## 3 Results
### Consequences of the Analysis of Experimental Data  
It should be noted that the relations \(\ln\alpha\) vs. \(\frac{1}{T}\) are known in the literature as the temperature criterion [39] and are also discussed in works [40; 41]. Equations (40) with (42), (43) are new elements in this respect and allow the determination of the isokinetic temperature. As is known, the temperature criterion is valid for low conversion degrees. In the meantime, in this work, both in the part concerning model analyses (Figure 1) and experimental data of the thermal dissociation of calcite (Table 4), a linear relationship was obtained for all data, i.e., for the analyzed range of variation of conversion degree: as well for total range, as with its limitation, respectively. While for model considerations this is acceptable, then for other more complicated solid decompositions after an initial stage with a high activation energy its value decreases with the conversion degree. The observations provided in [31] show that, in practice, different kinds of dependences of \(E\) on \(\alpha\) can occur (\(E=E(\alpha)\)). On the other hand, in \begin{table}
\begin{tabular}{c c c c c c c c} \hline \hline
**Heating Rate** & \(A_{0}\) & \(A_{1}\cdot 10^{-5}\), & \(A_{2}\) & \(\mathbf{r^{2}}\) & \(\alpha_{0}\) **acc.** & \(T_{0}\)**, **K acc.** & \(T_{a=0,5}\)**, **K** \\
**q, K (-60s)\({}^{-1}\)** & & **K** & & & **Equation (43)** & **Equation (42)** & **[5]** \\ \hline
1 & 893.70 & 1.302 & 110.52 & 0.9993 & 0.0266 & 879.05 & 894.95 \\
3 & 552.88 & 0.911 & 66.97 & 0.9999 & 0.0303 & 911.24 & 925.14 \\
5 & 530.03 & 0.889 & 64.05 & 1.0000 & 0.0315 & 928.01 & 942.14 \\
7.5 & 405.68 & 0.741 & 48.25 & 0.9999 & 0.0330 & 943.31 & 956.64 \\
10 & 463.43 & 0.824 & 55.46 & 0.9999 & 0.0325 & 955.59 & 969.13 \\
15 & 278.84 & 0.587 & 32.23 & 1.0000 & 0.0354 & 970.59 & 983.63 \\
25 & 366.81 & 0.717 & 43.17 & 0.9999 & 0.0343 & 991.37 & 1004.62 \\ average & & & & & 0.0319 \(\pm\) 0.0027 & 939.88 \(\pm\) 34.88 & \\ deviation & & & & & & \\ \hline \hline \end{tabular}
\end{table} 
Table 5: Results of the analysis of experimental data on the thermal decomposition of CaCO\({}_{3}\) in nitrogen for seven heating rates using the three-parameter Equation (40). Equations (35)-(38) with assumed Arrhenius parameters, the 0 th order kinetics, \(g(\alpha)=\alpha\) was used. Nevertheless, what distinguishes this work from previous considerations is the possible range of variation of \(\alpha\in[0.05;\,0.9]\) to be analyzed, which omits the extremely important initial range for low conversion degree, as well as the end of the process. The first remark that comes to mind for comparison is the value of initial temperature-for the model it is equal to average \(T_{0}=586.3\) K, while for the experimental data (Figures A1-A4) it depends on the adopted kinetic function and, see Table 4, on average it is equal to \(T_{0}=939.0\) K (depending on \(q\)). When the experimental data for \(q=\text{const}\) are analyzed using Equations (35) and (36), then \(T_{iso}=950-1061\) K. On the other hand, when we use isoconversion methods (\(\alpha=\text{const}\)) using Equations (37) and (38), we observe a wider range of variation \(T_{iso}=1074-1298\) K, which authorizes the conclusion that isoconversion methods are characterized by a much weaker increase in the \(\ln A\) factor in relation to activation energy. It should be noted that the parameters of the Arrhenius equation determined in this work from experimental data of the thermal decomposition of CaCO\({}_{3}\) in nitrogen have similar values and are in agreement with the data collected in [35] (e.g., [PERSON]): \(E=191\) kJ\(\cdot\)mol\({}^{-1}\), \(\ln A=15.4/\)\(A\)in \(s^{-1}\). For the four cases resulting from Equations (35)-(38), the determined Arrhenius law parameters can be treated as average values, as evidenced by the very small standard deviations. Nevertheless, these small variations generate an observable _KCE_.