The University of Maine DigitalCommons@UMaine Electronic Theses and Dissertations Fogler Library 2011 Identifying and Addressing Specific tudeS nt Difficulties in Advanced Thermal Physics Trevor I. Smith Follow this and additional works at: http://digitalcommons.library.umaine.edu/etd Part of the Educational Assessment, Evaluation, and Research Commons, and the Physics Commons Recommended Citation Smith, Trevor I., "Identifying and Addressing Specific tudeS nt Difficulties in Advanced Thermal Physics" (2011). Electronic Theses and Dissertations. 263. http://digitalcommons.library.umaine.edu/etd/263 This Open-Access Dissertation is brought to you for free and open access by DigitalCommons@UMaine. It has been accepted for inclusion in Electronic Theses and Dissertations by an authorized administrator of DigitalCommons@UMaine. IDENTIFYING AND ADDRESSING SPECIFIC STUDENT DIFFICULTIES IN ADVANCED THERMAL PHYSICS By Trevor I. Smith M.S.T. University of Maine, 2007 B.S. University of Maine, 2005 A DISSERTATION Submitted in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy (in Physics) The Graduate School The University of Maine May, 2011 Advisory Committee: John R. Thompson, Associate Professor of Physics, Advisor Donald B. Mountcastle, Associate Professor of Physics Michael C. Wittmann, Associate Professor of Physics Susan R. McKay, Professor of Physics Natasha M. Speer, Assistant Professor of Mathematics DISSERTATION ACCEPTANCE STATEMENT On behalf of the Graduate Committee for Trevor I. Smith, I affirm that this manuscript is the final and accepted dissertation. Signatures of all committee mem- bers are on file with the Graduate School at the University of Maine, 42 Stodder Hall, Orono, Maine. Submitted for graduation in May, 2011 John R. Thompson, Associate Professor of Physics (Date) ii c 2011 Trevor I. Smith All Rights Reserved iii LIBRARY RIGHTS STATEMENT In presenting this dissertation in partial fulfillment of the requirements for an advanced degree at The University of Maine, I agree that the Library shall make it freely available for inspection. I further agree that permission for “fair use” copying of this thesis for scholarly purposes may be granted by the Librarian. It is understood that any copying or publication of this dissertation for financial gain shall not be allowed without my written permission. Trevor I. Smith (Date) IDENTIFYING AND ADDRESSING SPECIFIC STUDENT DIFFICULTIES IN ADVANCED THERMAL PHYSICS By Trevor I. Smith Dissertation Advisor: Dr. John R. Thompson An Abstract of the Dissertation Presented in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy (in Physics) May, 2011 As part of an ongoing multi-university research study on student understanding of concepts in thermal physics at the upper division, I identified several student difficulties with topics related to heat engines (especially the Carnot cycle), as well as difficulties related to the Boltzmann factor. In an effort to address these dif- ficulties, I developed two guided-inquiry worksheet activities (a.k.a. tutorials) for use in advanced undergraduate thermal physics courses. Both tutorials seek to im- prove student understanding of the utility and physical background of a particular mathematical expression. One tutorial focuses on a derivation of Carnot’s theorem regarding the limit on thermodynamic efficiency, starting from the Second Law of Thermodynamics. The other tutorial helps students gain an appreciation for the origin of the Boltzmann factor and when it is applicable; focusing on the physi- cal justification of its mathematical derivation, with emphasis on the connections between probability, multiplicity, entropy, and energy. Student understanding of the use and physical implications of Carnot’s theorem and the Boltzmann factor was assessed using written surveys both before and after tutorial instruction within the advanced thermal physics courses at the University of Maine and at other institutions. Classroom tutorial sessions at the University of Maine were videotaped to allow in-depth scrutiny of student successes and failures following tutorial prompts. I also interviewed students on various topics related to the Boltzmann factor to gain a more complete picture of their understanding and inform tutorial revisions. Results from several implementations of my tutorials at the University of Maine indicate that students did not have a robust understanding of these physical prin- ciples after lectures alone, and that they gain a better understanding of relevant topics after tutorial instruction; Fisher’s exact tests yield statistically significant improvement at the α = 0:05 level. Results from other schools indicate that dif- ficulties observed before tutorial instruction in our classes (for both tutorials) are