Teaching Differentials in Thermodynamics using Spatial Visualization

TL;DR

This paper explores how spatial visualization can help students understand the total differential and cyclic rules in thermodynamics by providing geometric interpretations, addressing common mathematical difficulties in thermodynamics education.

Contribution

It introduces geometric interpretations of differential rules in thermodynamics to improve student comprehension through spatial visualization techniques.

Findings

Enhanced understanding of differential rules through visualization

Geometric explanations improve student problem-solving skills

Potential for improved thermodynamics teaching methods

Abstract

The greatest difficulty that is encountered by students in Thermodynamics classes is to find relationships between variables and solve a total differential equation that relates one thermodynamic state variable to two mutually-independent state variables. Rules of differentiation, including the total differential and the cyclic rule, are fundamental to solving thermodynamics problems. However, many students do not understand such basic mathematics principles, because ordinary calculus and thermodynamics textbooks do not provide specific geometric explanations for the differential rules. Spatial visualization allows students to develop a new line of reasoning. In this investigation, the total differential rule and the cyclic rule are interpreted geometrically.