  A new equation of state for a hot and dense hadron gas (HG) is obtained where
the finite hard-core size of baryons has been incorporated in a
thermodynamically consistent formulation of excluded volume correction. Our
model differs from other existing approaches on the following points. We assign
a hard-core volume only to each baryon and mesons though possess a small volume
but they can fuse and interpenetrate into one another. Use of the full quantum
statistics is made in obtaining the grand canonical partition function where
excluded-volume correction has been incorporated by explicitly integrating over
volume. We thus find that the new model works even for the cases of extreme
temperatures and/or densities where most of other approaches fail. The model
does not violate causality even at extreme densities. The temperature and
density dependence of various thermodynamical quantities, e.g. pressure, baryon
density, entropy and energy density compare well with the results of other
microscopic HG models. After suitable parametrization of the centre-of-mass
energy in terms of temperature and baryon chemical potential, we explore some
new freeze-out criteria which exhibit full independence of the collision energy
and of the structures of the colliding nuclei. We further demonstrate the
suitability of our model in explaining various experimental results of the
multiplicity-ratios of various particles and their antiparticles. Finally, we
use our excluded-volume model to obtain the transport behaviour of the hot
and/or dense HG such as shear viscosity to entropy ratio, speed of sound etc.
and compare the results with earlier calculations.
