Abstract. In this paper, novel models of the internal energy variation ΔU and the work W were investigated numerically using FORTRAN software. These are currently developed by employing a real gas theory represented by Berthelot state equation, which allows appearing the thermal and caloric imperfections. As opposed to past methodologies and models, it was observed that the new form of internal energy variation ΔU and the work W are exceptionally simple to use at any condition, especially critical to figure the adjustment of the internal energy variation ΔU and the work W when they fluctuates with pressure, it was previously difficult to obtain. This work is based on high theoretical development and strong numerical methods, furthermore, usually solves more accurate results and a higher speed of convergence. Applications of thermodynamics and physics to a variety of worked examples, especially the computation remains difficult in most fields, but with this study we extend the calculation whatever the circumstances. The comparison of error between the current model, which is based on real gas theory, and the PG model presents that the pressure-temperature combinations and the thermal-caloric imperfections effects play a significant role, and the error can reach up to 20%.

Key words: internal energy, work, high temperatures, high pressures, computational thermodynamics, real gas model, thermal and caloric imperfections.