Adsorption is an exothermic process while desorption is endothermic, i.e. having a cooling effect. The heat of desorption is the sum of latent heat of vaporization and the isosteric heat, i.e.

DHdes = DHlat + Qst                                              (1)

The sign of the isosteric heat is always the same as the sign of the latent heat of vaporization (or condensation). Thus, taking drying as an example, one must supply more heat than the latent heat of vaporization to dry water from a material.

The isosteric heat can be determined from the van't Hoff equation:

Qst = (RT2/P) (dAh/dT)M                                      (2)

where Ah is the activity of the adsorbed component. Pressure (P) is in Pa. 

An integral form Eq. (2) gives

ln (Ah) = Qst/(RT) + C                                            (3)

Experimental measurement of Qst often gives an exponentially decaying function with increasing adsorbate loading:

Qst = Q0 * exp(- y / yref)                                          (4)

where y and yref have the same unit, for example (wt.%). Thus, Qst is not a constant, but varying with the property of the materials (Q0) and the adsorbate activity [Ah in Eq. (3)] or loading [y in Eq. (4)].

The above only provides a main thread. For more details, you can refer to books or articles about drying, which will guide you through the topic. For example, Mulet et al (2002) Equilibrium isotherms and isosteric heats of morel. J. of Food Processing 53: 75-81. 

Thank you for the clear explanation. The paper I'm using for the model is assuming a constant value for Qst and the latent heat of vaporization. I'll try replacing Qst with the heat of desorption.

Thanks again.

Hello sir ,

I use silica gel-water pair for adsorption cooling system and i want to calculate the isosteric heat , so what is the value of R in the van't hoff equation ?