Entropy flow: a constitutive function. A. R. L. Nery, A. B. M. S. Bassi Universidade Estadual de Campinas, Instituto de Química, SP, Brazil. e-mail:
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The thermodynamics of continuous media seeks to describe the behavior of a body in a process through its thermo mechanic properties. For this description are used basic fields, which usually are the temperature, velocity and density fields, as well as the balance equations of mass, energy, and linear and angular momentum. But, for fully describing the behavior of a material body, it is necessary to use constitutive equations that place constraints on the body response to the process conditions. Each type of material has its own constitutive equations, that is, the type of function is a characteristic of the considered material. For example, the same force will not produce the same elongation on wires of zinc and rubber, both having the same diameter and length. Thus, in continuous media thermodynamics the determination of constitutive functions is extremely important to fully and accurately describe the process. Constitutive equations may be determined by the method of Lagrange multipliers [1], or through an algebraic method using balance equations, the entropy inequality and equilibrium conditions [2], or considering polynomial functions [3]. In textbooks of thermodynamics, the entropy flow is parallel to the heat flow and the proportionality constant is reciprocal to the absolute temperature. But this relation is found to be inappropriate to account for the thermodynamics of diffusion [4]. Müller [5] considered the entropy flow and the heat flow as independent constitutive quantities, so that the entropy flow is not necessarily parallel to the heat flow. Furthermore, using the Muller theory and the method of Lagrange multipliers, Liu indicated that the thermodynamic restrictions are not related to the type of process, but to the type of material [1]. Thus, it is the kind of material that will determine the entropy production. References: [1] I-Shi Liu, Method of Lagrange multipliers for exploitation of the entropy principle. Arch. Rational Mech. Anal. 46 (1972) 131 – 148. [2] I. Samhoýl, Thermodynamics of Reacting Mixtures of Any Symmetry with Heat Conduction, Diffusion and Viscosity. Arch. Rational Mech. Anal.147 (1999) 1 – 45. [3] J. D. Ingran, A. C. Eringen, A Continuum Theory of Chemically Reacting Media – II. Constitutive Equations of Reacting Fluid Mixtures. Int. J. Engng Sci. Vol. 5 (1967), pp. 289322. [4] C. Truesdell, Rational Thermodynamics. McGraw-Hill, New York, 1969. [5] I. Müller, On the Entropy Inequality. Arch. Rational Mech. Anal. 26 (1967) 181 – 141.
