This research delved into the energetic properties of catalysts synthesized from residual sludge from the textile, galvanic, and tannery industries. The experimental process consisted of an initial heat treatment to activate their catalytic properties and a thermal analysis employing differential scanning calorimetry (DSC). This technique permitted the investigation of the materials’ thermal behavior as a function of temperature, ranging from 142 to 550 °C, effectively controlling the heating rates and pressure conditions. The data gathered were the input for constructing specific heat models through polynomial regression employing the least squares method. These models were subsequently used to estimate variations in the enthalpy and entropy for both the sludge and catalysts through integration. Third-degree polynomials primarily characterized the specific heat models that accurately represented the samples’ thermal behavior, considering variations in their physicochemical properties that influenced it. The catalysts derived from residual sludge from the textile industry exhibited the models with the most robust statistical fit. Concurrently, the catalysts from the galvanic industry displayed noteworthy similarities with the bibliographic data across various temperature points. The mathematical models determined the specific heat (Cp) as a function of temperature, which, in turn, was used to estimate the enthalpy and entropy variations in the sludge and catalysts under study. The highest enthalpy value corresponded to the sludge and catalyst obtained from the tannery industry, with a Cp of 5.60 J/g-K at 603 K and 2.45 J/g-K at 445.6 K. Finally, the third-degree polynomials showed the best mathematical models since (1) they considered the variations in the physicochemical properties that intervened in the behavior of Cp as a function of temperature; (2) they presented a better statistical fit; and (3) they showed consistency with the existing information in the literature for the textile industry and the galvanic industries.
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