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
