Experimental Evaluation of Self-cooling

Method With the exception of installation of a thermocouple between two alum crystals pressed up together [1-3], no simple and reliable methods for the experimental determination of the magnitude of self-cooling in a decomposing solid existed until recent years. Verification of the above calculations was thus difficult. The situation changed for the better only very recently with the appearance of third-law methodology in TA [8]. 

In contrast to the second-law method, for the third-law method the influence of self-cooling manifests itself in overestimation of the E parameter. This is evident from Eqs. 4.10-4.12. Therefore, the ratio of these two values measured by different methods is a very sensitive indicator of self-cooling. 

If the only cause of overestimation of the experimental values Eexpt, calculated by the third-law method, is the self-cooling effect, then its magnitude can be easily determined. If it is also assumed that the E magnitude at the lower temperature is free of this effect (i.e., that the sample temperature, Tg, is equal to the furnace temperature, Tf) and corresponds to the true value of the E parameter, Etrue, then it becomes possible to determine the actual value of sample temperature for any higher decomposition temperature. This temperature is equal to  

The above assumption, that self-cooling is the only cause of overestimation of the experimental values Texpt, is valid only for reactants decomposing to gaseous products. For decompositions with formation of a solid product, there is an additional reason for overestimation related to the condensation effect (Sect. 8.2). Therefore, it is more appropriate to call this combined effect the apparent self-cooling effect. 

This difference can be easily explained. For formation of solid product on the reactant surface, heating of the sample in a high vacuum by radiation (for example, from the walls of an alumina container) occurs through an intermediate product layer, for example, CaO for the CaCOs decomposition. This means that the effective value of the emittance for heat transfer from the container walls to the calcite crystal covered by a CaO layer, is the product of the corresponding coefficients for the four surfaces AI2O3, CaO (outward side), CaO (inward side), and CaCOs. (The residual thermal conductivity through point contacts between CaCOs crystal and CaO nanoparticles is neglected.) If 

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