From Thermodynamics (fundamental equation): \begin{equation} dh = Tds + vdp \end{equation} h=specific enthalpy (Enthalpy/mass); T=Temperature; v=specific volume; s=specific entropy; p=pressure
I want: \begin{equation} (\frac{\partial h}{\partial T})_{p=const} \rightarrow dp=0 \end{equation}
Differentiating by product rule yields: \begin{equation} (\frac{\partial h}{\partial T})_{p} = (\frac{\partial (Tds)}{\partial T})_{p}\\ = ds + T(\frac{\partial d s}{\partial T})_{p} \end{equation}
I'm confused by the double differential $\partial d s$. What does this say? The above described method yields a wrong result.
For those interested, I want to derive the Gibbs-Helmholtz equation. I know a derivation from a book, which is a little different. I guess my mistake is that I need to tranform dh(s,p) to dh(T,p) to be able to differntiate by T? But I'm not sure...