The premature birth anniversary of J. Willard Gibbs

Today was the last lecture of 10.40, the dreaded Thermodynamics course of the MIT first year graduate curriculum in Chemical Engineering and a day of custom. The course, while evolving in details over the past years, has retained its capacity to inculcate a perpetual sense of fear and delirium across the class throughout the semester. Its apparent level of difficulty can be traced back to (or blamed upon) exclusively one man in the history of thermodynamics- Josiah Willard Gibbs (partners in crime include G. N. Lewis, James Clerk Maxwell and Ludwig Boltzmann :P). While mechanical and civil engineers revolve their lives around trivial heat pumps and thermodynamic cycles and while physics majors possibly escape the classical approach (most certainly the thermodynamics of solutions which is Gibbs area), possibly chemistry grad students are the only other sorry souls who have to endure the abstruse pain of Gibbs' calculus of thermodynamics and his geometric phase equilibria ideas.

But I like Gibbs. He is one of those towering figures in American Science (preceding giants like Feynman, McClintock and even G.N. Lewis) who's work was so original and ahead of its time that it evoked the interest of very few people in Gibbs' lifetime. It took a scientist of the greatness of Maxwell to immediately understand the significance of Gibbs' idea of the U-S-V surface (in this, they are almost like the Einstein-Eddington pair). Gibbs was a solitary figure who remained in the Yale campus all his life and produced an astoundingly rich body of work. Personally, the most significant aspect of Gibbs to me is that he made seminal contributions to both classical and statistical thermodynamics theory.

Back to 10.40 and today's lecture. Jeff Tester, the main instructor of the course is one of those classicists who revels in the joy of teaching this course which has been meticulously designed by him and his predecessors over the years. He filled his lectures with romantic connections to the historical development of the subject (one unfortunate consequence of this fact is that he was as abstruse as his idol Gibbs in some regard, but then this being his last year at MIT, one could overlook his indulgence) and his reverence to the likes of Carnot, Clausius, Gibbs, Boltzmann and Lewis. So as the custom goes, the last 10.40 lecture is marked with the celebration of Gibbs' birthday, although the actual date is in February. Legend has it that Bob Reid (Tester's predecessor as the 10.40 instructor and also incidentally Tester's PhD advisor) used to dress up as Gibbs to the lecture that day (tweed suit with flannels and all) and deliver his lecture in a New Haven accent. Tester did no such thing (though I think he could have pulled it off) but brought the customary cake (see picture) and tried to make sure fears were alleviated (or atleast momentarily forgotten) before the final exam week!

Most of the text is quite readable but for those who're curious about the formulae:
1. Bottom, top: The Gibbs Fundamental Equation in differential form
2. Bottom, bottom: The Gibbs Phase rule
3. Top, left: The fundamental statistical mechanical relation between the Helmholtz free energy and the canonical partition function.
4. Top, left: The kth Legendre transform of a first order homogenous function.


That's it for now until exams I suppose!