Thermodynamics based on the Clausius-Duhem Inequality
Thus far we have concentrated attention on a theory of thermodynamics which sets out from the thermodynamic inequality (2.2.3) and constructs the entropy explicitly. We turn now to describing an approach to thermodynamics which introduces entropy from the outset and uses the Clausius-Duhem inequality to reduce constitutive equations. This approach was first used by Coleman and Noll in a paper  which marks the beginning of the recent revival of activity in continuum thermodynamics. The importance of that paper does not lie in the novelty of its results; indeed for the class of elastic materials with linear viscosity considered by Coleman and Noll all the restrictions derived by them had been either derived before from different starting points or had been conjectured previously. Its importance is that it shows us how to exploit in a systematic way the idea that the second law of thermodynamics requires the Clausius-Duhem inequality to be satisfied in every process which is compatible with the balance laws for mass, momentum, moment of momentum and energy. In principle it will be necessary to supply non-zero body forces and radiation fields to maintain the processes envisaged.
KeywordsFree Energy Internal Energy Deformation Gradient Conductivity Tensor Fading Memory
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