Continuum Thermodynamics - Part II: Applications and Examples by Bettina Albers
Concept of Continuum in Thermodynamics
Continuum Mechanics and Thermodynamics
Continuum mechanics is a branch of mechanics that deals with the mechanical behavior of materials modeled as a continuous mass rather than as discrete particles. The French mathematician Augustin-Louis Cauchy was the first to formulate such models in the 19th century. Modeling an object as a continuum assumes that the substance of the object completely fills the space it occupies. Modeling objects in this way ignores the fact that matter is made of atoms , and so is not continuous; however, on length scales much greater than that of inter-atomic distances, such models are highly accurate. Fundamental physical laws such as the conservation of mass , the conservation of momentum , and the conservation of energy may be applied to such models to derive differential equations describing the behavior of such objects, and some information about the particular material studied is added through constitutive relations. Continuum mechanics deals with physical properties of solids and fluids which are independent of any particular coordinate system in which they are observed.
Continuum Mechanics and Thermodynamics is an interdisciplinary journal exploring new ideas in continuum and quasi-continuum modeling of systems with a large number of degrees of freedom and sufficient complexity to require thermodynamic closure. Major emphasis is placed on papers seeking to bridge the gap between discrete and continuum approaches as well as micro and macro scales, by means of homogenization, statistical averaging, and other mathematical tools aimed at the judicial elimination of small time and length scales. In particular, the journal focuses on simultaneous descriptions of complex systems at several disparate scales. Papers presenting and explaining new experimental findings are highly encouraged. Lastly, the journal publishes numerical studies that build our understanding of the physical nature of phenomena. In addition to research papers, the journal features invited review articles, short communications, and "comment-and-reply" on published papers.
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As with all sciences, thermodynamics is concerned with the mathematical modeling of the real world. In order that the mathematical deductions are consistent, we need some precise definitions of the basic concepts. The following is a discussion of some of the concepts we will need. Several of these will be further amplified in the lectures and in other handouts. They are also covered, although in a less detailed manner, in Chapters 1 and 2 of the book by Van Ness. There are two reasons for this.