  The formalism to augment the classical models of equation of state for real
gases with the quantum statistical effects is presented. It allows an arbitrary
excluded volume procedure to model repulsive interactions, and an arbitrary
density-dependent mean field to model attractive interactions. Variations on
the excluded volume mechanism include van der Waals (VDW) and Carnahan-Starling
models, while the mean fields are based on VDW, Redlich-Kwong-Soave,
Peng-Robinson, and Clausius equations of state. The VDW parameters of the
nucleon-nucleon interaction are fitted in each model to the properties of the
ground state of nuclear matter, and the following range of values is obtained:
$a = 330 - 430$ MeV fm$^3$ and $b = 2.5 - 4.4$ fm$^3$. In the context of the
excluded-volume approach, the fits to the nuclear ground state disfavor the
values of the effective hard-core radius of a nucleon significantly smaller
than $0.5$ fm, at least for the nuclear matter region of the phase diagram.
Modifications to the standard VDW repulsion and attraction terms allow to
improve significantly the value of the nuclear incompressibility factor $K_0$,
bringing it closer to empirical estimates. The generalization to include the
baryon-baryon interactions into the hadron resonance gas model is performed.
The behavior of the baryon-related lattice QCD observables at zero chemical
potential is shown to be strongly correlated to the nuclear matter properties:
an improved description of the nuclear incompressibility also yields an
improved description of the lattice data at $\mu = 0$.
