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

[This paper is part of the Focused Collection on Upper Division Physics Courses.] We report on several specific student difficulties regarding the second law of thermodynamics in the context of heat engines within upper-division undergraduate 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.

Figure 1

The engine entropy question (EEQ). Administered after lecture instruction and again after tutorial instruction.

Figure 2

Response frequencies on the EEQ pretest at (a) school 1 ($N=32$), (b) school 2 ($N=38$), and (c) school 1 and school 2 Combined ($N=70$). Green diagonally striped bars indicate students who used correct reasoning. Only four students (two from each school) answered all four parts of the EEQ using correct reasoning. The “Carnot” labels refer to questions about the Carnot engine, the “Better” labels refer to the questions about an engine that is (supposedly) more efficient than the Carnot engine, the “Uni” labels refer to questions regarding the change in entropy of the universe, and the “WS” labels refer to questions regarding the change in entropy of the working substance.

Figure 3

The finite reservoirs question (FRQ). Designed based on Carter’s problem 7.8 [8] and Baierlein’s problem 3.6 [37]. Given as a homework assignment in Thermo and in Stat Mech.