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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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Formats:
application/pdf
non-digital
Mirror:
http://dx.doi.org/10.1063/1.3680000
Access Rights:
Free access and
Available for purchase
A preprint of the work is available. A hard copy of the PERC 2011 proceedings is available for purchase from the AIP.
Restriction:
© 2011 American Institute of Physics
DOI:
10.1063/1.3680000
NSF Numbers:
0231032
0618877
0837829
1023120
0837214
0837301
PACSs:
01.40.-d
01.40.Fk
01.40.G-
05.70.Ce
Keywords:
Chain Rule, Multi-variable Calculus, Multiple Representations, PERC 2011, Partial Derivatives, Thermal Physics
Record Cloner:
Metadata instance created April 24, 2012 by Lyle Barbato
Record Updated:
May 15, 2012 by Vince Kuo
Last Update
when Cataloged:
February 6, 2012
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Record Link
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 October 22, 2014, 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 22 October 2014).
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. 22 Oct. 2014 <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} }
Refer Export Format

%A John Thompson
%A Corinne Manogue
%A David Roundy
%A Donald Mountcastle
%T Representations of partial derivatives in thermodynamics
%S PER Conference Invited Paper
%V 1413
%D August 3-4 2011
%P 85-88
%C Omaha, Nebraska
%U http://www.compadre.org/Repository/document/ServeFile.cfm?ID=11819&DocID=2669
%O Physics Education Research Conference 2011
%O August 3-4
%O application/pdf

EndNote Export Format

%0 Conference Proceedings
%A Thompson, John
%A Manogue, Corinne
%A Roundy, David
%A Mountcastle, Donald
%D August 3-4 2011
%T Representations of partial derivatives in thermodynamics
%B Physics Education Research Conference 2011
%C Omaha, Nebraska
%V 1413
%P 85-88
%S PER Conference Invited Paper
%8 August 3-4
%U http://www.compadre.org/Repository/document/ServeFile.cfm?ID=11819&DocID=2669


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