Investigating how graduate students connect microstates and macrostates with entropy

Abstract

As a first step in a larger study of student reasoning in upper-division thermal physics, we conducted thinkaloud interviews with 8 physics graduate students to probe their understanding of entropy. In this paper, we'll discuss results from a question which presented students with a novel system-a string in a bath of water-and asked students to rank the probabilities of particular arrangements of the string, define macrostates of the system, and discuss specifically what is meant by the entropy of the system. Exploring graduate students' understanding of entropy and their ability to solve problems and reason with entropic arguments will provide insights into how physicists develop a mature understanding of entropy as a physical quantity. We find a tendency for graduate students to project properties of macrostates onto constituent microstates, and discuss other observations. We identify connections to previous research and lay out the next steps for this project.

Comparing undergraduate and graduate student reasoning on a conceptual entropy questionnaire

“…This reasoning echos our prior observation that multiple graduate students appeared to project macrostate characteristics onto constituent microstates [6].…”

“…Some graduates appeared to project the likelihood of a macrostate on to constituent microstates, and some appeared to conflate macrostates with macroscopic objects. Throughout the question few graduate students related entropy with disorder, and half did not conceptually connect entropy with multiplicity [6].…”

“…1 by the intuitive ranking. Though, after considering part B of the question, many graduate students migrated to the correct answer (in total, six of the graduates settled on the correct ranking), and none settled on the intuitive ranking [6]. Three out of the ten undergraduates changed their answer, with two settling on the intuitive ranking.…”

“…Our goals for this research are to expand the literature on student reasoning in thermal physics by focusing on the microscopic perspective of entropy and the connection between entropy and probability which has received little attention within PER [5], and to provide a pseudo-longitudinal per- spective on student reasoning through a comparison of undergraduate and graduate student reasoning. This research follows a study on graduate student reasoning on entropy and related concepts [6,7]. We presented undergraduates with the same set of questions previously posed to graduate students, and this article focuses on part of the interview involving a system of a neutrally buoyant string waving in a bath of water-the same section of the interview discussed in our prior article on graduate student reasoning [6].…”

“…This research follows a study on graduate student reasoning on entropy and related concepts [6,7]. We presented undergraduates with the same set of questions previously posed to graduate students, and this article focuses on part of the interview involving a system of a neutrally buoyant string waving in a bath of water-the same section of the interview discussed in our prior article on graduate student reasoning [6]. In this system the microstates are directly visible, and conceptualizing the macrostates requires more abstraction.…”