A consistent thermodynamical model of incompressible media as limit case of quasi-thermal-incompressible materials

In this paper we extend the conditions of emph{quasi-thermal-incompressible materials} presented in cite{GMR} such that they satisfy all the principles of thermodynamics including the stability condition associated with the concavity of the chemical potential. We analyze the approximations for which a quasi-thermal-incompressible media can be considered as incompressible. As results the pressure cannot exceed a very large critical value and the compressibility coefficient must be greater than a lower limit which is very small. The analysis is first done in the case of fluids and then extended to the case of thermoelastic solids.