where E$_{0}$ is the vacuum energy in the absence of quasiparticle excitations or zero point energy. However, this energy term is not a constant but depends upon µ$_{B}$ and T. The B ( T, µ$_{B}$ ) can be derived as follows [23]: B ( T, µ$_{B}$ ) = B$_{0}$ − d 4 π 2 ∫ T T 0 dT ∫ ∞ 0 k $^{2}$dk ω 1 [ exp ( ω − µ$_{q}$ T )] ∓ 1 , (11) where B$_{0}$ is the integration constant i.e., the value of B ( T, µ$_{B}$ ) at T = T$_{0}$ . The expression for B ( T, µ$_{B}$ ) in Eq. (11) and the forms of Eq. (8-10) give a compelling evidence that B ( T, µ$_{B}$ ) may be treated as T and µ$_{B}$ -dependent bag constant term [24]. In our calculation we take B 1 / 4 0 = 185 MeV and T$_{0}$ = 100 MeV . We have also taken µ$_{B}$ = 3 µ$_{q}$ . The second thermodynamically consistent quasiparticle model is given by Bannur [16]. Bannur first figured out why there exists a thermodynamical incosistency in the quasiparticle description of Peshier et. al. The relation between pressure and grand canonical partition function can not hold good if the particles of the system have a temperature-dependent mass. So he used the definition of average energy and average number of particles and derived all the thermodynamical quantities from them in a consistent manner. In this model, the effective mass of the gluon is the same as given in Eq (4). However, the effective mass of the quarks involves the following relation: were m$_{q}$$_{0}$ is the rest mass of the quarks. In this calculation, we have used m$_{q}$$_{0}$ = 8 MeV for two light quarks ( u,d ), and m$_{q}$$_{0}$ = 80 MeV for strange quark. In the above Eq (12) m$_{th}$ represents the thermal mass of the quarks and it can be written as [23]: Taking these values for the effective masses, energy density can be derived from the grand canonical partition function in a thermodynamically consistent manner and is given as : m 2 q = m 2 q 0 $_{+}$√$_{2}$$_{m}$$_{q}$$_{0}$$_{m}$$_{th}$ + m 2 $_{th}$, (12) m 2 $_{th}$( T, µ ) = N 2 c − 1 8 N$_{c}$ [ T 2 + µ 2 q π 2 ] g $^{2}$( T ) , (13) ϵ = T 4 π 2 ∞ ∑ l =1 1 l 4 [ d$_{g}$ 2 ϵ$_{g}$ ( x$_{g}$l $^{) + (}$−1) l − $^{1}$d$_{q}$ cosh ( µ/T ) ϵ ( x$_{q}$l $^{) + (}$−1) l − $_{1}$d$_{s}$ 2 ϵ$_{s}$ ( x$_{s}$l ) ] , (14) IV. SECOND QUASIPARTICLE MODEL (QPM II)