not unique, and that the Boltzmann factor tutorial can be an effective replacement for lecture instruction. Additional research is suggested that would further examine these difficulties and inform instructional strategies to help students overcome them. IDENTIFYING AND ADDRESSING SPECIFIC STUDENT DIFFICULTIES IN ADVANCED THERMAL PHYSICS By Trevor I. Smith Dissertation Advisor: Dr. John R. Thompson A Lay Abstract of the Dissertation Presented in Partial Fulfillment of the Requirements for the Degree of Doctor of Philosophy (in Physics) May, 2011 Keywords: physics education research, thermodynamics, statistical mechanics, ad- vanced undergraduate, tutorials Physics education research (PER) is the study of how people think about, learn, understand, and teach topics in and related to physics. One goal of PER is to iden- tify student difficulties with a particular topic and to develop curricular materials to address these difficulties. Results in PER show that guided-inquiry worksheet activ- ities (a.k.a. tutorials) can be effective supplements to traditional lecture instruction in introductory physics classes. Recent research suggests that tutorials can also be useful within upper-division courses. I developed two tutorials for use within advanced undergraduate thermal physics courses. One tutorial improves students’ understanding of the relationship between heat engines (especially the Carnot cycle), entropy, and the Second Law of Ther- modynamics. Heat engines are an integral part of many thermodynamics courses, as they provide a practical scenario in which all three laws of thermodynamics must be considered. Carnot’s theorem is, in essence, a statement of the Second Law in the context of heat engines, but my results indicate that students do not make this connection. My tutorial helps students by guiding them through a derivation of Carnot’s theorem starting from a standard statement of the Second Law. My second tutorial helps students gain an appreciation for the physical and mathematical origin of the Boltzmann factor and when it is applicable. The Boltz- mann factor is a mathematical expression for the probability that a thermodynamic system has a certain energy. The Boltzmann factor may be used to determine many properties of the system and is, therefore, a cornerstone of statistical thermal physics. My results indicate that students often do not recognize situations in which the Boltzmann factor is appropriate, nor do they understand where this particular mathematical expression comes from. Results from implementing my tutorials within the advanced thermal physics courses at the University of Maine indicate that students gain a better understanding of relevant topics after tutorial instruction, compared to lectures alone. Results from other schools indicate that difficulties observed before tutorial instruction in our classes are not unique, and that the Boltzmann factor tutorial can be an effective replacement for lecture instruction. DEDICATION To my wife Ashley: for always supporting me. iv ACKNOWLEDGEMENTS Throughout my six years in grad school, and a total of ten years at the University of Maine, I’ve met and been helped by many different people (both personally and professionally). I’d like to take time to thank some of them. I sincerely apologize if I have left anyone out. First, however, I thank the National Science Foundation for funding this work under grants DUE-0817282, REC-0633951, and DRL-0633951. This support made my life a lot easier for the past four years. I also want to thank all of the students who have participated in my research. They have quite literally made this research possible and deserve credit for their efforts. And thank you for reading; otherwise my efforts to craft a coherent document would be wasted. I start the more personal acknowledgements by thanking my advisor, John Thompson, for all of his guidance and support throughout my doctoral work. The research I’ve conducted and curricular materials I’ve developed have been greatly enhanced by his input. He has provided me with the opportunity to collaborate with researchers all across the country and to travel to many different conferences to present, and get feedback on, my work. John has helped me strive to better my research through scrutiny and careful consideration. The hours spent one-on-one in his office (while seemingly tedious) were incredibly beneficial to my perspective on my research and my understanding of the “big picture” implications. Plus, he’s a pretty good guy (he has a nice singing voice, too). Thank you, John, for all of your help. Next I thank Don Mountcastle for checking my own understanding of the topics I was studying and allowing me nearly free rein in his courses. Don has always been a reality