  In this work, we have studied the isothermal compressibility ($\kappa_T$) as
a function of temperature, baryon chemical potential and centre-of-mass energy
($\sqrt{s_{NN}}$) using hadron resonance gas (HRG) and excluded-volume hadron
resonance gas (EV-HRG) models. A mass cut-off dependence of isothermal
compressibility has been studied for a physical resonance gas. Further, we
study the effect of heavier resonances ($>$ 2 GeV) on the isothermal
compressibility by considering the Hagedorn mass spectrum,
${\rho}(m)\sim{\exp(bm)}/{(m^2+m_0^2)^{5/4}}$. Here, the parameters, $b$ and
$m_0$ are extracted after comparing the results of recent lattice QCD
simulations at finite baryonic chemical potential. We find a significant
difference between the results obtained in EV-HRG and HRG models at a higher
temperatures and higher baryochemical potentials. The inclusion of the Hagedorn
mass spectrum in the partition function for hadron gas has a large effect at a
higher temperature. A higher mass cut-off in the Hagedorn mass spectrum takes
the isothermal compressibility to a minimum value, which occurs near the
Hagedorn temperature ($T_H$). We show explicitly that at the future low energy
accelerator facilities like FAIR (CBM), Darmstadt and NICA, Dubna the created
matter would be incompressible compared to the high energy facilities like RHIC
and LHC.
