Investigations of student understanding of entropy and of mixed second-order partial derivatives in upper-level thermodynamics

While much of physics education research (PER) has traditionally been conducted in introductory undergraduate courses, researchers have begun to study student understanding of physics concepts at the upper-level. In this dissertation, we describe investigations conducted in advanced undergraduate thermodynamics courses. We present and discuss results pertaining to student understanding of two topics: entropy and the role of mixed second-order partial derivatives in thermodynamics.; Our investigations into student understanding of entropy consisted of an analysis of written student responses to researcher-designed diagnostic questions. Data gathered in clinical interviews is employed to illustrate and extend results gathered from written responses. The question sets provided students with several ideal gas processes, and asked students to determine and compare the entropy changes of these processes. We administered the question sets to students from six distinct populations, including students enrolled in classical thermodynamics, statistical mechanics, thermal physics, physical chemistry, and chemical engineering courses, as well as a sample of physics graduate students. Data was gathered both before and after instruction in several samples.; Several noteworthy features of student reasoning are identified and discussed. These features include student ideas about entropy prior to instruction, as well as specific difficulties and other aspects of student reasoning evident after instruction. As an example, students from various populations tended to emphasize either the thermodynamic or the statistical definition of entropy. Both approaches present students with a unique set of benefits as well as challenges.; We additionally studied student understanding of partial derivatives in a thermodynamics context. We identified specific difficulties related to the mixed second partial derivatives of a thermodynamic state function, based on an analysis of student responses to homework and exam problems. Students tended to set these partial derivatives identically equal to zero. Students also displayed difficulties in relating the physical description of a material property to a corresponding mathematical statement involving partial derivatives.; We describe the development of a guided-inquiry tutorial activity designed to address these specific difficulties. This tutorial focused on the graphical interpretation of partial derivatives. Preliminary results suggest that the tutorial was effective in addressing several student difficulties related to partial derivatives.