DH ¼ DG À Tð@GÞ=@TÞ p
ð2:2Þ
yields the same result when T ! 0. From Eqs. (2.1) and (2.2) any competent thermodynamicist would easily realise that the slope of the free energy
curve with temperature is related to the entropy change by;
ð@ðDGÞ=@TÞ p ¼ ÀDS
whilst we have already shown that for the enthalpy curve (Appendix A);
ð@ðDHÞ=@TÞ p ¼ DC p
But what Richards, van’t Hoff and Haber all missed was that the slopes of
the free energy and enthalpy curves always become tangential to one another
as absolute zero is approached, and hence in the limit as T approaches zero so
too must DS and DC p . The bold step that Nernst then took was to look
beyond just the published data and extend his observations to all chemical
reactions. Nernst therefore assumed that this tangential behaviour for the
variation of DH and DG with T was the ‘norm’ and he expressed the consequence of this in his Heat Theorem published in 1906, viz.,
ΔG
ΔH
O
T
Fig. 2.3 Schematic variation of the enthalpy and the (Gibbs) free energy change with
temperature
62
D. Sheppard