Invoking the effects of thermal conductivity, compressive, viscosity, radiative losses, and heating-cooling misbalance, we derive the new general dispersion relation for the propagating slow MHD waves in the solar corona and solve it to determine the phase shifts of density and temperature perturbations along with their dependence on the equilibrium parameters of the plasma such as the background density and temperature. We also derive a new generalised mathematical expression for the polytropic index using the linear MHD model and find that in the presence of thermal conduction alone it remains close to its classical value for all the considered equilibrium density and temperature observed in typical coronal loops. Under the considered heating and cooling models, we find that the expected polytropic index can be matched with the observed value of 1.1 ± 0.02 in typical coronal loops if the thermal conductivity is enhanced by an order of magnitude compared to its classical value. We also explore the role of different heating functions for typical coronal parameters and find that although the polytropic indices remain close to 5/3, the phase difference between density and temperature perturbations is highly dependent on the form of heating function.
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