New results in extended thermodynamics

The subject of this thesis lays in the context of Extended Thermodynamics. The classical methodology to solve the system of balance equations, in E.T., leads to difficult calculations. Recently a new methodology has been proposed to overcome these difficulties and to have more elegant equations, easier to solve. During my PhD, I worked in the direction of proving that the new methodology can be applied to the many moments case, to materials different from ideal gases and also in the relativistic case and not only in the classical one; furthermore I have been able to find the exact solutions for many of these problems. After a brief introduction on Extended Thermodynamics, the new methodology will be shown, applied to the 5, the 13 and the 14 moments case for ideal gases. The last of these is a model obtained by Pennisi and myself. Afterwards I will show how we have applied the new methodology to dense gases and macromolecular fluids for the 13 and 14 moments case. After that I will present the results of my publications regarding the cases with an arbitrary but fixed number of moments for ideal gases, in the classical and in the relativistic context, and I will also show what happens when we consider their subsystems. Finally it will be considered a new kind of system of balance equations that is suggested from the non relativistic limit of the relativistic case.