- Physical Review Journals
All JournalsPhysics Magazine

Physical Review Physics Education Research

Reuse & Permissions

It is not necessary to obtain permission to reuse this article or its components as it is available under the terms of the Creative Commons Attribution 4.0 International license. This license permits unrestricted use, distribution, and reproduction in any medium, provided attribution to the author(s) and the published article's title, journal citation, and DOI are maintained. Please note that some figures may have been included with permission from other third parties. It is your responsibility to obtain the proper permission from the rights holder directly for these figures.

Export citation

Export citation

Choose format for download:

Download Citation
  • Open Access

Exploring student reasoning in statistical mechanics: Identifying challenges in problem-solving groups

Ebba Koerfer* and Bor Gregorcic

  • Department of Physics and Astronomy, Uppsala University, Box 516, SE-751 20 Uppsala, Sweden

  • *ebba.koerfer@physics.uu.se
PDF

Phys. Rev. Phys. Educ. Res. 20, 010105 – Published 12 February, 2024

DOI: https://doi.org/10.1103/PhysRevPhysEducRes.20.010105

Abstract

Statistical mechanics has received limited attention in physics education research and remains a relatively underrepresented topic even in research on upper-division physics courses. The purpose of this study was to explore potential challenges that physics students encounter when they solve statistical mechanics problems in groups. Adopting a grounded approach, we video recorded and analyzed nine small student groups engaging in collaborative problem solving on the topic. The analysis involved iterative thematic coding, which gave rise to ten emergent categories of challenges. These were later divided into two broad groupings: challenges with concepts and challenges with problem-solving strategies. In the first grouping, we list seven identified categories related to the concepts of macrostates and microstates, distinguishable and indistinguishable particles, temperature, entropy, energy, equilibrium, heat bath, the Boltzmann distribution, and the partition function. In the second grouping, we list three categories related to the inappropriate application of common relations, difficulty managing tensions between calculated results and qualitative reasoning, and coming up with definitions of new and inconsistent concepts. Some of our findings are supported by existing research on the topic, and others are previously unreported. Based on our findings, we propose that future research should investigate the relations between the identified challenges on one hand, and students’ epistemological framing, reasoning, and use of multiple representations on the other. Finally, we suggest that teachers should spend time engaging students in a conceptual discussion of the central ideas of statistical mechanics, motivating the choice and pointing out limitations of commonly used toy models, and linking course content to real-world phenomena.

View figure in article

Physics Subject Headings (PhySH)

Article Text

References (49)

