  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.
