Thermodynamic Behaviour of Viscous Variable Chaplygin Gas in a Flat Universe

Abstract

In this manuscript we have studied the thermodynamic stability of the viscous variable Chaplygin gas (VVCG) model. The equation of state p = −B ρ is employed, where B = B0V −n 3 and B0 is a positive universal constant. The bulk viscosity coefficient ξ = ξ0ρ 1 2 has also been included in our research. When a fluid satisfies the established stability requirements, we obtain the intriguing conclusion that ( ∂peff ∂V )S < 0 and ( ∂peff ∂V )T < 0 throughout the evolution for ξ0 < 0, when n without a certainty, are limited to the negative values. Additionally, the third law of thermodynamics is assured to be valid in this instance, as is the positivity of thermal heat capacity (cV ). Also we have discussed that how thermal variables depend on either temperature or volume. A new general equation of state for the VVCG model as a function of volume and temperature is obtained during the thermal process, which also shows that the cosmos is thermodynamically stable. Furthermore, the thermal and caloric equation-of-state parameters coincide at large volume in the limit T → 0.