Entropy flux far from equilibrium in solids and in non viscous gases

Mongiovì, M. S. ; Peruzza, R. A.

Bollettino della Unione matematica italiana, Série 8, 7B (2004) no. 2, pp. 381-396

Résumé

One of the main question arising in Extended Thermodynamics concerns the physical meaning of the temperature far from equilibrium. Some authors define thermodynamic temperature $T_{th}$ the inverse of the coefficient linking the entropy flux with the heat flux. Other authors, instead, define non-equilibrium temperature $\theta$ the inverse of the partial derivative of entropy with respect to energy, at density and heat flux constant. The aim of this paper is to determine the expression of entropy flux in some materials when phenomena far from equilibrium are considered, using the formulation of Extended Thermodynamics which uses the Lagrange multipliers, known as Rational Extended Thermodynamics. The case of thermal propagation that occurs in low-temperature crystals and the case of non viscous gases subject to heating are considered. It is shown that the non-equilibrium temperature and the thermodynamic temperature not agree, except near equilibrium, when second order terms in $q_i$ can be neglected. Approximate expressions for $T_{th}$ and $\theta$ are determined in both cases.