Partial differentiation and the coefficient of thermal expansion: a multivariable calculus activity connecting with chemistry

AbstractWe describe the components and implementation of an activity for multivariable calculus featuring applications to the field of chemistry. This activity focuses on the isobaric thermal expansion coefficient found using partial differentiation of the volume of an ideal gas with respect to temperature as pressure is held constant. Broader goals of this activity include enhancing calculus conceptual understanding, encouraging further interdisciplinary study and exploration, and cultivating mathematicians and scientists with broader and deeper backgrounds.Keywords: Multivariable calculusapplicationchemistry activitycoefficient of thermal expansionpartial differentiationideal gasphysical chemistryDisclaimerAs a service to authors and researchers we are providing this version of an accepted manuscript (AM). Copyediting, typesetting, and review of the resulting proofs will be undertaken on this manuscript before final publication of the Version of Record (VoR). During production and pre-press, errors may be discovered which could affect the content, and all legal disclaimers that apply to the journal relate to these versions also. AcknowledgementsWe thank the Saint Michael’s College S-STEM Committee and PI Prof. Michael Larsen for support of this initiative.We are very appreciative of all of the detailed and helpful feedback provided by the referees and editors during the review process, which has significantly improved the article. This work was substantially funded by NSF-DUE 1742241. We acknowledge Prof. Barbara O’Donovan (Saint Michael’s Engineering Coordinator) for her helpful remarks on this paper and collaboration on the overall interdisciplinary initiative. We recognize Prof. William (Sandy) Karstens (from the Saint Michael’s Physics Department) for his insightful feedback on a later draft of this paper. We acknowledge Prof. Timothy Guasco (from the Millikin University Chemistry Department) for his valuable comments on some later versions of this paper. We also thank all of our students who provided feedback on these efforts. These students include members of our undergraduate classes and beta testers of earlier versions of our classroom materials.Additional informationNotes on contributorsGeorge AshlineGeorge Ashline received his B.S. in mathematics from St. Lawrence University, his M.S. in mathematics from the University of Notre Dame, and his Ph.D. in mathematics (value distribution theory) from the University of Notre Dame in 1994. He has taught at Saint Michael’s College since 1995. He is a participant in Project NExT, an MAA program created for new or recent Ph.D.’s in the mathematical sciences who are interested in improving the teaching and learning of undergraduate mathematics. He is also actively involved in professional development programs in mathematics for K-12 teachers.Bret FindleyBret Findley graduated from Willamette University with a B.A. in German and chemistry and received his Ph.D. in physical chemistry from Dartmouth College in 1998. He joined the faculty at Saint Michael’s College in 2001 where he teaches general, environmental, and physical chemistry. His research interests include photo-induced electron transfer, molecular spectroscopy, solvatochromism, and chemistry pedagogy. He is also very interested in encouraging students to study more mathematics.Mitchell AndreaMitchell Andrea is a D.M.D. Candidate at the University of Connecticut School of Dental Medicine. He plans to pursue a residency in periodontology after graduation. He graduated from Saint Michael’s College in 2022 with a major in Biochemistry and minors in Mathematics and Business Administration. His undergraduate research focused on creating connections between mathematics and chemistry through the development of exercises for undergraduate courses.Dylan WawruckDylan Wawruck was employed as a Laboratory Technician at the University of Connecticut, where he began work in June 2022. He is starting work in February of 2023 as an Analytical & Stability Associate Scientist at New Chapter, where he will help establish product expiration periods. He graduated from Saint Michael's College in 2022 with a major in chemistry and a minor in mathematics. Sometimes, you may find him using his background to work with spreadsheets devoted to topics such as health and nutrition in his free time.