Measurement of Differential Adsorption Enthalpy

The calorimetry technique coupled with manometry shown in Fig. 7.12 allows the measure of the heat emanated by the adsorption of a given amount of gas on the solid. In thermodynamics it is essential to know at what function of state corresponds this adsorption heat. This depends on the calorimetric technique and experimental 

When an amount of gas is introduced in the calorimetric cells, two energetic exchanges must be taken into account thermal energy due to the adsorption and mechanical energy due to the expansion of the gas in the cells. Thermodynamically, the operation, which consists to introduce a given amount of gas into a vessel containing or not the adsorbent, is equivalent to the compression of gas enclosed in a cylinder by moving the piston [10]. This equivalent thermodynamic system is represented in Fig.7.14. 

Let us consider the adsorption of a single component in the sample cell. The amount of matter present in the system and their molar internal energies are defined 

The differential mechanical work exchanged with the outside world, assuming the transformation as reversible, is expressed by  

SWs = Vsdp - dn RT = Vsdp + dn RT Thus the differential heat in the sample is  

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