The Gibbs–Helmholtz equation was developed in the 1870's, while Nernst's heat theorem was developed in the early $20^{th}$ century (according to google/wikipedia). Nernst's heat theorem tells us that the change in entropy tends to be zero in absolute temperature. But did Nernst's heat theorem provide any new insight? Because if we put $T=0$ in the Gibbs–Helmholtz equation, then $\Delta G=\Delta H$. Anyone could have thereby concluded that as temperature approaches 0, entropy change becomes zero already in the $19^{th}$ century. I am quite confused regarding it, those were my assumptions (probably wrong), what was new about Nernst's heat theorem ?


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If you read the Wikipedia page for Nernst's Heat Theorem carefully, it explains that the novelty lies not in showing (as you point out) that as $T \rightarrow 0$, $\Delta G \rightarrow \Delta H$, but rather that as $T \rightarrow 0$, the slope of $\Delta G$ as a function of T goes to 0, that is

$$\lim_{T\rightarrow0} \left( \frac{\partial \Delta G}{\partial T} \right)_p =0$$

Then, since that slope is given by $-\Delta S$, it predicts the experimentally confirmed conclusion that as $T \rightarrow 0$, $\Delta S \rightarrow 0$,


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