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How to teach thermodynamics
This blog will give some wisdom guidance on how to teach thermodynamics, particularly in the opening weeks, to undergraduate engineering students. This blog started as a response post to nanomechanics engineer Zhigang Suo's 19 Dec 2010 request for suggestive advice on which textbook to use and how to teach thermodynamics, as he is apprehensive about teaching his first thermodynamics class (Engineering Science 181 Engineering Thermodynamics, Harvard). In any event, to give some quick advice on how to teach thermodynamics:
(a) Show students the visual timeline of how thermodynamics originated, namely how Parmenides’ 485 BC denial of the void, led to the development of the barometer (1643), the Guericke vacuum engine (1652), the gas laws (1658), the Papin digester (1679), then to the Papin engine (1690); which is the prototype engine model for the Carnot cycle (as described in steps by Papin), and hence the original model for the thermodynamic system, i.e. the volume of whatever substance is inside the piston and cylinder. It is important to understand the relation between the creation of the vacuum and work; and to get a visual of what exactly is the "working substance" (thermodynamic system), as defined in the Papin engine model.
(b) Introduce students to Boerhaave’s law (1720), i.e. that all bodies of the universe can be made to expand or contract in volume; this is the opening citation to Lavoisier’s caloric theory, based on experiments using Papin's digester. This is very important to the understanding of entropy.
(c) Then introduce student's to Roger Boscovich's 1758 stationary point atom model of gases (one in a long line of atomic theories), in which the atoms of the gas were thought to oscillate about points of equilibrium, rather than to move about in trajectories; this view seems to be the model that scientists, in particular Lavoisier and Carnot, had in mind, prior to August Kronig's 1856 paper on "A General Theory of Gases", and Clausius' 1857 followup paper "On the Nature of the Motion which we Call Heat", which launched the kinetic theory of gases (and hence statistical mechanics). As Kronig put it: "the molecules of a gas do not oscillate about definite positions of equilibrium, but instead move about with velocity." Lavoiser speaks of caloric particles as something that is accumulated in the intersticies of the regions between the atoms of gas; thus both he and Carnot (who adopted Lavoisier's theory) seem to have had a Boscovich-type model in mind when they were of the view that all physical bodies expand and contract to their original atomic configuration, based on the number of caloric particles in them, the caloric amount remaining unchanged (as described by Carnot as the re-establishment in the equilibrium in the caloric), per each engine cycle. This is very important to the inderstanding of the difference between a "reversible" cycle and "irreversible" cycle or process; and hence to the underlying understanding of the second law and entropy increase.
(d) Then introduce students to Gustave Coriolis’ principle of the transmission of work, as derived in his 1829 Calculation of the Effect of Machines; there's no English translation (you have to do your own French to English translation to read the derivation), but this is where most of the geometry behind Clausius' derivation of internal energy stems, and is the origin of the mathematical definition of work.
(e) Then introduce students to the mechanical equivalent of heat (1842); this is also a difficult concept to understand, but it was through this model that "caloric" became converted into "entropy"; and beyond this the entire unit system of energy (joule) is based on this measurement. The true name of entropy is called "transformation content", as explained in great detail by Clausius, and it is based on this model that heat and work are equivalent or transformable into each other, and hence caloric is not indestructible as Lavoisier and Carnot viewed things.
(f) Then I would strongly suggest the required reading assignment of the first 38-pages (mathematical introduction + first law derivation) of Rudolf Clausius’ The Mechanical Theory of Heat, the 1879 2nd edition translation by Walter Browne (~$20 new at Amazon). All engineering thermodynamics textbooks are simply a rehashing of this 1879 textbook, which is the core of all of thermodynamics. This textbook should be a required purchase for all engineers. As Einstein put it, of all the books in science, the theory contained in Clausius' textbook is the least likely, of all universal theories, to ever be overthrown.
All of this should be introduced in the first week or so of class, then you can go on to fill in the rest of the class with whatever engineering textbook you choose. Students looking for a fuller or deeper understanding of entropy can then go back later and read the key chapters of Clausius' textbook (3, 4, 5, 9, 10), on his or her own time. The math of thermodynamics is certainly difficult, but more often than not it is the intuitive basis that is the more difficult aspect of why one is learning the math and doing the derivations. Introduction to this foundation may help with this.