Date of Award


Level of Access Assigned by Author

Campus-Only Thesis

Degree Name

Master of Science (MS)




John R. Thompson

Second Committee Member

Donald B. Mountcastle

Third Committee Member

Michael C. Wittmann


In this thesis we describe results from an ongoing investigation at the advanced undergraduate level of student understanding of various thermal physics concepts as well as the related mathematical concepts. This work focuses in particular on the concepts of thermodynamic work and internal energy changes during thermodynamic processes, as well as the mathematical concepts that are necessary to correctly answer physics questions pertaining to the First Law of Thermodynamics. This thesis is focused on student understanding of the physics and the mathematics which must be utilized in order to successfully answer physics questions pertaining to the First Law. We have analyzed and compared written responses to isomorphic questions, one in a physics context along with a nearly identical mathematical question devoid of all physical context. The physics questions involve interpretation of ideal gas processes on P- V diagrams, while the analogous qualitative mathematical questions ask about the signs of and comparisons between the magnitudes of various integrals. Research in physics education attributes incorrect student responses on physics questions to specific difficulties with physics concepts; however, it is possible that an incomplete understanding of the underlying mathematics may affect responses to physics questions. The purpose of the isomorphic question pairs is to allow us to better diagnose in which content area, physics or mathematics, the student difficulties originate. We collected data in Physical Thermodynamics (PHY 462), and from students in a third-semester calculus course (MAT 228) during the last week of instruction. This written data is supplemented by interview data from students before, during, and after their enrollment in PHY 462. The results of this study indicate that before explicit instruction on the First Law, student understanding of mathematical concepts can impact their performance on physics questions pertaining to thermodynamic work. Our investigation also identifies several incorrect mathematical reasoning strategies, such as symmetry and length of integration path, students employ when solving various integrals. These strategies provide an explanation for certain incorrect student responses to physics questions involving thermodynamic quantities. Some difficulties are addressed by instruction.