Assessing Student Understanding of Partial Derivatives in Thermodynamics

We are engaged in a research project to study teaching and learning in upper-level thermal physics courses. We have begun to explore student functional understanding of mathematical concepts when applied in thermal physics contexts. We report here preliminary findings associated with partial differentiation and the Maxwell relations, which equate mixed second partial derivatives of various state functions. Our results suggest that students are often unable to apply the appropriate mathematical concepts and operations to the physical situations encountered in the course, despite having taken the prerequisite mathematics courses.