  1. D. V. Schroeder, An Introduction to Thermal Physics (OUP Oxford, Oxford, 2021).
  2. B. W. Dreyfus, B. D. Geller, D. E. Meltzer, and V. Sawtelle, Resource letter TTSM-1: Teaching thermodynamics and statistical mechanics in introductory physics, chemistry, and biology, Am. J. Phys. 83, 5 (2015).
  3. W. M. Christensen, D. E. Meltzer, and C. A. Ogilvie, Student ideas regarding entropy and the second law of thermodynamics in an introductory physics course, Am. J. Phys. 77, 907 (2009).
  4. T. I. Smith, W. M. Christensen, D. B. Mountcastle, and J. R. Thompson, Identifying student difficulties with entropy, heat engines, and the Carnot cycle, Phys. Rev. ST Phys. Educ. Res. 11, 020116 (2015).
  5. B. R. Bucy, J. R. Thompson, and D. B. Mountcastle, What is entropy? Advanced undergraduate performance comparing ideal gas processes, AIP Conf. Proc. 818, 81 (2006).
  6. 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).
  7. T. J. Bing and E. F. Redish, Epistemic complexity and the journeyman-expert transition, Phys. Rev. ST Phys. Educ. Res. 8, 010105 (2012).
  8. D. E. Meltzer, Observations of general learning patterns in an upper-level thermal physics course, AIP Conf. Proc. 1179, 31 (2009).
  9. D. B. Mountcastle, B. R. Bucy, and J. R. Thompson, Student estimates of probability and uncertainty in Advanced Laboratory and Statistical Physics Courses, AIP Conf. Proc. 951, 152 (2007).
  10. T. I. Smith, D. B. Mountcastle, and J. R. Thompson, Identifying student difficulties with conflicting ideas in statistical mechanics, AIP Conf. Proc. 1513, 386 (2013).
  11. T. I. Smith, J. R. Thompson, and D. B. Mountcastle, Student understanding of Taylor series expansions in statistical mechanics, Phys. Rev. ST Phys. Educ. Res. 9, 020110 (2013).
  12. M. E. Loverude, Student understanding of basic probability concepts in an Upper-Division Thermal Physics Course, AIP Conf. Proc. 1179, 189 (2009).
  13. M. E. Loverude, Investigating student understanding for a statistical analysis of two thermally interacting solids, AIP Conf. Proc. 1289, 213 (2010).
  14. M. E. Loverude, Identifying student resources in reasoning about entropy and the approach to thermal equilibrium, Phys. Rev. ST Phys. Educ. Res. 11, 020118 (2015).
  15. R. Leinonen, M. A. Asikainen, and P. E. Hirvonen, Grasping the second law of thermodynamics at university: The consistency of macroscopic and microscopic explanations, Phys. Rev. ST Phys. Educ. Res. 11, 020122 (2015).
  16. N. Erceg, I. Aviani, V. Mešić, M. Glunčić, and G. Žauhar, Development of the kinetic molecular theory of gases concept inventory: Preliminary results on university students’ misconceptions, Phys. Rev. Phys. Educ. Res. 12, 020139 (2016).
  17. N. Crossette, M. Vignal, and B. R. Wilcox, Investigating graduate student reasoning on a conceptual entropy questionnaire, Phys. Rev. Phys. Educ. Res. 17, 020119 (2021).
  18. K. D. Rainey, M. Vignal, and B. R. Wilcox, Designing upper-division thermal physics assessment items informed by faculty perspectives of key content coverage, Phys. Rev. Phys. Educ. Res. 16, 020113 (2020).
  19. K. D. Rainey, M. Vignal, and B. R. Wilcox, Validation of a coupled, multiple response assessment for upper-division thermal physics, Phys. Rev. Phys. Educ. Res. 18, 020116 (2022).
  20. J. Haglund, S. Andersson, and M. Elmgren, Language aspects of engineering students’ view of entropy, Chem. Educ. Res. Pract. 17, 489 (2016).
  21. J. Haglund, Good use of a ‘Bad’ Metaphor: Entropy as disorder, Sci. Educ. 26, 205 (2017).
  22. W. C. H. Lo, Student understanding of statistical mechanics, Ph.D. thesis, North Carolina State University, NC, 2022.
  23. M. E. Loverude and B. S. Ambrose, Editorial: Focused collection: PER in Upper-Division Physics Courses, Phys. Rev. ST Phys. Educ. Res. 11, 020002 (2015).

  24. We identified a few cases where student groups were considered in the context of statistical mechanics content. Students were interviewed individually or in groups in Ref. [10] as well as in Ref. [11], the latter also considered videotapes of small student groups working on a tutorial together.

  25. E. Koerfer, Student intuitions in statistical mechanics [Student project, Uppsala University (2022)].
  26. E. Koerfer and B. Gregorcic, Student Intuitions in Statistical Mechanics [Conference presentation abstract], GIREP 2022 Effective Learning in Physics from Contemporary Physics to Remote Settings, Ljubljana (2022).
  27. F. Mandl, Statistical Physics, The Manchester Physics Series (Wiley, Chichester, 1987), 2nd ed.

  28. While some examples appear to be exceptions to this, like the seemingly continuous energy range of a knocked out electron from an ionized atom, the system can always be forced to have discrete states by enclosing it in a finite volume. This is comparable to limiting the length of a waving string to a finite value. The general waveform is then described by a Fourier series with discrete harmonic modes rather than a Fourier integral [27].

