Exploring the logical equivalence of the first and second laws of thermodynamics in heat engine cycles

This paper builds upon a 2024 IJMEE paper, which formally established the logical equivalence of the first and second laws of thermodynamics. Logical equivalence means that both laws are either true or false together; however, this does not imply that the laws are identical or necessarily derivable from one another. As stated in the 2024 paper, “… if we can know that the first and second laws are equivalent, then we should know.” Accordingly, the present work investigates how this equivalence informs our understanding of heat engine cycles. Through a truth table analysis and application to real and hypothetical heat engine cycles , this paper shows that a violation of one law necessitates the violation of the other, even if numerical calculations appear to suggest otherwise. Understanding this relationship not only clarifies the interconnectedness of the two laws but also provides students and educators with a valuable conceptual framework for analyzing thermodynamic systems. This insight enriches problem-solving strategies and reinforces the critical role of equilibrium and energy conservation in determining the feasibility of thermodynamic processes.