## 3 Results
### Thermokinetic Analysis of Experimental Data  
The starting point for kinetic considerations is Equation (13) and the assumption that \(g(\alpha)=\alpha\) (e.g., [PERSON] in [35]). This is supported by Equation (33) as well as the calculations presented in Table 4, although it will be necessary to verify this assumption. The calculations were based on the experimental data presented in [19] (Table 1a in [19]) for thermal dissociation of calcite in nitrogen under dynamic conditions. Bearing in mind the need to determine \(E\) and \(\ln A\), it was found that there are at least two possibilities to analyze the experimental data. The first option is to use the relationship:  
\[\ln\Big{(}\frac{\alpha}{T^{2}}\Big{)}=\ln\left(\frac{A\cdot R}{q\cdot E}\right) -\frac{E}{R\cdot T},\ q=\text{const} \tag{35}\]  
while the second one uses the Doyle approximation for the intercept presented in [20]: \begin{table}
\begin{tabular}{c c c c c} \hline \hline
**Conversion Degree, \(\alpha_{0}\)** & \(\frac{F}{R}\) **in Equation (33)** & **Intercept in Equation (33)** & **In\(A\)** & **\(E_{r}\)** \\  & & **Equation (33)** & **(\(A\) in \(\text{s}^{-1}\))** & **kJ mol\({}^{-1}\)** \\ \hline
0.1 & 24056 & 24.451 & 32.236 & 200.00 \\
0.2 & 24052 & 24.451 & 32.231 & 199.97 \\
0.3 & 24053 & 23.347 & 32.231 & 199.97 \\
0.4 & 24054 & 23.062 & 32.234 & 199.99 \\
0.5 & 24055 & 22.840 & 32.235 & 199.99 \\
0.6 & 24062 & 22.668 & 32.246 & 200.05 \\
0.7 & 24055 & 22.504 & 32.235 & 199.99 \\
0.8 & 24055 & 22.371 & 32.236 & 200.00 \\ average \(\pm\) standard deviation & - & - & 32.236 \(\pm\) 0.004 & 200.00 \(\pm\) 0.02 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Summary of calculation results for five different heating rates and for constant values of the conversion degree \(\alpha_{0}\). \(\log A=\) 14.00 \(\ln A=\) 32.236 \(r^{2}=\) 1.0000. Equations (35) and (36) can be applied to isoconversional analyses in the form:  
\[\ln\left(\frac{q}{T_{0}^{2}}\right)=\ln\left(\frac{A\cdot R}{E\cdot\alpha_{0}} \right)-\frac{E}{R\cdot T_{0}},\ \alpha_{0}=\text{const} \tag{37}\]  
when Equation (37) is a special case of Equation (33) and Equation (38):  
\[\ln q=\ln\left(\frac{0.005\cdot A\cdot E}{R\cdot\alpha_{0}}\right)-\frac{E}{R \cdot T_{0}},\ \alpha_{0}=\text{const} \tag{38}\]  
Experimental data of the thermal dissociation of calcite in nitrogen for the seven heating rates in the coordinate system of Equation (35) are presented in Figure 5.  
Equations (35)-(38) generate _KCE_ and therefore the individual estimators were statistically verified-all relationships are significant with a probability of at least 99.99%. The relevant graphs are shown in Appendix A in Figures 11-14, while whether the determined isokinetic temperatures can be considered authoritative will be prese \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline
**Heating Rate, \(q\), K (60s)\({}^{-1}\)** & **\(\frac{E}{R}\) in Equation (36)** & **Intercept in Equation (36)** & **\(r^{2}\)** & **\(E_{r}\)** & **InA** & **\(T_{0}\), K** \\ \hline
1 & 24,576 & 24.712 & 0.9994 & 204.32 & 15.81 & 876.3 \\
3 & 24,651 & 23.798 & 0.9986 & 204.95 & 15.99 & 909.7 \\
5 & 24,222 & 22.849 & 0.9988 & 201.38 & 15.57 & 927.6 \\
7.5 & 24,612 & 22.837 & 0.9991 & 204.62 & 15.94 & 943.0 \\
10 & 24,565 & 22.484 & 0.9992 & 204.23 & 15.88 & 954.6 \\
15 & 24,685 & 22.176 & 0.9997 & 205.23 & 15.97 & 971.4 \\
25 & 24,836 & 21.850 & 0.9997 & 206.49 & 16.15 & 990.6 \\ average & - & - & & \(204.46\pm 1.44\) & \(15.90\pm 0.17\) & \(939.0\pm 35.6\) \\ \(\pm\) standard deviation & - & - & & \(204.46\pm 1.44\) & \(15.90\pm 0.17\) & \(939.0\pm 35.6\) \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Analysis of experimental data of thermal dissociation of calcite in nitrogen based on Equation (36)–Doyle approximation. Figure 5: Experimental data of thermal dissociation of calcite in nitrogen for seven heating rates and nines positions of \(\alpha\) = const. in the coordinate system of Equation (35).