On steady motions in thermodynamics

摘要

We herein refine the strategy first formalized by Coleman and Noll for deducing constitutive restrictions from the Clausius-Duhem inequality. Specifically, we establish a key lemma that for certain materials allows the Coleman-Noll procedure to be carried out within just the class of steady motions. By so shrinking the size of the process class needed to employ the Coleman-Noll procedure, our lemma simultaneously enlarges the class of real materials that we know must be mindful of certain of the constitutive restrictions that descend from the principles of thermodynamics. In particular, our lemma allows a thermodynamic analysis, using just steady motions, of fluids of differential type--a constitutive class that the rheological community frequently lays down as governing material response in steady motions, although it is ambivalent about the use of such forms in more general motions. Thermodynamics is thus shown to deliver significant constitutive restrictions without anything being postulated for material response on nonsteady motions.