I am currently teaching (or will soon be teaching) the following courses:

MCG3740 — MÈCANIQUE DES FLUIDES I — Automne 2013

MCG3341 — FLUID MECHANICS II — Winter 2014

Curriculum Design (What is Entropy?)

I am very interested in curriculum design and always re-evaluate how I present topics to students.

There is probably no concept other than entropy that is so fundamental to a mechanical engineer while being so poorly presented in the standard textbooks. Entropy is the driving force behind many thermodynamics processes and places very strong restrictions on the efficiency of all energy-conversion systems. It is of enormous importance for engineering applications.

At a recent workshop held at the Massachusetts Institute of Technology entitled Meeting the Entropy Challenge, Robert Silbey, the former MIT dean of science who taught thermodynamics for forty years, admitted during a panel discussion on teaching the second law that, when he has to teach entropy, he always gives himself the same advise Arturo Toscanini gave to his orchestra before performing Beethoven's ninth symphony: "Courage, have courage!" [1]. During the course of this discussion, it became clear that even the world experts on thermodynamics and entropy have trouble teaching it to students.

When first introducing this idea to mechanical-engineering students, the most common technique is to begin, after the definition of a cycle, with the work of Carnot and Clausius and a discussion of "irreversibility". Unfortunately, in many engineering programs, the only physical explanations of what entropy actually is are based on loosely defined concepts such as "disorder". These explanations are confusing at best, and wrong at worst. It has become more common in the last ten years among the chemistry and chemical-engineering communities to teach entropy as "spreading of energies among accessible energy states" [2, 3]. This definition is far superior to the traditional disorder-based metaphors, however it is not as useful for mechanical engineers, who are not accustomed to thinking in terms of accessible energy states of a system.

The definition of "entropy as likelihood" afforded by kinetic theory [4, 5] is very simple to explain and makes mechanical-engineering students much more comfortable with the concept during their studies and more confident and skilled in its use during their careers as engineers. Students already have an intuition that an isolated system, left to itself, will move towards a stable equilibrium. For example, two bodies in thermal contact will eventually settle to the same temperature and neither will spontaneously become hotter than the other, just as a drop of dye added to a bowl of water will spread evenly throughout the liquid and will never spontaneously re-concentrate into a drop. It is easy to show that these systems move to these stable configurations only because they are overwhelmingly the most likely. Just as students become comfortable with the relationship between internal energy and a substance's microscopic molecular motion, they can come to understand that entropy is related to the likelihood of a system's microscopic configuration in a way that is completely in agreement with all traditional entropic relations. Using this approach, it is also possible to define entropy earlier in an introductory course (before the definition of a cycle) and show students the fundamental nature of the concept. With this picture of entropy, it is easy to give students a physical depiction of many other important thermofluidic concepts, such as how the interplay between energy and entropy ensures that, for equilibrium thermodynamics, any two independent intensive properties can be used to determine all other intensive state properties of a pure substance (this is usually presented as the state postulate and is another fundamentally important idea that students are often expected simply to accept with no further explanation).


  1. Silbey, R., Beretta, G. P., Cengel, Y., Foley, A., Gyftopoulos, E. P., Hatsopoulos, G. N., Keck, J. C., Lewins, J., Lior, N., Nieuwenhuizen, T. M., Steinfeld, J., von Spakovsky, M. R., Wang, L.-S., and Zanchini, E., "Discussion on teaching the second law", AIP Conference Proceedings, 1033 (1): 309-316, 2008.
  2. Leff, H., "Entropy, its language, and interpretation", Foundations of Physics, 37: 1744-1766, 2007.
  3. Lambert, F. L., "Entropy is simple, qualitatively, Journal of Chemical Education, 79 (10): 1241-1246, 2002.
  4. Müller, I., Thermodynamics, Pitman Publishing, Boston, 1985.
  5. Müller, I. and Weiss, W., Entropy and Energy: A Universal Competition, Springer, Berlin Heidelberg, 2005.