  An extension of Hadron Resonance Gas (HRG) model is constructed to include
interactions using relativistic virial expansion of partition function. The
non-interacting part of the expansion contains all the stable baryons and
mesons and the interacting part contains all the higher mass resonances which
decay into two stable hadrons. The virial coefficients are related to the phase
shifts which are calculated using K-matrix formalism in the present work. We
have calculated various thermodynamics quantities like pressure, energy
density, and entropy density of the system. A comparison of thermodynamic
quantities with non interacting HRG model, calculated using the same number of
hadrons, shows that the results of above formalism are larger. A good agreement
between equation of state calculated in K-matrix formalism and lattice QCD
simulations is observed. Specifically the lattice QCD calculated interaction
measure is well described in our formalism. We have also calculated second
order fluctuations and correlations of conserved charges in K-matrix formalism.
We observe a good agreement of second order fluctuations and baryon-strangeness
correlation with lattice data below the cross-over temperature.
