  Here we present a physically transparent generalization of the multicomponent
Van der Waals equation of state in the grand canonical ensemble. For the
one-component case the third and fourth virial coefficients are calculated
analytically. It is shown that an adjustment of a single model parameter allows
us to reproduce the third and fourth virial coefficients of the gas of hard
spheres with small deviations from their exact values. A thorough comparison of
the compressibility factor and speed of sound of the developed model with the
one and two component Carnahan-Starling equation of state is made. It is shown
that the model with the induced surface tension is able to reproduce the
results of the Carnahan-Starling equation of state up to the packing fractions
0.2-0.22 at which the usual Van der Waals equation of state is inapplicable. At
higher packing fractions the developed equation of state is softer than the gas
of hard spheres and, hence, it breaks causality in the domain where the
hadronic description is expected to be inapplicable. Using this equation of
state we develop an entirely new hadron resonance gas model and apply it to a
description of the hadron yield ratios measured at AGS, SPS, RHIC and ALICE
energies of nuclear collisions. The achieved quality of the fit per degree of
freedom is about 1.08. We confirm that the strangeness enhancement factor has a
peak at low AGS energies, while at and above the highest SPS energy of
collisions the chemical equilibrium of strangeness is observed. We argue that
the chemical equilibrium of strangeness, i.e. $\gamma_s \simeq 1$, observed
above the center of mass collision energy 4.3 GeV may be related to the
hadronization of quark gluon bags which have the Hagedorn mass spectrum, and,
hence, it may be a new signal for the onset of deconfinement.
