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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.
We describe a study on the conceptual difficulties faced by college students in understanding hydrodynamics of ideal fluids. This study was based on responses obtained in hundreds of written exams and oral interviews, which were held with first-year
We study the maximum efficiency of a Carnot cycle heat engine based on a small system. It is revealed that due to the finiteness of the system, irreversibility may arise when the working substance contacts with a heat bath. As a result, there is a wo
Entropy is one of the most basic concepts in thermodynamics and statistical mechanics. The most widely used definition of statistical mechanical entropy for a quantum system is introduced by von Neumann. While in classical systems, the statistical me
Knowledge of quantum mechanical systems is becoming more important for many science and engineering students who are looking to join the emerging quantum workforce. To better prepare a wide range of students for these careers, we must seek to develop
Recently, Zhang {em et al.} [PRA, {bf 75}, 062102 (2007)] extended Kieus interesting work on the quantum Otto engine [PRL, {bf 93}, 140403 (2004)] by considering as working substance a bipartite quantum system $AB$ composed of subsystems $A$ and $B$.