Teaching the Second Law

moderator: Robert J. Silbey, Department of Chemistry, Massachusetts Institute of Technology, MIT
author: Joseph Smith, Department of Mechanical Engineering, Massachusetts Institute of Technology, MIT
author: Howard Butler
author: Andrew Foley, U.S. Coast Guard Academy
author: Kimberly Hamad-Schifferli, Center for Future Civic Media, Massachusetts Institute of Technology, MIT
author: Bernhardt Trout, Department of Chemical Engineering, Massachusetts Institute of Technology, MIT
author: Jeffrey Lewins, Magdalene College, University of Cambridge
author: Enzo Zanchini, University of Bologna
author: Michael von Spakovsky, Department of Mechanical Engineering, Virginia Tech Transportation Institute
published: July 24, 2013,   recorded: October 2007,   views: 3102

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Robert Silbey is an old hand at teaching chemistry (40 years and counting), yet each time he turns to the Second Law of Thermodynamics, he’s “always very nervous.” From this panel of educators, we get a sense of how challenging a classroom subject the Second Law can be.

Joseph Smith notes that the teaching approach “depends on the application,” and applications are both theoretical and practical. Students must first ask what is entropy, and why is it needed, says Smith. He focuses on “idealizations that often get ignored,” such as isolation, equilibrium and system boundaries. “If we don’t get those straight in the beginning student’s mind, then there’s a lot of confusion.”

To Howard Butler’s way of thinking, “teaching the Second Law is much more difficult and challenging a task than teaching Newton’s Second Law of Motion,” both because the concepts involved are so much more complex and abstract, and because the Second Law takes on very different forms depending on which thermodynamic domain is being considered.”

Andrew Foley “tries not to worry too much about what entropy is.” Instead, he handles the whole concept as if it were an accounting problem: “money being moved through a mint.” We can “shove the property of energy instead of money, and produce a form of accounting for energy equations.” Says Foley, “First Law, Second Law -- it’s all accounting.”

As engineering and biology converge, “it’s important that students understand the thermodynamics of biological molecules,” says Kim Hamad- Schifferli. She demonstrates the Boltzmann distribution with such biological examples as the coiling of DNA from its double-stranded to single-stranded form. Hamad- Schifferli acknowledges that entropy is very difficult for students to grasp viscerally, and that “one thing that helps greatly is the lattice model -- the entropy of mixing two gases, for example.”

Bernhardt Trout also invokes Boltzmann, “who believed in atoms vehemently, without substantive proof.” This is because “he didn’t want to believe in the soul, he wanted to believe we are nothing but matter and motion.” Trout says that while we can get a more accurate, mathematical description of atoms, “we owe it to our students to teach them about these most fundamental issues to try to reengage the original questions in the original context in which they existed.”

Jeffery Lewins reminisces about being “Keenanized” during his college years. He notes that “in the great book, Professor Keenan uses the energy-entropy volume space quite late to discuss equilibrium.” Lewins suggests that more can be made of this space in teaching.

Enzo Zanchini discusses “a rigorous definition of entropy valid also for nonequilibrium states.” He considers closed systems, and lays out a thorough set of basic definitions, going over the First Law and energy, and the Second Law and entropy.

“There are so many textbooks on thermodynamics, so many schools of thought, says Michael von Spakovsky because “there is not a whole lot of agreement on a lot of things.” He recounts how a unified theory developed at MIT helped resolve key issues in thermodynamics, by proposing “a broader, self-consistent quantum kinematics and dynamics. … Entropy becomes an intrinsic property of matter, including single particles.”

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