Identifying student difficulties with conflicting ideas in statistical mechanics

Smith, Trevor I.; Mountcastle, Donald B.; Thompson, John R.

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Identifying student difficulties with conflicting ideas in statistical mechanics

written by Trevor I. Smith, Donald B. Mountcastle, and John R. Thompson

In statistical mechanics there are two quantities that directly relate to the probability that a system at a temperature fixed by a thermal reservoir has a particular energy. The density of states function is related to the multiplicity of the system and indicates that occupation probability increases with energy. The Boltzmann factor is related to the multiplicity of the reservoir and indicates that occupation probability decreases with energy. This seems contradictory until one remembers that a complete probability distribution is determined by the total multiplicity of the system and its surroundings, requiring the product of these two functions. We present evidence from individual and group interviews that students knew how each of these functions relates to multiplicity but did not recognize the need to combine the two to characterize the physical scenario.

Physics Education Research Conference 2012
Part of the PER Conference series
Philadelphia, PA: August 1-2, 2012
Volume 1513, Pages 386-389

download 334kb .pdf
Published: January 24, 2013

Subjects	Levels	Resource Types
Education Foundations - Alternative Conceptions Thermo & Stat Mech - Ensembles = Boltzmann Distribution = Density of States	- Upper Undergraduate	- Reference Material = Research study

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Access Rights:: Free access and
Available for purchase; A preprint of the work is available. A hard copy of the PERC 2012 proceedings is available for purchase from the AIP.
Restriction:: © 2012 American Institute of Physics
DOI:: 10.1063/1.4789733
NSF Number:: 0817282
PACSs:: 01.30.Cc; 01.40.Fk; 01.40.G-; 05.20.-y
Keywords:: Multiple Concepts, PERC 2012
Record Cloner:: Metadata instance created July 1, 2013 by Zachary Davis
Record Updated:: December 17, 2013 by Lyle Barbato
Last Update when Cataloged:: January 24, 2013
Other Collections:: The PER-Central

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<a href="https://www.compadre.org/portal/items/detail.cfm?ID=12859">Smith, T, D. Mountcastle, and J. Thompson. "Identifying student difficulties with conflicting ideas in statistical mechanics." Paper presented at the Physics Education Research Conference 2012, Philadelphia, PA, August 1-2, 2012.</a>

AIP Format

T. Smith, D. Mountcastle, and J. Thompson, , presented at the Physics Education Research Conference 2012, Philadelphia, PA, 2012, WWW Document, (https://www.compadre.org/Repository/document/ServeFile.cfm?ID=12859&DocID=3391).

AJP/PRST-PER

T. Smith, D. Mountcastle, and J. Thompson, Identifying student difficulties with conflicting ideas in statistical mechanics, presented at the Physics Education Research Conference 2012, Philadelphia, PA, 2012, <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=12859&DocID=3391>.

APA Format

Smith, T., Mountcastle, D., & Thompson, J. (2012, August 1-2). Identifying student difficulties with conflicting ideas in statistical mechanics. Paper presented at Physics Education Research Conference 2012, Philadelphia, PA. Retrieved May 1, 2025, from https://www.compadre.org/Repository/document/ServeFile.cfm?ID=12859&DocID=3391

Chicago Format

Smith, T, D. Mountcastle, and J. Thompson. "Identifying student difficulties with conflicting ideas in statistical mechanics." Paper presented at the Physics Education Research Conference 2012, Philadelphia, PA, August 1-2, 2012. https://www.compadre.org/Repository/document/ServeFile.cfm?ID=12859&DocID=3391 (accessed 1 May 2025).

MLA Format

Smith, Trevor I., Donald Mountcastle, and John Thompson. "Identifying student difficulties with conflicting ideas in statistical mechanics." Physics Education Research Conference 2012. Philadelphia, PA: 2012. 386-389 Vol. 1513 of PER Conference. 1 May 2025 <https://www.compadre.org/Repository/document/ServeFile.cfm?ID=12859&DocID=3391>.

BibTeX Export Format

@inproceedings{ Author = "Trevor I. Smith and Donald Mountcastle and John Thompson", Title = {Identifying student difficulties with conflicting ideas in statistical mechanics}, BookTitle = {Physics Education Research Conference 2012}, Pages = {386-389}, Address = {Philadelphia, PA}, Series = {PER Conference}, Volume = {1513}, Month = {August 1-2}, Year = {2012} }

Refer Export Format

%A Trevor I. Smith %A Donald Mountcastle %A John Thompson %T Identifying student difficulties with conflicting ideas in statistical mechanics %S PER Conference %V 1513 %D August 1-2 2012 %P 386-389 %C Philadelphia, PA %U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=12859&DocID=3391 %O Physics Education Research Conference 2012 %O August 1-2 %O application/pdf

EndNote Export Format

%0 Conference Proceedings %A Smith, Trevor I. %A Mountcastle, Donald %A Thompson, John %D August 1-2 2012 %T Identifying student difficulties with conflicting ideas in statistical mechanics %B Physics Education Research Conference 2012 %C Philadelphia, PA %V 1513 %P 386-389 %S PER Conference %8 August 1-2 %U https://www.compadre.org/Repository/document/ServeFile.cfm?ID=12859&DocID=3391

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