# Gibbs–Helmholtz equation

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 ?

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 $$T \rightarrow 0$$, $$\Delta S \rightarrow 0$$,