of simplicity. We compare our results with the experimental data [@Abelev:2013vea] and again, find that our model explains the data very well over all the centralities.

![The variations of freeze-out volume for $\pi^{-}$. Solid symbols are HBT data points [@Adamova:2003; @Braun-Munzinger:2014lba] and open symbols are those obtained in our model calculations.](freeze-out_volume.pdf){height="25em"}

Now, we need to know $\sqrt{s_{NN}}$ dependence of chemical freeze-out volume in unit slice of rapidity to calculate transverse momentum spectra, transverse energy at midrapidity etc. Figure 5 describes the chemical freeze-out volume (dV/dy) for $\pi^{-}$ for the most central collisions at various $\sqrt{s_{NN}}$ starting from 2.7 GeV to 5.02 TeV calculated in our model with Boltzmann approximation. To calculate the dV/dy for $\pi^{-}$, we use the experimental midrapidity yield of $\pi^{-}$ [@Chatterjee:2015fua] and divide it by the corresponding number density calculated in our model. At $\sqrt{s_{NN}}$=5.02 TeV, we use the AMPT data for the midrapidity yield for $\pi^{+}$ [@Ma:2016fve] in the absence of the experimental data. We compare our model results with the HBT data [@Adamova:2003; @Braun-Munzinger:2014lba], which represents the kinetic freeze-out volume, and find that our model results follow the same trend as observed in the HBT data. While HBT data correspond to the kinetic freeze-out volume, 