  The ambiguities and inconsistencies in previous thermodynamic treatments for
the quark mass density-dependent model are addressed. A new treatment is
suggested to obtain the self-consistent results. A new independent variable of
effective mass is introduced to make the traditional thermodynamic calculation
with partial derivative still practicable. The contribution from physical
vacuum has been discussed. We find that the properties of strange quark matter
given by quark mass density-dependent model are nearly the same as those
obtained by MIT bag model after considering the contribution of the physical
vacuum.
