On Thermodynamics and the Nature of the Second Law: I. Single Phase Continua. Supplement.
CALIFORNIA UNIV BERKELEY DEPT OF MECHANICAL ENGINEERING
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The present supplement contains some additional development concerning the mathematical statement of the second law and restrictions on the heat conduction vector and internal energy, as well as two examples which demonstrate some shortcomings of the Clausius-Duhem inequality. One of the examples, when studied with the use of the Clausius-Duhem inequality, leads to results that imply the possibility of a perpetual motion of the second kind. In the second example, which is concerned with a rigid heat conductor in thermal equilibrium, the Clausius-Duhem inequality requires that if heat is added to the medium the resulting spatially homogeneous temperature of the conductor decreases. Moreover, the inequality denies the possibility of propagation of heat in the conductor as a thermal wave with finite speed. The inequalities proposed here do not suffer from these shortcomings.