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We consider two possible ways, i.e., the Maxwellian Iteration and theChapman-Enskog Method, to recover Relativistic Ordinary Thermodynamics fromRelativistic Extended Thermodynamics of Polyatomic gases with N moments. Bothof these methods give the Eckart equations which are the relativistic versionof the Navier-Stokes and Fourier laws as a first iteration. However, thesemethods do not lead to the same expressions of the heat conductivity \chi, theshear viscosity \mu, and the bulk viscosity \nu which appear as coefficients inthe Eckart equations. In particular, we prove that the expressions of \chi,\mu, and \nu obtained via the Chapman-Enskog method do not depend on N , whilethose obtained through the Maxwellian Iteration depend on N . Moreover, we alsoprove that these two methods lead to the same results in the nonrelativisticlimit.

On two possible ways to recover Ordinary Thermodynamics from Extended Thermodynamics of Polyatomic gases