On the moment methods and irreversible thermodynamics

In this paper we investigate the kinetic foundation of irreversible thermodynamics by means of the moment methods proposed by Grad sind by Eu, respectively. First we show that the moment methods yield a weak solution of the Boltzmann equation. On the other hand, the entropy balance equation can be satisfied only by the strong solution of the Boltzmann equation. Second, we reformulate the energy balance equation in an alternative form where dissipative energy as well as a generalized work I-form are included in this new equation. Assume that the dissipative energy is semi-positive definite. The local form of the second, law of thermodynamics is then formulated in terms of the inaccessibility condition of Caratheodory. We then show that our new formulation of the second law is equivalent to Kelvin's principle and Clausius' principle. Finally we obtain a calotropy balance equation where the calotropy density function is a state function in the thermodynamic space. (C) 1997 American Institute of Physics.