  This article explores the van der Waals gas model proposed to describe the
hadronic stages of nuclear fireball evolution during the cooling stage. Two
different models were proposed for the early and late stages of hadronization.
At the initial stage, a two-component meson model consisting of $\pi^0$ and
$\pi^+$ mesons was suggested, and at the later stage, a two-component nucleon
model consisting of protons and neutrons was proposed. The interaction
potential for both models was represented by a rectangular well, and the
statistical sum was calculated using the saddle-point method. The analytic
expressions for pressure and chemical potentials obtained from the model were
compared with the corresponding numerical results of other authors obtained
earlier using quantum chromodynamics (QCD) methods. The possibility of applying
and using the effective chemical potential is also analyzed.
