Heat Capacity Changes During Transformations

The only unknown function is the heat flow due to the reaction alone. 

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Figure 3.26 Subtraction technique for elimination of effect of sample heat capacity change. The endotherm from the DTA trace represents both the latent heat of transformation as well as a shift in heat capacity of the sample during the transformation. The baseline (which is the sample temperature lag relative to the reference) shifts most rapidly near the center of the endotherm, where the conversion of reactant to product is most fervent. The right-hand trace represents a DTA endotherm with the effects of sample heat capacity changes subtracted out. Note that in this case, where the total heat capacity of the product is less than the reactant, this subtraction has resulted in an endotherm of larger area.

Before actual data can be fit to a model, extraneous effects manifested in the trace must be removed, such as the shift in baseline as a result of the change in heat capacity of the sample during the transformation (see section 3.7.2). It may, for some device designs (e.g. post-type DTA), be difficult to purify the instrument output to represent only the latent heat from the transformation because of random baseline float. Hence, the data set fitting a particular model is a necessary but insufficient criterion for guaranteeing that the model describes the measured phenomenon. 

As a first approximation it is assumed that the change in value for the product of density and heat capacity during the course of reaction can be neglected and that all calculations may use a mean value. Furthermore it is recommendable to transfer the time variable into a dimensionless form. Substitution and transformation yields ... 

Heat is also required to transform moisture from a liquid to gas (latent heat Cw = 2260 kJ kg ). The total heat depends on the moisture content of the material and the rate of change is determined by the evaporating rate. Evaporation can also be described by the equations of chemical kinetics. If the mass change of water during the heating process in known, the kinetic parameters can be estimated by the methods introduced previously. In Samanta et al. [4], a 1% mass of moisture content was assumed, while in Keller et al. [1] a 0.5% mass of moisture content was taken. In both cases, the effects of moisture evaporation on heat capacity was assumed roughly as a triangular function dependent on temperature without kinetic considerations. 

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