The emergent Universe scenario is obtained in flat Universe with equation of state (EoS) (\(P =B\rho -A\rho ^{{1}/{2}}\)) (where A and B are constants) as per Mukherjee et al. The EoS of this emergent Universe (EU) model can describe the current accelerated expansion and the initial singularity of the Universe. Following the standard thermodynamical criteria, stability of the EU models has been discussed. It is noted from thermal stability and positivity of adiabatic sound speed that B satisfies the values \(B=\frac{1}{3}, 1\) in the EU model. So, the emergent models with \(B=0, -\frac{1}{3}\) are not supported with the stability issue. Further, the third law of thermodynamics is obeyed in this case for \(B <-1\) (or with \(A=0\), but it is outside the EU), i.e., any of the four discrete value of B \( (= 0, -\frac{1}{3}, \frac{1}{3}, 1)\) does not support this third law. The specific heat at constant volume \(c_{v}\) obeys the relation \(c_{v}\ge 0\) for \(T\ge 0\) in the EU models. Two characteristic volume scales, critical volume \(V_{c}\) and flip volume \(V_{f}\) are obtained from zero pressure and zero deceleration condition in this model. Physically, these should follow the relation \(V_{f}> V_{c}\), which are actually followed in the EU model for \(B=\frac{1}{3},1\).

在状态条件为（EoS）（\（P = B \ rho -A \ rho ^ {{{1} / {2}} \））的平坦宇宙中获得紧急宇宙场景，其中A和B为常数。根据Mukherjee等。这个新兴的宇宙（EU）模型的EoS可以描述宇宙的当前加速膨胀和初始奇点。遵循标准的热力学标准，已经讨论了EU模型的稳定性。从绝热声速的热稳定性和正性注意到，B满足EU模型中的值\（B = \ frac {1} {3}，1 \）。因此，带有\（B = 0，-\ frac {1} {3} \）的紧急模型稳定性问题不支持。此外，在这种情况下，对于\（B <-1 \）（或使用\（A = 0 \），但在EU之外），遵循热力学第三定律，即B 的四个离散值中的任何一个\（（= 0，-\ frac {1} {3}，\ frac {1} {3}，1）\）不支持该第三定律。在恒定的体积比热\（C_ {V} \）服从关系\（C_ {V} \ GE 0 \）为\（T \ GE 0 \）在欧盟的模型。在该模型中，从零压力和零减速条件获得了两个特征体积标度，即临界体积\（V_ {c} \）和翻转体积\（V_ {f} \）。从物理上讲，这些应遵循以下关系\（V_ {f}> V_ {c} \），实际上在EU模型中遵循\（B = \ frac {1} {3}，1 \）。