Journal Article Detail Page

American Journal of Physics
written by R. K. P. Zia, Edward F. Redish, and Susan R. McKay
The Legendre transform is a powerful tool in theoretical physics and plays an important role in classical mechanics, statistical mechanics, and thermodynamics. In typical undergraduate and graduate courses the motivation and elegance of the method are often missing, unlike the treatments frequently enjoyed by Fourier transforms. We review and modify the presentation of Legendre transforms in a way that explicates the formal mathematics, resulting in manifestly symmetric equations, thereby clarifying the structure of the transform. We then discuss examples to motivate the transform as a way of choosing independent variables that are more easily controlled. We demonstrate how the Legendre transform arises naturally from statistical mechanics and show how the use of dimensionless thermodynamic potentials leads to more natural and symmetric relations.
American Journal of Physics: Volume 77, Issue 7, Pages 614-622
Subjects Levels Resource Types
Thermo & Stat Mech
- General
- Second and Third Law
= Thermodynamic Potentials
- Upper Undergraduate
- Graduate/Professional
- Reference Material
= Article
Intended Users Formats Ratings
- Educators
- application/pdf
  • Currently 0.0/5

Want to rate this material?
Login here!


Access Rights:
Available by subscription
Restriction:
© 2009 American Journal of Physics
Additional information is available.
DOI:
10.1119/1.3119512
ISSN Number:
0002-9505
Keywords:
Fourier transform, Legendre polynomials, free energy, thermodynamic potential
Record Cloner:
Metadata instance created August 31, 2011 by Harvey Gould
Record Updated:
August 31, 2011 by Harvey Gould
Last Update
when Cataloged:
March 26, 2009
ComPADRE is beta testing Citation Styles!

Record Link
AIP Format
R. Zia, E. Redish, and S. McKay, Am. J. Phys. 77 (7), 614 (2009), WWW Document, (http://dx.doi.org/10.1119/1.3119512).
AJP/PRST-PER
R. Zia, E. Redish, and S. McKay, Making sense of the Legendre transform Am. J. Phys. 77 (7), 614 (2009), <http://dx.doi.org/10.1119/1.3119512>.
APA Format
Zia, R., Redish, E., & McKay, S. (2009, March 26). Making sense of the Legendre transform. Am. J. Phys., 77(7), 614-622. Retrieved July 24, 2014, from http://dx.doi.org/10.1119/1.3119512
Chicago Format
Zia, R, E. Redish, and S. McKay. "Making sense of the Legendre transform." Am. J. Phys. 77, no. 7, (March 26, 2009): 614-622, http://dx.doi.org/10.1119/1.3119512 (accessed 24 July 2014).
MLA Format
Zia, Royce, Edward F. Redish, and Susan McKay. "Making sense of the Legendre transform." Am. J. Phys. 77.7 (2009): 614-622. 24 July 2014 <http://dx.doi.org/10.1119/1.3119512>.
BibTeX Export Format
@article{ Author = "Royce Zia and Edward F. Redish and Susan McKay", Title = {Making sense of the Legendre transform}, Journal = {Am. J. Phys.}, Volume = {77}, Number = {7}, Pages = {614-622}, Month = {March}, Year = {2009} }
Refer Export Format

%A Royce Zia
%A Edward F. Redish
%A Susan McKay
%T Making sense of the Legendre transform
%J Am. J. Phys.
%V 77
%N 7
%D March 26, 2009
%P 614-622
%U http://dx.doi.org/10.1119/1.3119512
%O application/pdf

EndNote Export Format

%0 Journal Article
%A Zia, Royce
%A Redish, Edward F.
%A McKay, Susan
%D March 26, 2009
%T Making sense of the Legendre transform
%J Am. J. Phys.
%V 77
%N 7
%P 614-622
%8 March 26, 2009
%@ 0002-9505
%U http://dx.doi.org/10.1119/1.3119512


Disclaimer: ComPADRE offers citation styles as a guide only. We cannot offer interpretations about citations as this is an automated procedure. Please refer to the style manuals in the Citation Source Information area for clarifications.

Citation Source Information

The AIP Style presented is based on information from the AIP Style Manual.

The APA Style presented is based on information from APA Style.org: Electronic References.

The Chicago Style presented is based on information from Examples of Chicago-Style Documentation.

The MLA Style presented is based on information from the MLA FAQ.

This resource is stored in a shared folder.

You must login to access shared folders.

Save to my folders

Supplements

Contribute