Identifying student difficulties with entropy, heat engines, and the Carnot cycle

Abstract

We report on several specific student difficulties regarding the Second Law of Thermodynamics in the context of heat engines within upper-division undergraduates thermal physics courses. Data come from ungraded written surveys, graded homework assignments, and videotaped classroom observations of tutorial activities. Written data show that students in these courses do not clearly articulate the connection between the Carnot cycle and the Second Law after lecture instruction. This result is consistent both within and across student populations. Observation data provide evidence for myriad difficulties related to entropy and heat engines, including students' struggles in reasoning about situations that are physically impossible and failures to differentiate between differential and net changes of state properties of a system. Results herein may be seen as the application of previously documented difficulties in the context of heat engines, but others are novel and emphasize the subtle and complex nature of cyclic processes and heat engines, which are central to the teaching and learning of thermodynamics and its applications. Moreover, the sophistication of these difficulties is indicative of the more advanced thinking required of students at the upper division, whose developing knowledge and understanding give rise to questions and struggles that are inaccessible to novices.

Investigating how graduate students connect microstates and macrostates with entropy

“…In 2015, Dreyfus [1] thoroughly catalogued and summarized prior research on student learning in thermodynamics and statistical mechanics across the disciplines of physics, chemistry, and biology. Current PER literature on upperdivision thermal physics is limited, and work specifically related to entropy has mostly explored its thermodynamic and macroscopic contexts such as ideal gases [2], heat engines [3], thermal equilibrium [4], and the 2 nd law [5,6]. Other research from across the natural sciences also has addressed students' understanding of entropy [7][8][9][10].…”

Designing upper-division thermal physics assessment items informed by faculty perspectives of key content coverage

“…Several studies across these disciplines have found students have particular difficulties distinguishing between heat and temperature [12][13][14]. Other investigations have looked at student difficulties with entropy [15][16][17][18], appropriate applications of the ideal gas law [19,20], and energy in the context of the first law of thermodynamics [21,22]. Most of these studies have investigated student conceptual understanding in the realm of introductory thermodynamics content, mainly at the high school and introductory-college level [5].…”

“…Some researchers have investigated student reasoning in thermal physics through interviews, reviews of student coursework, or conceptual assessments, while others have utilized tutorials. In particular, Smith et al created tutorials to investigate student reasoning using the Boltzmann factor to compare relative probabilities of states [23] and to address students' conceptions of entropy when approaching Carnot cycles [15]. We utilized a subset of questions from these tutorials to inform item development for our assessment.…”

Editorial: Focused Collection: PER in Upper-Division Physics Courses

“…Members of the University of Maine Physics Education Research Laboratory and former members of the group who are now collaborating faculty from Rowan University and North Dakota State University contributed two articles on empirical research of student thinking as well as on the development of curricular materials for upper level thermodynamics statistical mechanics. One article, by Smith et al [36] presents evidence from written work and interviews of persistent student difficulties with heat engines and the second law. The second article by Smith, Mountcastle, and Thompson [37] focuses on student understanding of the Boltzmann factor and its connections to multiplicity and entropy.…”