Developed a thermodynamics module for the HEPLean/PhysLean repository, focusing on ideal gas adiabatic relations and entropy-directed modeling. The work defined entropy for ideal gas processes and formally verified core adiabatic relationships using Lean, supporting more accurate simulations and educational use cases. The module’s modular and testable design, accompanied by clear documentation, established a foundation for future extensions and maintenance. By leveraging formal verification and thermodynamics expertise, the implementation improved the fidelity of ideal-gas adiabatic process modeling. No bug fixes were reported during this period, reflecting a focus on new feature development and robust, well-documented code contributions in Lean.