Smith, Christensen, Mountcastle, and Thompson on entropy, heat engines, and the Carnot cycle

Trevor I. Smith, Warren M. Christensen, Donald B. Mountcastle, and John R. Thompson

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

Phys. Rev. ST Phys. Educ. Res. 11, 020116 – Published 23 September 2015

[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.

Clark, Thompson, and Mountcastle on PV diagrams in physics and engineering

J. W. Clark, J. R. Thompson, and D. B. Mountcastle
Investigating Student Conceptual Difficulties in Thermodynamics Across Multiple Disciplines: The First Law and P-V Diagrams
Proceedings of 121st ASEE (American Society for Engineering Education) Annual Conference and Exposition (2014).

Thermodynamics is a core part of the curriculum in physics and many engineering fields. While individual courses in each discipline appear to cover many of the same topics at some level, the emphasis, applications, and many representations are idiosyncratic to the field. Education researchers in both disciplines have studied thermodynamics learning and teaching. Physics education researchers have identified student difficulties with foundational concepts such as heat, temperature, and entropy as well as with larger grain-sized ideas such as state variables, path-dependent processes, etc.  Engineering education research shows analogous findings and has identified additional difficulties unique to engineering contexts, such as confusion between steady-state and equilibrium processes.
     An open question is the extent to which discipline-specific research findings apply across disciplines.  Previous work by us and our colleagues in physics education research has explored student difficulties with thermodynamics and statistical mechanics in upper-division physics courses.  We have recently broadened the scope of our own investigation to include mechanical and chemical engineering courses, to see whether similar difficulties are present in these disciplines and how certain instructional pedagogies may affect student learning.  At our institution, thermodynamics is not covered in the introductory physics course sequence, so for most students this is their first formal encounter with the topic.
     Our initial focus is on the First Law of Thermodynamics and its constituent elements, as this topic is fundamental to all the courses of interest.  We have administered hand-written, free- response questions to students at various points before and/or after instruction.  The questions discussed here require interpretation of graphical information about thermodynamic processes. We have coded responses according to student reasoning (e.g., area under the curve, time- related) provided in the data so as not to confine our understanding of student ideas  We find that most reasoning patterns are present in all disciplines although the frequency varies by discipline. Initial answering patterns are similar across disciplines with a high proportion of students responding with incorrect ideas.  The post-instruction patterns are improved but show persistence of some specific difficulties (e.g. work is path-independent).  These outcomes vary between courses and are consistent with disciplinary emphasis and individual instructional practice.

Smith, Thompson, and Mountcastle on the Boltzmann Factor

Trevor I. Smith, John R. Thompson, and Donald B. Mountcastle

Addressing Student Difficulties with Statistical Mechanics: The Boltzmann Factor

AIP Conf. Proc. -- October 24, 2010 -- Volume 1289, pp. 305-308
2010 PHYSICS EDUCATION RESEARCH CONFERENCE; doi:10.1063/1.3515230

As part of research into student understanding of topics related to thermodynamics and statistical mechanics at the upper division, we have identified student difficulties in applying concepts related to the Boltzmann factor and the canonical partition function. With this in mind, we have developed a guided-inquiry worksheet activity (tutorial) designed to help students develop a better understanding of where the Boltzmann factor comes from and why it is useful. The tutorial guides students through the derivation of both the Boltzmann factor and the canonical partition function. Preliminary results suggest that students who participated in the tutorial had a higher success rate on assessment items than students who had only received lecture instruction on the topic. We present results that motivate the need for this tutorial, the outline of the derivation used, and results from implementations of the tutorial. ©2010 American Institute of Physics

Smith, Christensen, Thompson on entropy, engines, and cycles

Trevor I. Smith Warren M. Christensen and John R. Thompson
Addressing Student Difficulties with Concepts Related to Entropy, Heat Engines and the Carnot Cycle
AIP Conf. Proc. -- November 5, 2009 -- Volume 1179, pp. 277-280
2009 PHYSICS EDUCATION RESEARCH CONFERENCE; doi:10.1063/1.3266735

