Temperature–pressure and thermal-caloric imperfections effects on Gibbs and Helmholtz free energies

The paper focuses on exploration the effects of thermal and caloric imperfections on Gibbs and Helmholtz free energies. Despite the complexity and theoretical challenges involved, previous studies have often overlooked this aspect especially when dealing with real gases. This work stands out by tackling the issue of interactions in gases using the accurate Berthelot state equation. The study introduces a framework for computation the change in Gibbs and Helmholtz energies in gases. This work builds upon relationships grounded in real gas theory offering a concept applicable under various conditions particularly at high pressures and temperatures. As a result, the behavior of real gases deviates from models leading to energy outcomes compared to high temperature or perfect gas models. In conclusion, we provide an error analysis that highlights discrepancies between gas models, high temperature models and the real gas model for each type of energy. When the relative error between the current model RG and previous models exceeds more than 20% at high pressures, this comparison serves to establish the limitations of perfect gas and high temperature models. The obtained results are very impressive. Serve as an inspiration to delve deeper into advanced thermodynamics especially in high pressure environments.