  The constraints imposed by the relativistic compressibility hypothesis on the
square of the speed of sound in a medium are obtained. This result allows to
obtain purely hydrodynamic conditions for the physical reality of a perfect
energy tensor representing the energetic evolution of a perfect fluid in local
thermal equilibrium. The results are applied to the paradigmatic case of the
generic ideal gases. Then the physical reality of the ideal gas Stephani models
is analyzed and the Rainich-like theory for ideal gas solutions is built.
