Interstitial Working and a Nonclassical Continuum Thermodynamics

Abstract

Twenty years ago Coleman and Noll [11.1] succeeded in clarifying and making rigorous a procedure by which the laws of thermodynamics could be used to deduce constitutive restrictions on a vast variety of materials. Almost from the very beginning, indeed in a paper by Coleman and Mizel [11.2] in the same year as [11.1], it began to be clear that the procedure of Coleman and Noll, when applied to the usual forms of the basic laws of thermodynamics, in many cases imposed extraordinarily severe restrictions on the long range spatial dependence allowable in constitutive quantities. Indeed, for the class of rigid heat conductors in which the energy ε, the entropy η, and the heat flux q at a particle X may depend on the current value of the temperature θ and its first n spatial gradients at X, Coleman and Mizel [11.2] showed that thermodynamics and the procedure of [11.1] allowed ε and η to depend on at most the value of θ at X — no gradients of temperature could appear in these quantities at all.