  We study phase shifts of the propagating slow waves in coronal loops invoking
the effects of thermal conductivity, compressive viscosity, radiative losses
and heating-cooling imbalance. We derive a general dispersion relation and
solve it to determine the phase shifts of density and temperature perturbations
relative to the velocity and their dependence on the equilibrium parameters
($\rho_0$, $T_0$). We estimate phase difference ($\Delta \phi$) between density
and temperature perturbations and its dependence on $\rho_0$ and $T_0$. The
effect of viscosity on the phase shifts was found negligible. The role of
radiative losses along with h/c imbalance for chosen specific heating function
($H(\rho, T) \propto \rho^{-0.5} T^{-3}$) in determining phase shifts, is found
to be significant for the high density and low temperature loops. The h/c
imbalance can increase the phase difference ($\Delta \phi \approx 140^\circ$)
for low temperature loops compared to the constant heating case ($\Delta \phi
\approx 30^\circ$). We derive a general expression for the polytropic index. We
find that in the presence of thermal conduction alone, the polytropic index
remains close to its classical value for all the considered $\rho_0$ and $T_0$.
However, it reduces to a value $1.2$ when loop density is decreased by an order
of magnitude compared to its normal coronal value. We find that the inclusion
of radiative losses, with or without h/c imbalance, cannot explain the observed
polytropic index. The thermal ratio ($d$) needs to be enhanced by an order of
magnitude, in order to explain its observed value $1.1 \pm 0.02$ in the solar
loops. We also explore the role of different heating functions for typical
coronal parameters and found that although the polytropic index remains close
to its classical value, the phase difference is highly dependent on the form of
heating function (The abstract is restructured).
