Thermodynamic relations between solid-material systems and thermal-fluid systems

Introductory engineering undergraduate students frequently struggle to comprehend the fundamental theories of thermodynamics in thermal-fluid systems due to an inability to visualize abstract transfers of work and heat between a system and its surroundings. In contrast, students typically find greater success conceptualizing material in introductory solid mechanics courses where they can physically see, touch, and visualize dimensional changes to structural members under a load. To bridge this gap, this manuscript introduces foundational thermodynamic relations through the tangible evaluation of stress and strain in incompressible solids. This mechanical analysis is then extrapolated to compressible solid systems under hydrostatic pressure, demonstrating how normal stresses and volumetric strains directly map to pressure and volume changes. Showing that the resulting energy equations derived from solid systems are identical to those traditionally used in thermal-fluid systems provides students with a clear, solid-energy-based visual bridge that strengthens their conceptual understanding of engineering thermodynamics.