  We summarize the derivation of the finite temperature, finite chemical
potential thermodynamic potential in the bag-model approximation to quantum
chromodynamics (QCD) that includes a finite $s$-quark mass in the Feynman
diagram contributions for both zero-order and two-loop corrections to the quark
interaction. The thermodynamic potential for quarks in QCD is a desired
ingredient for computations of the equation of state in the early universe,
supernovae, neutron stars, and heavy-ion collisions. The 2-loop contributions
are normally divergent and become even more difficult in the limit of finite
quark masses and finite chemical potential. We introduce various means to
interpolate between the low and high chemical potential limits. Although
physically well motivated, we show that the infinite series Pad\'e rational
polynomial interpolation scheme introduces spurious poles. Nevertheless, we
show that lower order interpolation schemes such as polynomial interpolation
reproduce the Pad\'e result without the presence of spurious poles. We propose
that in this way one can determine the equation of state for the two-loop
corrections for arbitrary chemical potential, temperature and quark mass. This
provides a new realistic bag-model treatment of the QCD equation of state. We
compute the QCD phase diagram with up to the two-loop corrections. We show that
the two-loop corrections decrease the pressure of the quark-gluon plasma and
therefore increase the critical temperature and chemical potential of the phase
transition. We also show, however, that the correction for finite $s$-quark
mass in the two-loop correction serves to decrease the critical temperature for
the quark-hadron phase transition in the early universe.
