AAPT Abstract Archive

Abstract Information

  Session: Upper Division and Graduate Posters
  Paper Type: Poster
  Title: Legendre Transforms for Dummies
  Meeting: 2014 Summer Meeting: Minneapolis, Minnesota
  Location: N/A
  Time: 5:00PM
  Author: Carl E. Mungan, U.S. Naval Academy
410-293-6680, mungan@usna.edu
  Co-Author(s): None
  Abstract: Legendre transforms appear in two places in a standard undergraduate physics curriculum: (1) in classical mechanics when one switches from Lagrangian to Hamiltonian dynamics, and (2) in thermodynamics to motivate the connection between the internal energy, enthalpy, and Gibbs and Helmholtz free energies. Both uses can be compactly motivated if the Legendre transform is properly understood. Unfortunately, that transform is often relegated to a footnote in a textbook, or worse is presented as a complicated mathematical procedure. In this poster, I simplify the idea to the point that the Legendre transform can be elegantly presented in class in a sensible and accessible manner. In a nutshell, a Legendre transform simply changes the independent variables in a function of two variables by application of the product rule.
  Footnotes: None
  Presentation: Mungan-Poster.pdf

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