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Escape from Carnot : A new way to introduce the mysterious property, Entropy.

Dr Andrew C Foley P.E U.S Coast Guard Academy, New London, CT

Introduction Entropy and its use within the second law of thermodynamics is undoubtedly one of the harder concepts in an undergraduate engineering degree. The vast majority of engineers fall into one of two categories when use of the second law is discussed. The first are those that can effectively get by without the second law, able to solve most problems with careful use of the first law. The second category are those that use the second law correctly but simply as a tool without an in depth physical understanding. This is not uncommon in engineering as one simply has to think of the widespread use of Laplace transforms, or more recently the surge in the use of complex stress analysis or computational fluids software where users do not understand the intricacies of the tool but use them anyway. While not ideal this approach is invariably successful as long as the limitations of the tool are not exceeded. Comfort is gained in the knowledge that numerous previous users have successfully used the same tools and hence undertaken a type of ‘validation by the masses’. If in doubt about these assertions the author challenges the reader to ask several engineers/academics to briefly describe the physical nature of entropy. To further elaborate on the issue of understanding entropy one only needs examine several core thermodynamic texts. (e.g Cengel & Boles (2006), Rogers & Mayhew (1980)) The second law is invariably introduced by using abstract heat engines and assorted assumptions, which eventually allow an expression for the property entropy, as heat flux over temperature to be derived. This can add to confusion as heat flux itself is not a property but rather energy in motion. Also the idea of energy exchanges between at least two reservoirs always being necessary and then the actual Kelvin-Planck statement of the Second Law itself only add to the confusion. i.e. ‘It is impossible for any device to exchange heat from a single reservoir and produce a net amount of work”. Even after one goes through the classical build up to the above statement, attentive students will still ask “how does that statement come from that example ?”. As an instructor who has successfully brought his class to relative mastery of the first law, it always proves disheartening to suddenly see a class start to flounder with the second law. Klotz(1964) eludes to this difficulty with the statement “ the heart of the difficulty in understandin the concept of increase in entropy is a verbal one …… “ He goes on to state “ one should realize that entropy is essentially a mathematical function”. So promoting the “simply use it as a tool” approach used by the second type of user described in the opening paragraph.. Recognizing the conceptual difficulties while still holding out for a physical understanding of entropy this paper describes a method of bringing the second law ‘on line’ in a consistent manner with how the first law is already being taught. (Foley

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Foley, A. (2007, June), Escape From Carnot: A New Way To Introduce The Mysterious Property, Entropy. Paper presented at 2007 Annual Conference & Exposition, Honolulu, Hawaii. 10.18260/1-2--1584