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We analyse the phase shifts of standing, slow magnetohydrodynamic (MHD) wavesin solar coronal loops using a linear MHD model taking into account the role ofthermal conductivity, compressive viscosity, radiative losses, andheating-cooling misbalance. We estimate the phase shifts in time and space ofdensity and temperature perturbations with respect to velocity perturbationsand also calculate the phase difference between density and temperatureperturbations. The overall significance of compressive viscosity is found to benegligible for most of the loops considered in the study. For loops with highbackground density and/or low background temperature, the role of radiativelosses (with heating-cooling misbalance) is found to be more significant. Alsothe effect of heating-cooling misbalance with a temperature- anddensity-dependent heating function is found to be more significant in the caseof longer loop lengths ($L=500$\, Mm). We derived a general expression for thepolytropic index [$\gamma_{\rm eff}$] and found that under linear MHD theeffect of compressive viscosity on polytropic index is negligible. Theradiative losses with constant heating lead to a monotonic increase of$\gamma_{\rm eff}$ with increasing density whereas the consideration of anassumed heating function [$H(\rho,T) \propto \rho^{a}T^{b}$, where $a=-0.5$ and$b=-3$] makes the $\gamma_{\rm eff}$ peak at a certain loop density. We alsoexplored the role of different heating functions by varying the free parameters$a$ and $b$ for a fixed loop of $\rho_0 = 10^{-11}$\, kg $\text{m}^{-3}$, $T_0= 6.3$\, MK and loop length $L= 180$\, Mm. We find that the consideration ofdifferent heating functions [$H(\rho,T)$] leads to a significant variation inthe phase difference between density and temperature perturbations; however,the polytropic index remains close to a value of 1.66.

Role of Non-Ideal Dissipation with Heating-Cooling Misbalance on the Phase Shifts of Standing Slow Magnetohydrodynamic Waves