This paper presents the heat and mass transfer model and the design analysis of ALCHEMIST (Atmospheric Laboratory for the study of Circulation at High-altitude, Exchange of Markers and Intercontinental routes between Stratosphere and Troposphere). It is an innovative hybrid balloon project. It is constituted by coupling an external unconventional parachute envelope and a Hydrogen balloon. The dynamic equilibrium conditions with the surrounding atmosphere are considered. The system has been modeled as a limited unsteady irreversible thermodynamic living system. The mission is considered as an evolution of the system in equilibrium with the surrounding environment. Hence, a thermodynamic model based on irreversible thermodynamics is presented. The results according to both first and second law are produced and compared to actual flight data. The primary physical processes responsible for balloon performance aloft are accurately modeled in the proposed optimization process. The results demonstrate that the system could be optimized up to a stratospheric altitude around 30 km and shows that second law optimization produces an effective performance improvement.