From Engines to Entropy: Connecting Second Thermodynamic Principle Formulations via Johnstone’s Triangle

The Second Thermodynamic Principle is conceptually complex and historically multifaceted, making it a challenge in science education. This paper employs Johnstone's Triangle—a model distinguishing macroscopic, Microscopic, and symbolic levels of representation—as a pedagogical framework to relate the three foundational interpretations of the Second Principle: Carnot's macroscopic efficiency limits, Boltzmann's statistical entropy, and Carathéodory's formal axiomatization. By aligning these formulations with Johnstone's levels, we propose a comprehensive educational strategy for fostering deep conceptual understanding in thermodynamics..