When is the Assumption that Enthalpy is Constant over Temperature Change Invalid? In a question, I was asked to integrate the Gibbs-Helmholtz equation to derive some formula. Then the next question asked:


  Identify one assumption that you have made in deriving the above equation and identify one
  scenario where it is a very bad assumption, and explain why the assumption fails


Now the assumption that was made was the $\Delta H_{\mathrm{fus}}$ is constant over the change in temperature. However, could someone please explain when and why this assumption fails. 

Thanks.
The $G{-}H$ equation describes the effect of $T$ on $\Delta G$ at constant pressure. But, along the fusion contour of $T$ vs $p$, $T$ is a unique function of $p$. So, along this contour, $p$ is changing. So the $G{-}H$ equation is not valid to use for a change of phase such as fusion. The $G{-}H$ equation was developed to describe the effect of $T$ on $\Delta G$ for chemical reactions at constant pressure, usually for the change from separate pure reactants to separate pure products at the standard pressure of $1\ \mathrm{bar}$.