  We calculate the free energy, entropy and pressure of the Quark Gluon Plasma
(QGP) at finite temperature and density with a given fraction of spin-up and
spin-down quarks using a MIT bag model with corrections up to ${\cal O} (g^4
\ln g^2)$. The expressions for the specific heat and the spin susceptibility
are derived in terms of Fermi momentum and temperature. The effects of
interaction between the quarks on the properties of the QGP phase are also
investigated. Within our phenomenological model, we estimate the transition
temperature $T_c$ by constructing the phase boundary between the hadronic phase
and the QGP phase. Finally, we compute the equation of state of the QGP and its
dependence on the temperature and the density.
