Extended thermodynamics for dense gases up to whatever order

•Entropy Principle, symmetry conditions and Galilean Invariance up to whatever order.•Second order expressions in the physical variables.•We change variables from the Lagrange multipliers to the physical variables.•At first order our results are the same known in literature.•At second order they are completely new.

The 14 moments model for dense gases, introduced in the last years by Arima, Taniguchi Ruggeri, Sugiyama, is here considered. They have found the closure of the balance equations up to second order with respect to equilibrium; here the closure is found up to whatever order with respect to equilibrium, but for a more constrained system where more symmetry conditions are imposed and this in agreement with the suggestion of the kinetic theory. The results, when restricted at second order with respect to equilibrium, are the same of the previously cited model but under the further restriction of full symmetries.