We study the phase structure of the QGP-Hadron system under quasi-static equilibrium using the Ramanathan et al. statistical model for the QGP fireball formation in a hadronic medium. While in the earlier published studies we had used the Peshier effective potential which is appropriate for the deconfined QGP phase but could be extrapolated to the transition region from the higher momentum regime, in this paper we study the same system using the Cornell and Richardson potentials which are more relevant for the low momentum confinement regime, but could again be extrapolated to the transition region from below. Surprisingly, the overall picture in both the cases are quite similar with minor divergences,(though,the results with the Richardson potential shows a sizable deviation from the other two potentials), thus indicating the robustness of the model and its self-consistency. The result of our numerical results pertaining to the variation of the velocity of sound in the QGP-Hadron medium with temperature in the various scenarios considered by us, is that, the phase transition seems to be a gentle roll-over of phases rather than a sharp transition of either the first or second order, a result in conformity with recent lattice calculations, but with much less effort.
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