content_image/369851.jpg content_image/369852.jpg content_image/369850.jpg
with ϵ$_{i}$ ( x$_{i}$l ) = ( x$_{i}$l ) $^{3}$K$_{1}$ ( x$_{i}$l ) + 3( x$_{i}$l ) $^{2}$K$_{2}$ ( x$_{i}$l ), where K$_{1}$ and K$_{2}$ are the modified Bessel functions with x$_{i}$ = m$_{i}$ T and index i runs for gluons, up-down quarks q, and strange quark s. 

Here d$_{i}$ are the degeneracies associated with the internal degrees of freedom. Now, by using the thermodynamic relation ϵ = T ∂ p ∂T − p , pressure of system at µ$_{q}$ = 0 can be obtained as: 

<img src='content_image/369851.jpg'>

where p$_{0}$ is the pressure at a reference temperature T$_{0}$ . We have used p$_{0}$ =0 at T$_{0}$ =100 MeV in our calculation. Using the relation between the number density n$_{q}$ and the grand canonical partition function, we can get the pressure for a system at finite µ$_{B}$ : 

<img src='content_image/369852.jpg'>

Thus all the thermodynamical quantities can be obtained in a consistent way by using this model. 

## V. EOS FOR A HADRON GAS 

There is no deconfinement transition, if the hadron gas consists of point-like particles, and consequently HG pressure is always larger than QGP pressure. Therefore, inclusion of a repulsive interaction between two baryons having a hard-core size reduces the HG pressure and hence it stabilizes the formation of QGP at high baryon densities. Recently we have proposed a thermodynamically consistent excluded volume model for hot and dense hadron gas (HG). In this model, the grand canonical partition function for the HG with full quantum statistics and after incorporating excluded volume correction can be written as [25]: 

where g$_{i}$ is the degeneracy factor of ith species of baryons, E$_{i}$ is the energy of the particle ( E$_{i}$ = √ k 2 + m 2 $_{i}$), V 0 i is the eigenvolume of one baryon of ith species and ∑ j N$_{j}$V 0 j is the total occupied volume and N$_{j}$ represents total number of baryons of jth species. 

Now we can write Eq.(17) as: 

<img src='content_image/369850.jpg'>

