# 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 $$1\ \mathrm{bar}$$.