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A recent 15 moments relativistic model of extended thermodynamics for polyatomic gases is here considered; it is based on a new hierarchy of moments that takes into account the total energy, i.e., the rest energy and the energy of the molecular internal mode. The classical limit was there studied but only for the equations in integral form. However, after that, these equations were manipulated to obtain the closure up to first order with respect to equilibrium but expressed in terms of physical variables. Therefore, it is necessary to perform the non relativistic limit also of the resulting final closure and compare it with the known results concerning the classical case. This goal is realized in the present article. Another result here obtained is the expansions of the scalar coefficients appearing in the closure as finite polynomials in  where c is the light speed. The characteristic equations for determining the wave velocities are here deducted also for the subsystems with 5 moments (Euler equations), and with 6 or 14 moments. All the present results holds in the non polytropic case; the polytropic case is obtained only as a subcase. 

relativistic extended thermodynamics, rarefied polyatomic gas, non relativistic limit.