  We find that an equation of state for hot hadronic matter consisting of all
baryons having $M < 2$ GeV and all mesons having $M < 1.5$ GeV, along with
Hagedorn resonances in thermal and chemical equilibrium, matches rather
smoothly with lattice equation of state (p4 action, ${N_\tau}=8$) for T up to
$\approx 200$ MeV, when corrected for the finite volume of hadrons.
  Next we construct two equations of state for strongly interacting matter;
one, HHL, in which the above is matched to the lattice equation of state at
$T=165$ MeV and the other, HHB, where we match it to a bag model equation of
state with critical temperature $T_c=165$ MeV. We compare particle spectra,
thermal photon spectra and histories of evolution of the quark-gluon plasma
produced in the central collision of gold (lead) nuclei at RHIC (LHC) energies,
considering ideal hydrodynamical expansion of the system. The particle and
thermal photon spectra are seen to differ only marginally, for the two
equations of state. The history of evolution shows differences in the evolution
of temperature and radial velocity, as one might expect.
  We calculate intensity interferometry of thermal photons and find it to be
quite distinct for the two equations of state, especially for the outward
correlation. The longitudinal correlation also shows a dependence on the
equation of state, though, to a smaller extent.
