On the thermodynamic stability of the modified Chaplygin gas

This work discusses the thermodynamic stability of an exotic fluid known as modified Chaplygin gas [MCG]. In the literature, one considers such a fluid as a perfect one which obeys the adiabatic equation of state P=Bρ−A/Aρα, where P stands for the pressure and ρ is the energy density of the fluid; the parameters A and B are positive constants, and α⩾0. Extending the analysis presented in [F.C. Santos, M.L. Bedran, V. Soares, On the thermodynamic stability of the generalized Chaplygin gas, Phys. Lett. B 636 (2006) 86-90] to the MCG, it is remarked that if the energy density of the Chaplygin fluid in its generalized form (B=0) or modified form (B≠0) depends on volume only, the temperature of the fluid remains zero at any pressure or volume it may attain. One sets up a scenario to determine the corresponding thermal equation of state of the MCG and it reveals that the MCG only presents thermodynamic stability during any expansion process if its thermal equation of state depends on temperature only, P=P(T). This scenario also establishes physical constraints on the parameters B and α of this equation. Moreover, the modified Chaplygin gas may cool down through any thermodynamic process without facing any critical point or phase transition.