real world too. That’ll do for a title. Jeff Corriveau’s Deflocked for the 15th of September … Continue reading “Reading the Comics, September 16, 2015: Celebrity Appearance Edition”

The Geometry of Thermodynamics (Part 2)

Originally posted on carnotcycle:
James Clerk Maxwell and the geometrical figure with which he proved his famous thermodynamic relations Historical background Every student of thermodynamics sooner or later encounters the Maxwell relations – an extremely useful set of statements of equality among partial derivatives, principally involving the state variables P, V, T and S. They…

The Geometry of Thermodynamics (Part 1)

Originally posted on carnotcycle:
Volume One of the Scientific Papers of J. Willard Gibbs, published posthumously in 1906, is devoted to Thermodynamics. Chief among its content is the hugely long and desperately difficult “On the equilibrium of heterogeneous substances (1876, 1878)”, with which Gibbs single-handedly laid the theoretical foundations of chemical thermodynamics. In contrast to…

The Liquefaction of Gases – Part I

Originally posted on carnotcycle:
Photo credit: Scientific American On Monday 3 December 1877, the French Academy of Sciences received a letter from Louis Cailletet, a 45 year-old physicist from Châtillon-sur-Seine. The letter stated that Cailletet had succeeded in liquefying both carbon monoxide and oxygen. Liquefaction as such was nothing new to 19th century science, it…

Reblog: Mixed-Up Views Of Entropy

Originally posted on carnotcycle:
Tucked away at the back of Volume One of The Scientific Papers of J. Willard Gibbs, is a brief chapter headed ‘Unpublished Fragments’. It contains a list of nine subject headings for a supplement that Professor Gibbs was planning to write to his famous paper “On the Equilibrium of Heterogeneous Substances”.…