I would like to ask which guarantees if the Gibbs free energy has a minimum in closed system (e.g. in a chemical reaction system) at constant pressure and temperature? Why does it not decrease ad infinitum?
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3 Answers
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As this is a closed system but not an isolated system, so we can add heat to the system. And, at the same time, we can increase its volume. By doing so, we may be able to keep temperature and pressure and increase entropy (note microstate increases because the position opportunity is increased). If this can reduce Gibbs free energy continuously? I guess there is a limit because the particle speed is capped by the light speed. At certain volume, adding heat may not be able to keep up pressure. By then, the volume can not be further increased as well. So Gibbs free energy cannot decrease forever.
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We must find the minimum of $G$ taking into account the constraints imposed on the system.
An evident example : for a chemical reaction, when all the products have disappeared, the system can no longer evolve. So the interval of evolution is evidently limited.
Still for a chemical reaction, if the products are in excess, we can plot the evolution of $G$ as a function of the extend of the reaction $\xi$ and find the minimum which corresponds to the law of mass action.
answered Aug 18, 2021 at 17:24
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Interatomic potentials have a finite minimum which means that the overall enthalpy of the system has a finite minimum. And any finite system also has a finite maximum entropy.
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$\begingroup$ We state exclusively that the entropy of a spontaneous process is continuously increasing in an isolated, finite, isochoric system. Why does the entropy have a maximum? What prevents the endless increasing? $\endgroup$– TobiRCommented Jul 5, 2016 at 13:42
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$\begingroup$ @TobiR The second law states that $\dot{S}\geq 0$, not $>0$. And it has a finite maximum because, in quantum mechanics, states are discretised, and so a finite-sized system has only a finite number of possible microstates. $\endgroup$– lemonCommented Jul 5, 2016 at 14:04
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$\begingroup$ Lemon, thank you for your answer. I know that dS>=0, my problem was only if the maximum exists or not. Your argumentation was convincing for me. $\endgroup$– TobiRCommented Jul 5, 2016 at 14:15