One of the main question arising in Extended Thermodynamics concerns the physical meaning of the temperature far from equilibrium. Some authors define thermodynamic temperature the inverse of the coefficient linking the entropy flux with the heat flux. Other authors, instead, define non-equilibrium temperature 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 can be neglected. Approximate expressions for and are determined in both cases.
Una delle principali questioni che sorge nella termodinamica estesa riguarda il significato fisico della temperatura lontano dall'equilibrio. Alcuni autori definiscono temperatura termodinamica il reciproco del coefficiente che lega il flusso di entropia e il flusso di calore. Altri autori, invece, definiscono temperatura di non-equilibrio 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
@article{BUMI_2004_8_7B_2_381_0,
author = {M. S. Mongiov\`\i\ and R. A. Peruzza},
title = {Entropy flux far from equilibrium in solids and in non viscous gases},
journal = {Bollettino dell'Unione Matematica Italiana},
volume = {7-A},
year = {2004},
pages = {381-396},
zbl = {1177.74038},
mrnumber = {2072943},
language = {en},
url = {http://dml.mathdoc.fr/item/BUMI_2004_8_7B_2_381_0}
}
Mongiovì, M. S.; Peruzza, R. A. Entropy flux far from equilibrium in solids and in non viscous gases. Bollettino dell'Unione Matematica Italiana, Tome 7-A (2004) pp. 381-396. http://gdmltest.u-ga.fr/item/BUMI_2004_8_7B_2_381_0/
[1] --, A thermodynamical approach to Eddington factors, J. Math. Phys., 32 (2), (1991), 544-550. | MR 1088383 | Zbl 0850.76881
[2] --, Temperature jumps at the boundary of a rarifield gas, Continuum Mech. Thermodyn., 12 (2000), 19-29. | MR 1753004 | Zbl 0943.76067
[3] --, On the temperatures of a rarefieds gas in non-equilibrium, Meccanica, 34 (1999), 103-113. | Zbl 0964.76078
[4] , Sulla conduzione del calore, Atti Sem. Mat. Fis. Univ. Modena, 3 (1948), 83-101. | MR 32898 | Zbl 0035.26203
[5] -, Entropy Flux and Absolute temperature in Extended Irreversible Thermodynamics, J. Non-Equilib. Thermodyn., 20 (1995), 263-273. | Zbl 0834.73008
[6] , Principles of the kinetic theory of gases, Handbuch der Physik XII, Thermodynamik der Gase, Springer-Verlag, Berlin (1958), 205-294. | MR 135535
[7] -, Solution of the linearized phonon Boltzmann equation, Phys. Rev., 148 (2), (1966), 766-778.
[8] -, Thermal conductivity, second sound and phonon hydrodynamic phenomena in nonmetal crystals, Phys. Rev., 148 (2), (1966), 778-788.
[9] --, Extended Irreversible Thermodynamics revisited (1988-1998), Rep. Prog. Phys., 62 (1999), 1035-1142. | MR 1704603 | Zbl 0852.73005
[10] --, Extended Irreversible Thermodunamics, Springer-Verlag, Berlin (2001). | Zbl 0974.74003
[11] -, Possible experiment to check the reality of a nonequilibrium temperature, Phys. Rev. A, 45 (12), (1992), 8371-8373.
[12] -, Nonequilibrium temperature versus local-equilibrium temperature, Phys. Rev. E, 49 (2) (1994), 1040-1048.
[13] , On extended thermodynamics of ideal and real gases, Extended Thermodynamics Systems, and editors, Taylor and Francis (1992), 140-182.
[14] , Method of Lagrange multipliers for exploitation of the entropy principle, Arch. Rat. Mech. Anal., 46 (1972), 131-148. | MR 337164 | Zbl 0252.76003
[15] -, Extended Thermodynamics of classical and degenerate gases, Arch. Rat. Mech. Anal., 83 (4) (1983), 285-332. | MR 714978 | Zbl 0554.76014
[16] , Some considerations about Nonlinear Extended Thermodynamic Theories with different number of fields, J. Non-Equilib. Thermodyn., 24 (1999), 147-153. | Zbl 0954.74004
[17] , Thermodynamic pressure in nonlinear nonequilibrium thermodynamics of dilute nonviscous gases, Phys. Rev. E, 63 (2001), 1-4. | Zbl 1042.82038
[18] , Non-linear Non-viscous Hydrodynamical Models for Charge Transport in the framework of Extended Thermodynamic methods, Math. Comp. Modelling, 35 (2002), 813-820. | Zbl 0995.82513
[19] , Nonlinear Extended Thermodynamics of a Diluite Nonviscous Gas, Math. Comp. Modelling, 36 (2002), 951-962. | MR 1945051 | Zbl 1029.80001
[20] -, Rational Extended Thermodynamics, Springer-Verlag, Berlin (1998). | MR 1632151 | Zbl 0895.00005
[21] , On isotropic Integrity Bases, Arch.Rat.Mech.Anal., 18, (1965), 282-292. | MR 173211 | Zbl 0129.00902
[22] --, Continuum approach to Phonon Gas and Shape Changes of Second Sound via Shock Waves Theory, Il Nuovo Cimento D, 16 (1), (1994), 15-44.
[23] --, Shock Waves in Crystalline Dielettrics at Low Temperature, J. Phys.: Condens.Matter, 14 (2002), 3553-3564.
[24] , A new representation theorem for isotropic functions, Arch. Rat. Mech. Anal., 36 (1970), 166-197. | MR 340303 | Zbl 0327.15030