  We study two recently proposed equations of state (EOS) which are obtained
from high temperature QCD, and show how they can be adapted to use them for
making predictions for relativistic heavy ion collisions. The method involves
extracting equilibrium distribution functions for quarks and gluons from the
EOS, which in turn will allow a determination of the transport and other bulk
properties of the quark gluon plasma. Simultaneously, the method also yields a
quasi particle description of interacting quarks and gluons. The first EOS is
perturbative in the QCD coupling constant and has contributions of $O(g^5)$.
The second EOS is an improvement over the first, with contributions upto $
O(g^6 ln(\frac{1}{g}))$; it incorporates the nonperturbative hard thermal
contributions. The interaction effects are shown to be captured entirely by the
effective chemical potentials for the gluons and the quarks, in both the cases.
The chemical potential is seen to be highly sensitive to the EOS. As an
application, we determine the screening lengths which are, indeed the most
important diagnostics for QGP. The screening lengths are seen to behave
drastically differently depending on the EOS considered., and yield, therefore,
a way to distinguish the two equations of state in heavy ion collisions.
