Isosteric heat in MS Sorption

Hello everyone,

I have a question concerning the formalism used to calculate the isosteric heat of adsorption (qst) in Sorption. According to the documentation, it is calculated as:

qst = RT  - + mu_intra          (eq. 1)

The intramolecular chemical potential mu_intra is zero if the molecule has no internal degrees of freedom, so I am only interested in the expression qst = RT - . is the mean energy. I am now wondering how the relationship between this very simple formula and the more complicated "fluctuation formula" can be established:

qst = RT - ( - ) /  ( - ^2)          (eq. 2)

Is eq. 1 merely an approximation to the more precise eq. 2, or are there more fundamental differences in the derivation? I would be happy about any references that could give hints on a link between these two expressions.

Best regards

Michael Fischer