# 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 bar.