Identifying student difficulties with conflicting ideas in statistical mechanics

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

doi:10.1063/1.4789733

Cited by 8 publications

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References 4 publications

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“…We have previously reported two related studies on students' understanding of Taylor series expansions [15] and the relationship between the Boltzmann factor and the density of states as expressions of multiplicity [61]. These results support our current claim that deriving the Boltzmann factor is subtle and complex, and a robust understanding of its physical meaning is not trivial.…”

Section: Summary and Implications For Future Worksupporting

confidence: 80%

Student understanding of the Boltzmann factor

Smith

Mountcastle

Thompson

2015

Phys. Rev. ST Phys. Educ. Res.

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[This paper is part of the Focused Collection on Upper Division Physics Courses.] 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.

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Section: Summary and Implications For Future Worksupporting

confidence: 80%

Student understanding of the Boltzmann factor

Smith

Mountcastle

Thompson

2015

Phys. Rev. ST Phys. Educ. Res.

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Student understanding of the first law and second law of thermodynamics

Brown

Singh

2021

Eur. J. Phys.

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We discuss common student difficulties with the first and second laws of thermodynamics found using a validated conceptual multiple-choice survey called the survey of thermodynamic processes and first and second laws suitable for introductory physics courses. The analysis of data from more than a thousand students using the validated survey at six different colleges in the US shows that not only introductory but also advanced physics students have many common difficulties with these concepts after traditional lecture-based instruction in relevant concepts. The findings of the common student difficulties with the first and second laws of thermodynamics discussed here can be useful for developing effective curricula and pedagogies in order to reduce student difficulties.

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