Document Type
Article
Publication Title
Physical Review Special Topics – Physics Education Research
Publisher
American Institute of Physics
Publication Date
9-23-2015
Publication Number
020123
Volume Number
11
Abstract/ Summary
We present results of our investigation into student understanding of the physical significance and utility of the Boltzmann factor in several simple models. We identify various justifications, both correct and incorrect, that students use when answering written questions that require application of the Boltzmann factor. Results from written data as well as teaching interviews suggest that many students can neither recognize situations in which the Boltzmann factor is applicable nor articulate the physical significance of the Boltzmann factor as an expression for multiplicity, a fundamental quantity of statistical mechanics. The specific student difficulties seen in the written data led us to develop a guided-inquiry tutorial activity, centered around the derivation of the Boltzmann factor, for use in undergraduate statistical mechanics courses. We report on the development process of our tutorial, including data from teaching interviews and classroom observations of student discussions about the Boltzmann factor and its derivation during the tutorial development process. This additional information informed modifications that improved students’ abilities to complete the tutorial during the allowed class time without sacrificing the effectiveness as we have measured it. These data also show an increase in students’ appreciation of the origin and significance of the Boltzmann factor during the student discussions. Our findings provide evidence that working in groups to better understand the physical origins of the canonical probability distribution helps students gain a better understanding of when the Boltzmann factor is applicable and how to use it appropriately in answering relevant questions.
Repository Citation
T.I. Smith, D.B. Mountcastle, and J.R. Thompson, “Student understanding of the Boltzmann factor,” Phys. Rev. ST Phys. Educ. Res. 11, 020123 (2015).
Citation/Publisher Attribution
T.I. Smith, D.B. Mountcastle, and J.R. Thompson, “Student understanding of the Boltzmann factor,” Phys. Rev. ST Phys. Educ. Res. 11, 020123 (2015).
DOI
10.1103/PhysRevSTPER.11.020123
Version
publisher's version of the published document
Creative Commons License
This work is licensed under a Creative Commons Attribution 4.0 International License.
Included in
Science and Mathematics Education Commons, Statistical, Nonlinear, and Soft Matter Physics Commons