Thermodynamic behaviour of a variable Chaplygin gas in a flat universe with bulk viscosity

In this research paper, we have discussed the thermodynamic behavior of the viscous variable Chaplygin gas (VVCG) model. The equation of state p=-B/ρ p = - B ρ has been used, where B=B₀V-n/3 B = B 0 V - n 3 and B₀ B 0 is a positive universal constant. Our study also includes the bulk viscosity coefficient, ξ =ξ ₀ρ 1/2 ξ = ξ 0 ρ 1 2 . As long as the values of n remain negative, we arrive at the intriguing conclusion that when a fluid satisfies the established stability conditions, then for ξ ₀<0 ξ 0 < 0 , (∂ peff∂ V)S<0 ( ∂ p eff ∂ V ) S < 0 and (∂ peff∂ V)T<0 ( ∂ p eff ∂ V ) T < 0 throughout the entire evolution. Furthermore, it can be confirmed that both the positivity of the thermal heat capacity ( cV c V ) and the third law of thermodynamics are applicable in this situation. Additionally, this model has been compared graphically with the VCG model, and we have discussed how all the thermal variables are functions of volume or temperature. A new general equation of state has been obtained for the VVCG model as a function of volume and temperature during a thermal process, which also shows that the universe is thermodynamically stable. Furthermore, when T→ 0 T → 0 , the parameters of the