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.
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