Thermodynamic permeability and permittivity of polarizable systems

Article type: Research Article

Authors: Zimmels, Y.^a

Affiliations: [a] Department of Civil Engineering, Technion-Israel Institute of Technology, Haifa 32000, Israel

Abstract: Relative and absolute thermodynamic permeabilities are defined as system variables and supplements to the classical point permeability, which expresses the ratio of \mathbf{B} to \mathbf{H}, at the position where these vectors exist. The thermodynamic permeability gives a measure for the net contribution of a system to the energy stored in the field, and as such it reflects also the effect of constraints that are imposed on this field. If the system is permeable, then a fixed \mathbf{B} field involves a negative absolute thermodynamic permeability, whereas the reverse is true in a fixed \mathbf{H} field. It is shown that weighted average permeabilities of systems that are either connected in parallel, with \mathbf{H} being uniform across them, or in series, with \mathbf{B} being uniform, are a direct consequence of related thermodynamic permeabilities. Derivatives of point permeabilities and thermodynamic permeabilities are used to define sets of field dependent temperature, pressure and chemical potential. Whereas the field dependent temperature, pressure and chemical potential are functions of a derivative of the point permeability, the pressure is a function of such a derivative as well as of the thermodynamic permeability. Examples of thermodynamic permeabilities which are obtained for toroids of different properties and for a sphere in a uniform field are illustrated and discussed. It is shown that in the case of the sphere, the thermodynamic permeability reflects the effect of partition of its own energy within and outside its physical boundaries. Furthermore, the field dependent entropy, temperature, pressure and chemical potential, of the matter enclosed within the sphere depend on properties of its own as well as on those of its surroundings. Finally, the results obtained for magnetic fields apply to electric fields once the relevant magnetic variables are replaced by their electric counterparts.

DOI: 10.3233/JAE-1999-132

Journal: International Journal of Applied Electromagnetics and Mechanics, vol. 10, no. 2, pp. 123-141, 1999