  In this paper we consider the conditions on quasi-thermal-incompressible so
that they satisfy all the principles of thermodynamics, including the stability
condition associated with the concavity of the chemical potential. We analyze
the approximations under which a quasi-thermal-incompressible medium can be
considered as incompressible. We find that the pressure cannot exceed a very
large critical value and that the compressibility factor must be greater than a
lower limit that is very small. The analysis is first done for the case of
fluids and then extended to the case of thermoelastic solids.
