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.

Abstract (VO)

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.

Riassunto

Una delle principali questioni che sorge nella termodinamica estesa riguarda il significato fisico della temperatura lontano dall'equilibrio. Alcuni autori definiscono temperatura termodinamica $T_{th}$ il reciproco del coefficiente che lega il flusso di entropia e il flusso di calore. Altri autori, invece, definiscono temperatura di non-equilibrio $\theta$ il reciproco della derivata parziale dell'entropia rispetto all'energia a densità e flusso di calore costanti. Lo scopo fondamentale di questo lavoro è di determinare le espressioni complete del flusso di entropia in alcuni materiali quando vengono considerati fenomeni lontano dall'equilibrio termodinamico. Per tale scopo si utilizza la formulazione della termodinamica estesa, conosciuta come Termodinamica Estesa Razionale, che usa i moltiplicatori di Lagrange. Si prendono in esame due situazioni fisiche particolarmente semplici ma molto importanti: il caso della propagazione termica che avviene nei cristalli a bassa temperatura e il caso dei gas non viscosi soggetti a riscaldamento. Si mostra che la temperatura di non-equilibrio e la temperatura termodinamica in generale non coincidono, e si determinano le espressioni approssimate della loro differenza

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