Basic Concepts of Thermomechanics
نویسندگان
چکیده
This paper is intended to serve as a model for the first few chapters of future textbooks on continuum mechanics and continuum thermomechanics. It may be considered an update of the paper Lectures on the Foundations of Continuum Mechanics and Thermodynamics [N2] by one of us (W.N.), published in 1973, and an elaboration of topics treated in Part 3, entitled Updating the Non-Linear Field Theories of Mechanics, of the booklet [FC] by W.N.. 1 The present paper differs from most existing textbooks on the subject in several important respects: 1) It uses the mathematical infrastructure based on sets, mappings, and families, rather than the infrastructure based on variables, constants, and parameters. (For a detailed explanation, see The Conceptual Infrastructure of Mathematics by W.N. [N1].) 2) It is completely coordinate-free and R I -free when dealing with basic concepts. 3) It does not use a fixed physical space. Rather, it employs an infinite variety of frames of reference, each of which is a Euclidean space. The motivation for avoiding physical space can be found in Part 1, entitled On the Illusion of Physical Space, of the booklet [FC]. Here, the basic laws are formulated without the use of a physical space or any external frame of reference. 4) It considers inertia as only one of many external forces and does not confine itself to using only inertial frames of reference. Hence kinetic energy, which is a potential for inertial forces, does not appear separately in the energy balance equation. In particle mechanics, inertia plays a fundamental role and the subject would collapse if it is neglected. Not so in continuum mechanics, where it is often appropriate to neglect inertia, for example when analyzing the motion of toothpaste when it is extruded slowly from a tube.
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تاریخ انتشار 2009