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Student (Mis)application of Partial Differentiation to Material Properties
written by
Brandon Bucy, John R. Thompson, and Donald B. Mountcastle
Students in upper-level undergraduate thermodynamics courses were asked about the relationship between the complementary partial derivatives of the isothermal compressibility and the thermal expansivity of a substance. Both these material properties can be expressed with first partial derivatives of the system volume. Several of the responses implied difficulty with the notion of variables held fixed in a partial derivative. Specifically, when asked to find the partial derivative of one of these quantities with respect to a variable that was initially held fixed, a common response was that this (mixed second) partial derivative must be zero. We have previously reported other related difficulties in the context of the Maxwell relations, indicating persistent confusion applying partial differentiation to state functions. We present results from student homework and examination questions and briefly discuss an instructional strategy to address these issues.
Physics Education Research Conference 2006
Part of the PER Conference series Syracuse, New York: July 26-27, 2006 Volume 883, Pages 157-160
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Record Link
<a href="https://www.per-central.org/items/detail.cfm?ID=5262">Bucy, B, J. Thompson, and D. Mountcastle. "Student (Mis)application of Partial Differentiation to Material Properties." Paper presented at the Physics Education Research Conference 2006, Syracuse, New York, July 26-27, 2006.</a>
AIP Format
B. Bucy, J. Thompson, and D. Mountcastle, , presented at the Physics Education Research Conference 2006, Syracuse, New York, 2006, WWW Document, (https://www.compadre.org/Repository/document/ServeFile.cfm?ID=5262&DocID=2101).
AJP/PRST-PER
B. Bucy, J. Thompson, and D. Mountcastle, Student (Mis)application of Partial Differentiation to Material Properties, presented at the Physics Education Research Conference 2006, Syracuse, New York, 2006, <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=5262&DocID=2101>.
APA Format
Bucy, B., Thompson, J., & Mountcastle, D. (2006, July 26-27). Student (Mis)application of Partial Differentiation to Material Properties. Paper presented at Physics Education Research Conference 2006, Syracuse, New York. Retrieved December 5, 2024, from https://www.compadre.org/Repository/document/ServeFile.cfm?ID=5262&DocID=2101
Chicago Format
Bucy, B, J. Thompson, and D. Mountcastle. "Student (Mis)application of Partial Differentiation to Material Properties." Paper presented at the Physics Education Research Conference 2006, Syracuse, New York, July 26-27, 2006. https://www.compadre.org/Repository/document/ServeFile.cfm?ID=5262&DocID=2101 (accessed 5 December 2024).
MLA Format
Bucy, Brandon, John Thompson, and Donald Mountcastle. "Student (Mis)application of Partial Differentiation to Material Properties." Physics Education Research Conference 2006. Syracuse, New York: 2006. 157-160 Vol. 883 of PER Conference. 5 Dec. 2024 <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=5262&DocID=2101>.
BibTeX Export Format
@inproceedings{
Author = "Brandon Bucy and John Thompson and Donald Mountcastle",
Title = {Student (Mis)application of Partial Differentiation to Material Properties},
BookTitle = {Physics Education Research Conference 2006},
Pages = {157-160},
Address = {Syracuse, New York},
Series = {PER Conference},
Volume = {883},
Month = {July 26-27},
Year = {2006}
}
Refer Export Format
%A Brandon Bucy %A John Thompson %A Donald Mountcastle %T Student (Mis)application of Partial Differentiation to Material Properties %S PER Conference %V 883 %D July 26-27 2006 %P 157-160 %C Syracuse, New York %U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=5262&DocID=2101 %O Physics Education Research Conference 2006 %O July 26-27 %O application/pdf
EndNote Export Format
%0 Conference Proceedings %A Bucy, Brandon %A Thompson, John %A Mountcastle, Donald %D July 26-27 2006 %T Student (Mis)application of Partial Differentiation to Material Properties %B Physics Education Research Conference 2006 %C Syracuse, New York %V 883 %P 157-160 %S PER Conference %8 July 26-27 %U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=5262&DocID=2101 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 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. Student (Mis)application of Partial Differentiation to Material Properties:Know of another related resource? Login to relate this resource to it. |
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