A visual and intuitive approach to teaching and learning the concept of thermodynamic entropy

Abstract

We all experience entropy and Thermodynamics in day-to-day life, whether or not we recognize it. To some extent, most people have a somewhat intuitive knowledge regarding the interaction and transfer of energy. Despite this, many students struggle with Thermodynamics in classroom settings. The equations and mathematics can be overwhelming and frustrating, in part because it is often hard to visualize thermodynamic interactions. This is especially true for the concept of entropy, which many consider to be one of the toughest thermodynamic principles to comprehend. Today's students have a plethora of distractions available to them. If students feel bored or frustrated with the material, oftentimes they will browse the Internet on their laptops or pull out their phones to entertain themselves. They learn differently, more intuitively, experiencing short attention spans. Therefore, the material and presentation methods should be clear, intuitive and engaging. The primary focus of this paper is to help students to understand, and instructors to explain, the fundamental concept of entropy at the macro level by utilizing intuitive and example-based approaches. This paper seeks to cut through the volumes worth of material written on the subject in order to simplify the topic of entropy to something that is clear and easy to understand. To accomplish this, the paper contributes by (1) introducing examples of spontaneous processes that most people should already understand, (2) providing a brief review of the general operations of heat engines and the Carnot cycle, (3) framing the Carnot cycle in relation to entropy, (4) discussing non-ideal heat engines, (5) showing analogies to help the reader understand the significance of the ratio Q/T as a definition for entropy, (6) adding some brief notes on entropy that are beyond the general scope of this paper, and (7) presenting brainteasers designed to engage students in the classroom. We relate these examples to the idea of the Carnot cycle and to some quantitative formulas. The point of this approach is to provide students with examples that translate textbook explanations to real life and help in comprehension of the material. We believe that when using these intuitive examples students tend to better understand the concept of entropy. This paper should be considered as reporting on work in progress. The presented information is meant to be supplemental in nature and not to replace existing textbooks or other teaching and learning methodologies. The work in this paper has been presented to 35 students in a Thermodynamics classroom setting. Following the presentation, it has been assessed and received very positive feedback. This visual, intuitive and engaging approach to teaching and learning has also been tested in the past for topics in Statics (explaining center of gravity), Calculus (explaining integration and explaining derivation by chain, product, and quotient rules), Differential Equations, Control Systems, Digital Signal Processing, Newton's Laws of Motion, and Computer Algorithms. In all of these cases, students highly praised the approach and found it to be very effective for learning.