Thermodynamical behaviour of the viscous generalized chaplygin gas in a flat universe

In this paper, we delve into the viscous generalized Chaplygin gas (VGCG) model, focusing on its thermodynamic stability. We utilize an equation of state represented as p=-A/ρ^α , where A is a positive universal constant, incorporating bulk viscosity into our analysis. Our study reveals how the thermodynamic properties of the universe change as we vary the bulk viscosity parameter. By examining the thermal equation of state, we find that the equation of state parameter has a direct dependency on temperature. Additionally, we investigate how this exotic viscous fluid contributes to the accelerated expansion of the universe. A key finding is that for the fluid to meet standard stability conditions, the viscosity parameter must be strictly negative, ensuring that (∂p/∂V)_S<0 and (∂p/∂V)_T<0 are satisfied throughout cosmic evolution. Our analysis indicates that the fluid maintains stability during adiabatic processes. We also demonstrate that this model upholds the condition of positive heat capacity at constant volume (c_V) and adheres to the third law of thermodynamics.