Extended Thermodynamics is the natural framework in which to study the physics of fluids, because it leads to symmetric hyperbolic systems of field laws, thus assuming important properties such as finite propagation speeds of shock waves and well posedness of the Cauchy problem. The closure of the system of balance equations is obtained by imposing the entropy principle and that of galilean relativity. If we take the components of the mean field as independent variables, these two principles are equivalent to some conditions on the entropy density and its flux. The method until now used to exploit these conditions, with the macroscopic approach, has not been used up to whatever order with respect to thermodynamical equilibrium. This is because it leads to several difficulties in calculations. Now these can be overcome by using a new method proposed recently by Pennisi and Ruggeri. Here we apply it to the 14 moments model. We will also show that the 13 moments case can be obtained from the present one by using the method of subsystems.
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