We report the rationale behind and preliminary results from a guided-inquiry conceptual worksheet (a.k.a. tutorial) dealing with Carnot's efficiency and the Carnot cycle. The tutorial was administered in an upper-level thermodynamics course at the University of Maine. The tutorial was implemented as the third in a three-tutorial sequence designed to improve students' understanding of entropy and its applications. Initial pre- and post-tutorial assessment data suggest that student understanding of heat engines and the Carnot cycle improved as a result of tutorial instruction

Pollock, Thompson, and Mountcastle on Variables in PV diagrams

E.B. Pollock, J.R. Thompson, D.B. Mountcastle
Student Understanding of the Physics and Mathematics of Process Variables In P-V Diagrams
Physics Education Research Conference Proceedings 2007

Students in an upper-level thermal physics course were asked to compare quantities related to the First Law of Thermodynamics along with similar mathematical questions devoid of all physical context. We report on a comparison of student responses to physics questions involving interpretation of ideal gas processes on P-V diagrams and to analogous mathematical qualitative questions about the signs of and comparisons between the magnitudes of various integrals. Student performance on individual questions combined with performance on the paired questions shows evidence of isolated understanding of physics and mathematics. Some difficulties are addressed by instruction.

©2007 American Institute of Physics

AIP Conf. Proc. -- November 12, 2007 -- Volume 951, pp. 168-171
2007 PHYSICS EDUCATION RESEARCH CONFERENCE; DOI:10.1063/1.2820924

Mountcastle, Bucy, Thompson on Probability and Uncertainty

D.B. Mountcastle, B.R. Bucy, J.R. Thompson
Student Estimates of Probability and Uncertainty in Advanced Laboratory and Statistical Physics Courses
Physics Education Research Conference Proceedings 2007

Equilibrium properties of macroscopic systems are highly predictable as n, the number of particles approaches and exceeds Avogadro's number; theories of statistical physics depend on these results. Typical pedagogical devices used in statistical physics textbooks to introduce entropy (S) and multiplicity () (where S = k ln()) include flipping coins and/or other equivalent binary events, repeated n times. Prior to instruction, our statistical mechanics students usually gave reasonable answers about the probabilities, but not the relative uncertainties, of the predicted outcomes of such events. However, they reliably predicted that the uncertainty in a measured continuous quantity (e.g., the amount of rainfall) does decrease as the number of measurements increases. Typical textbook presentations assume that students understand that the relative uncertainty of binary outcomes will similarly decrease as the number of events increases. This is at odds with our findings, even though most of our students had previously completed mathematics courses in statistics, as well as an advanced electronics laboratory course that included statistical analysis of distributions of dart scores as n increased.

©2007 American Institute of Physics

AIP Conf. Proc. -- November 12, 2007 -- Volume 951, pp. 152-155
2007 PHYSICS EDUCATION RESEARCH CONFERENCE; DOI:10.1063/1.2820919

Bucy PhD: Thermo, Entropy, and Partial Differentials

Brandon R. Bucy
Investigations of Student Understanding of Entropy and of Mixed Second-Order Partial Derivatives in Upper-Level Thermodynamics
Unpublished Ph.D. dissertation, August 2007

Bucy, Thompson, Mountcastle on Partial Differentiation

B.R. Bucy, J.R. Thompson, D.B. Mountcastle
Student (Mis)application of Partial Differentiation to Material Properties
2006 Physics Education Research Conference Proceedings, edited by P. Heron, L. McCullough, and J. Marx, AIP Conference Proceedings 883, 157-160 (2007)

Bucy, Thompson, Mountcastle on Entropy

B.R. Bucy, J.R. Thompson, D.B. Mountcastle
What is Entropy? Advanced Undergraduate Performance Comparing Ideal Gas Processes
2005 Physics Education Research Conference Proceedings, edited by P. Heron, L. McCullough, and J. Marx, AIP Conference Proceedings 818, 77-80 (2006)

Thompson, Bucy, and Mountcastle on partial derivatives in thermo

J.R. Thompson, B.R. Bucy, D.B. Mountcastle
Assessing Student Understanding of Partial Derivatives in Thermodynamics
2005 Physics Education Research Conference Proceedings, edited by P. Heron, L. McCullough, and J. Marx, AIP Conference Proceedings 818, 77-80 (2006)