  29. F. Reif, Fundamentals of Statistical and Thermal Physics (McGraw-Hill, New York, 1965).
  30. C. Kittel and H. Kroemer, Thermal Physics (W.H. Freeman, San Francisco, CA, 1980), 2nd ed.
  31. T. A. Moore and D. V. Schroeder, A different approach to introducing statistical mechanics, Am. J. Phys. 65, 26 (1997).
  32. J. J. Sakurai, Modern quantum mechanics (Addison-Wesley, Reading, MA, 2011), 2nd ed.
  33. B. Glaser and A. Strauss, Discovery of Grounded Theory: Strategies for Qualitative Research (Routledge, New York, 2017).
  34. S. Booth and F. Marton, Learning and Awareness (Routledge, New York, 1997).
  35. V. Braun and V. Clarke, Thematic analysis, in APA Handbook of Research Methods in Psychology, Vol. 2: Research Designs: Quantitative, Qualitative, Neuropsychological, and Biological, APA Handbooks in Psychology® (American Psychological Association, Washington, DC, 2012), pp. 57–71.
  36. K. A. Ericsson and H. A. Simon, How to study thinking in everyday life: Contrasting think-aloud protocols with descriptions and explanations of thinking, Mind Cult. Act. 5, 178 (1998).
  37. D. W. Johnson and R. T. Johnson, Learning Together and Alone: Cooperative, Competitive, and Individualistic Learning (Prentice-Hall, Inc, Englewood Cliffs, NJ, 1987), 2nd ed.

  38. One example in the literature defines a new term (the distribution), something between a macrostate and microstate, for a particular system such as this one. It says how many particles are in each energy state but not which ones they are; this latter information is given by the microstate [39].

  39. D. Trevena, 2—some basic ideas, in Statistical Mechanics (Elsevier Ltd., New York, 2002), pp. 5–17.
  40. D. Hammer, Student resources for learning introductory physics, Am. J. Phys. 68, S52 (2000).

  41. These are the students’ own words, we will not define intuition here but we discuss how it has been defined in the literature in Sec. 5, and we note that it is potentially interesting for future studies.

  42. B. D. Geller, B. W. Dreyfus, J. Gouvea, V. Sawtelle, C. Turpen, and E. F. Redish, Entropy and spontaneity in an introductory physics course for life science students, Am. J. Phys. 82, 394 (2014).
  43. D. Hammer, A. Elby, R. E. Scherr, and E. F. Redish, Resources, framing, and transfer, in Transfer of Learning from a Modern Multidisciplinary Perspective (Information Age Publishing, Greenwich, CT, 2005), pp. 89–119.
  44. T. J. Bing and E. F. Redish, Analyzing problem solving using math in physics: Epistemological framing via warrants, Phys. Rev. ST Phys. Educ. Res. 5, 020108 (2009).
  45. A. J. Richards, D. C. Jones, and E. Etkina, How students combine resources to make conceptual breakthroughs, Res. Sci. Educ. 50, 1119 (2020).
  46. C. R. Samuelsson, Resourceful students: Engaging students in active and systematic investigations in laboratories involving thermal phenomena, Ph.D. thesis, Uppsala University, 2023.
  47. J. Airey and C. Linder, Social semiotics in university physics education, in Multiple Representations in Physics Education, edited by D. F. Treagust, R. Duit, and H. E. Fischer, Models and Modeling in Science Education (Springer International Publishing, Cham, 2017), pp. 95–122.
  48. V. Talanquer, Chemistry education: Ten heuristics to tame, J. Chem. Educ. 91, 1091 (2014).
  49. M. Kryjevskaia, P. R. L. Heron, and A. F. Heckler, Intuitive or rational? Students and experts need to be both, Phys. Today 74, No. 8, 28 (2021).

Outline

Information

Phys. Rev. Phys. Educ. Res. 20, 010105– Published 12 February, 2024
  • Received 6 November 2023
  • Accepted 9 January 2024
Crossmark - Check for updates button
Creative Commons Logo

Published by the American Physical Society under the terms of the Creative Commons Attribution 4.0 International license. Further distribution of this work must maintain attribution to the author(s) and the published article’s title, journal citation, and DOI.

Published by the American Physical Society

Sign In to Your Journals Account

Filter

Filter

Article Lookup

Enter a citation