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Why is entropy change a better way of determining a spontaneous process compared to the change in internal energy?

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  • $\begingroup$ There is a law of Thermodynamics that tells us something about the direction in which entropy evolves. Does that give you a hint? $\endgroup$ – Floris Nov 5 '14 at 2:40
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The change in internal energy is not a relevant quantity for spontaneous evolution of a system. Consider an isolated system made of two blocks of the same material at two different temperatures such that $T_1>T_2$. Heat will flow from $1$ to $2$ but the total change in internal energy is $\Delta U_{1+2}=0$. This information is therefore not useful.

On the other hand, the change in total entropy is $\Delta S_{1+2}=Q/T_2-Q/T_1>0$ and can tell us about the direction of the process.

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Entropy change is not better nor worse than any other quantity obtained from a Legendre transformation, but its applicability when is convenient is different. If the system is isolated (internal energy is constant) and some internal constraints are relaxed then entropy is maximized when equilibrium is reestablished. On the other hand, if the interaction is such that the entropy is kept constant then internal energy is minimized in equilibrium. While these two conditions are completely equivalent mathematically constant entropy - minimum energy interaction is difficult to achieve in practice, but constant energy - maximum entropy is easy.

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because G=H_TS, and entropy of system at constant pressure must increase if its enthalpy remains constant and know that we've a spontaneous reaction when ¤s>0,

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  • $\begingroup$ This is not even a whole sentence. It should probably rather be a comment than an answer (once you have enough reputation, you can comment on any post). Otherwise, please expand your answer and elaborate on your point. $\endgroup$ – Martin Nov 5 '14 at 8:08

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