Thermodynamics of Irreversible Processes

Abstract

The thermodynamics of irreversible processes is a continuum theory of processes in matter with no reference to its molecular constitution. The reductionist tradition of natural philosophy, however, inevitably requires molecular theoretical foundations in the form of a particulate theory of matter based on the concept of particles (e.g., atoms and molecules) currently held in science. The kinetic theory of fluids has been primarily developed to provide macroscopic phenomena and thermodynamics of reversible and irreversible processes in continuum matter with molecular theoretical foundations. In such a theory a suitable kinetic equation is used for the distribution function of the system in the phase space or the Hilbert space, but in practice the solution of the kinetic equation is sought in such a way as to help understand at the thermodynamic level of description the macroscopic phenomena which we experience or observe in nature and in the laboratory. Therefore the solution is a particular solution corresponding to our thermodynamic level of understanding of the natural phenomena of interest. It is then inevitable that we examine what is really meant by the thermodynamic level of description in the first place. In the course of our scientific training we have been taught thermodynamics of reversible processes, and a great deal of our scientific reasoning and thinking processes is molded and influenced by equilibrium thermodynamics, especially when we are concerned with macroscopic phenomena in continuum matter, but the subject is not very useful for us when we face irreversible macroscopic processes. Consequently our first task in attempting to study the kinetic theory of matter is in establishing a theoretical formalism for macroscopic phenomena in continuum matter on the foundations of the laws of thermodynamics as we know of at present in the forms proposed by their formulators. We then develop a solution procedure for the kinetic equation for the distribution function of matter in the phase space or the Hilbert space depending on whether the classical or quantum mode of description is adopted for the development of the theory, in such a way that the thermodynamics of irreversible processes is described from the molecular viewpoint. We are thus motivated to develop first a thermodynamic theory of irreversible processes without using the molecular picture of matter. In this endeavor we take the position that the first task is to develop a logical structure within the framework of the original form of the laws of thermodynamics as phrased by their formulators. Since the most difficult and unsettled part of the theory is concerned with the mathematical representation of the second law of thermodynamics, we will devote close attention to it, but will be brief with the representation of the first law of thermodynamics and other conservation laws as well as the zeroth law regarding the temperature, since there is nothing new for us to add to them at present. Applications of the theory developed for irreversible processes will be deferred to a later chapter. We will assume that the substance does not have an intrinsic angular momentum. We also assume that the system consists of an r-component non-reactive mixture. Therefore the case of chemical reactions is excluded, but it is easy to modify the theory to include the case of chemical reactions. After completing the formulation of the theory under the assumptions taken, we will point out where the necessary modifications must be made to include chemical reactions. Since the kinetic theory part of this work does not deal with fluids with an angular momentum, we will not consider the irreversible thermodynamics of such fluids.