Thermodynamic interaction between two discrete systems in non-equilibrium
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Abstract
A systematic description of the interaction between two systems is presented within the framework of thermodynamics of discrete systems. We distinguish between two situations: a contact between an equilibrium system and a non-equilibrium one, and a contact between two non-equilibrium systems. In the second case the state space includes replacement quantities, which reduce the situation to a contact between an equilibrium system and a non-equilibrium one. Interacting discrete systems form a composite (compound) system which is also a discrete one. Thus a compound system can be described as if it were composed of two subsystems, or by ignoring this fact, as a plain single discrete system, whose composition of sub-systems is not taken into consideration. These descriptions cause different degrees of accuracy which are expressed by excess quantities. Such an excess quantity vanishes if the discrete system is really not composed of subsystems. Aim of this paper is to calculate the excess quantities of power and energy exchange and to derive the excess entropy in the special case of an endoreversible compound system.
References
1 Wilmanski, K., Thermomechanics of Continua, chap. 4, Springer, Berlin, 1988.Search in Google Scholar
2 Jou, D., Casas-Vazquez, J., Lebon, G., Extended Irreversible Thermodynamics, 3rd ed., chap. 2, Springer, Berlin, 2001.10.1007/978-3-642-56565-6Search in Google Scholar
3 Muschik, W., Papenfuss, C., Ehrentraut, H., Concepts of Continuum Thermodynamics, chap. 3, Technische Universität Berlin, Kielce University of Technology, Kielce, Poland, 1997.Search in Google Scholar
4 Muschik, W., Papenfuss, C., Ehrentraut, H., A sketch of continuum thermodynamics, J. Non-Newtonian Fluid Mech., 96 (2001), 255.10.1016/S0377-0257(00)00141-5Search in Google Scholar
5 Muschik, W., Aspects of Non-Equilibrium Thermodynamics, sec. 1.1, World Scientific, Singapore, 1990.10.1142/0991Search in Google Scholar
6 Truesdell, C., Bharatha, S., The Concepts and Logic of Classical Thermodynamics as a Theory of Heat Engines, p. xiii, Springer, New York, 1977.10.1007/978-3-642-81077-0Search in Google Scholar
7 Muschik, W., Fundamentals of non-equilibrium thermodynamics, in: Non-Equilibrium Thermodynamics with Application to Solids, 1–63, Ed. Muschik, W., Springer, Wien, 1993.10.1007/978-3-7091-4321-6_1Search in Google Scholar
8 Schottky, W., Thermodynamik, sec. 1, paragr. 1, Springer, Berlin, 1929, reprint 1973.10.1007/978-3-642-88482-5_1Search in Google Scholar
9 Muschik, W., Empirical foundation and axiomatic treatment of non-equilibrium temperature, Arch. Rat. Mech. Anal., 66 (1977), 379.10.1007/BF00248902Search in Google Scholar
10 Muschik, W., Brunk, G., A concept of non-equilibrium temperature, Int. J. Engng. Sci., 15 (1977), 377.10.1016/0020-7225(77)90047-7Search in Google Scholar
11 Muschik, W., Fundamental remarks on evaluating dissipation inequalities, in: Recent Developments in Nonequilibrium Thermodynamics, 388–397, Eds. Casas-Vazquez, J., Jou, D., Lebon, G., Lecture Notes in Physics 199, Springer, Berlin, 1984.10.1007/BFb0016044Search in Google Scholar
12 Muschik, W., Entropies of heat conducting discrete or multi-temperature systems with use of non-equilibrium temperatures, Int. J. Engng. Sci., 18 (1980), 1399.10.1016/0020-7225(80)90096-8Search in Google Scholar
13 Muschik, W., Domínguez-Cascante, R., On extended thermodynamics of discrete systems, Physica A, 233 (1996), 523.10.1016/S0378-4371(96)00249-XSearch in Google Scholar
14 Muschik, W., Gümbel, S., Does Clausius’ inequality exist for open systems?, J. Non-Equilib. Thermodyn., 24 (1999), 97–106.10.1515/JNETDY.1999.005Search in Google Scholar
15 Hoffmann, K.-H., Burzler, J.M., Schubert, S., Endoreversible thermodynamics, J. Non-Equilib. Thermodyn., 22 (1997), 311.Search in Google Scholar
16 Keller, J.U., Ein Beitrag zur Thermodynamik fluider Systeme, Physica, 53 (1971), 602.10.1016/0031-8914(71)90117-0Search in Google Scholar
17 Muschik, W., Fundamentals of dissipation inequalities, J. Non-Equilib. Thermodyn., 4 (1979), 277.10.1515/jnet.1979.4.5.277Search in Google Scholar
18 Kestin, J., Local-equilibrium formalism applied to mechanics of solids, Int. J. Solids Struct., 29 (1992), 1827.10.1016/0020-7683(92)90174-RSearch in Google Scholar
19 Kestin, J., Internal variables in the local-equilibrium approximation, J. Non-Equilib. Thermodyn., 18 (1993), 360.10.1515/jnet.1993.18.4.360Search in Google Scholar
20 Maugin, G.A., Muschik, W., Thermodynamics with internal variables. Part 1. General concepts, J. Non-Equilib. Thermodyn., 19 (1994), 217.10.1515/jnet.1994.19.3.217Search in Google Scholar
21 Maugin, G.A., The Thermomechanics of Nonlinear Irreversible Behavior. An Introduction, chap. 9, World Scientific, Singapore, 1999.10.1142/3700Search in Google Scholar
22 De Groot, S.R., Mazur, P., Non-Equilibrium Thermodynamics, chap. III, North-Holland, Amsterdam, 1961.Search in Google Scholar
© Walter de Gruyter
Articles in the same Issue
- Gerard A. Maugin, 60 years young
- Non-linear phenomena in thermoacoustic engines
- Entropy production in polarizable bodies with internal variables
- Thermodynamic interaction between two discrete systems in non-equilibrium
- Inconsistency in the Moment’s method for solving the Boltzmann equation
- Modelling mass transport through a porous partition: Effect of pore size distribution
- Time scales for energy transfer
Articles in the same Issue
- Gerard A. Maugin, 60 years young
- Non-linear phenomena in thermoacoustic engines
- Entropy production in polarizable bodies with internal variables
- Thermodynamic interaction between two discrete systems in non-equilibrium
- Inconsistency in the Moment’s method for solving the Boltzmann equation
- Modelling mass transport through a porous partition: Effect of pore size distribution
- Time scales for energy transfer
