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Representations of partial derivatives in thermodynamics
written by
John R. Thompson,
Corinne A. Manogue,
David J. Roundy, and
Donald B. Mountcastle
One of the mathematical objects that students become familiar with in thermodynamics, often for the first time, is the partial derivative of a multivariable function. The symbolic representation of a partial derivative and related quantities present difficulties for students in both mathematical and physical contexts, most notably what it means to keep one or more variables fixed while taking the derivative with respect to a different variable. Material properties are themselves written as partial derivatives of various state functions (e.g., compressibility is a partial derivative of volume with respect to pressure). Research in courses at the University of Maine and Oregon State University yields findings related to the many ways that partial derivatives can be represented and interpreted in thermodynamics. Research has informed curricular development that elicits many of the difficulties using different representations (e.g., geometric) and different contexts (e.g., connecting partial derivatives to specific experiments).
Physics Education Research Conference 2011
Part of the PER Conference Invited Paper series Omaha, Nebraska: August 3-4, 2011 Volume 1413, Pages 85-88
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Record Link
<a href="http://www.compadre.org/PER/items/detail.cfm?ID=11819">Thompson, J, C. Manogue, D. Roundy, and D. Mountcastle. "Representations of partial derivatives in thermodynamics." Paper presented at the Physics Education Research Conference 2011, Omaha, Nebraska, August 3-4, 2011.</a>
AIP Format
J. Thompson, C. Manogue, D. Roundy, and D. Mountcastle, presented at the Physics Education Research Conference 2011, Omaha, Nebraska, 2011, WWW Document, (http://www.compadre.org/Repository/document/ServeFile.cfm?ID=11819&DocID=2669).
AJP/PRST-PER
J. Thompson, C. Manogue, D. Roundy, and D. Mountcastle, Representations of partial derivatives in thermodynamics, presented at the Physics Education Research Conference 2011, Omaha, Nebraska, 2011, <http://www.compadre.org/Repository/document/ServeFile.cfm?ID=11819&DocID=2669>.
APA Format
Thompson, J., Manogue, C., Roundy, D., & Mountcastle, D. (2011, August 3-4). Representations of partial derivatives in thermodynamics. Paper presented at Physics Education Research Conference 2011, Omaha, Nebraska. Retrieved July 31, 2015, from http://www.compadre.org/Repository/document/ServeFile.cfm?ID=11819&DocID=2669
Chicago Format
Thompson, J, C. Manogue, D. Roundy, and D. Mountcastle. "Representations of partial derivatives in thermodynamics." Paper presented at the Physics Education Research Conference 2011, Omaha, Nebraska, August 3-4, 2011. http://www.compadre.org/Repository/document/ServeFile.cfm?ID=11819&DocID=2669 (accessed 31 July 2015).
MLA Format
Thompson, John, Corinne Manogue, David Roundy, and Donald Mountcastle. "Representations of partial derivatives in thermodynamics." Physics Education Research Conference 2011. Omaha, Nebraska: 2011. 85-88 Vol. 1413 of PER Conference Invited Paper. 31 July 2015 <http://www.compadre.org/Repository/document/ServeFile.cfm?ID=11819&DocID=2669>.
BibTeX Export Format
@inproceedings{
Author = "John Thompson and Corinne Manogue and David Roundy and Donald Mountcastle",
Title = {Representations of partial derivatives in thermodynamics},
BookTitle = {Physics Education Research Conference 2011},
Pages = {85-88},
Address = {Omaha, Nebraska},
Series = {PER Conference Invited Paper},
Volume = {1413},
Month = {August 3-4},
Year = {2011}
}
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%A John Thompson
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%0 Conference Proceedings 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.
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The AIP Style presented is based on information from the AIP Style Manual. The AJP/PRST-PER presented is based on the AIP Style with the addition of journal article titles and conference proceeding article titles. 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. Representations of partial derivatives in thermodynamics:Know of another related resource? Login to relate this resource to it. |
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