## 3 Results and Discussion
\[\rm H^{0}(T)-H^{0}(298.15)=\int_{298.15}^{T}C^{0}_{p}dT, \tag{9}\]  
\[\rm S^{0}(T)=S^{0}(298.15)+\int_{298.15}^{T}\frac{C_{p}}{T}dT. \tag{10}\]  
A function of \(\rm\Phi^{xx}(T)\) has been calculated on the basis \(\rm S^{0}(T)\) and \(\rm H^{0}(T)-H^{0}(298.15)\):  
\[\rm\Phi^{xx}(T)=S^{0}(T)-\frac{H^{0}(T)-H^{0}(298.15)}{T}. \tag{11}\]  
These equations make it possible to calculate changes in thermodynamic properties with temperature variations based on the experimental data of heat capacity \(\rm C^{0}_{p}(T)\) (Table 7). \begin{table}
\begin{tabular}{c c c c c} \hline
**T, K** & \(\rm C^{0}_{p}(T)\pm\Delta J/(mol\cdot K)\) & \(\rm S^{0}(T)\pm\Delta J/(mol\cdot K)\) & \(\rm H^{0}(298.15)\pm\Delta J/mol\) & \(\rm\Phi^{xx}(T)\pm\Delta J/(mol\cdot K)\) \\ \hline  & & \multicolumn{3}{c}{NdNa\({}_{2}\)NiMnO\({}_{5}\)} \\
298.15 & 215 \(\pm\) 8 & 239 \(\pm\) 7 & - & 239 \(\pm\) 16 \\
300 & 213 \(\pm\) 8 & 240 \(\pm\) 17 & 430 \(\pm\) 20 & 239 \(\pm\) 16 \\
325 & 180 \(\pm\) 7 & 256 \(\pm\) 18 & 5340 \(\pm\) 210 & 240 \(\pm\) 17 \\
350 & 148 \(\pm\) 6 & 269 \(\pm\) 19 & 9440 \(\pm\) 370 & 241 \(\pm\) 17 \\
375 & 241 \(\pm\) 9 & 283 \(\pm\) 20 & 14,550 \(\pm\) 570 & 244 \(\pm\) 17 \\
400 & 278 \(\pm\) 11 & 300 \(\pm\) 21 & 21,110 \(\pm\) 830 & 247 \(\pm\) 17 \\
425 & 282 \(\pm\) 11 & 317 \(\pm\) 22 & 28,170 \(\pm\) 1100 & 260 \(\pm\) 17 \\
450 & 237 \(\pm\) 9 & 331 \(\pm\) 23 & 34,620 \(\pm\) 1360 & 254 \(\pm\) 18 \\
475 & 195 \(\pm\) 8 & 343 \(\pm\) 24 & 40,010 \(\pm\) 1570 & 259 \(\pm\) 18 \\
500 & 233 \(\pm\) 9 & 354 \(\pm\) 24 & 45,450 \(\pm\) 1780 & 263 \(\pm\) 18 \\
525 & 262 \(\pm\) 10 & 366 \(\pm\) 25 & 51,650 \(\pm\) 2020 & 268 \(\pm\) 19 \\
550 & 286 \(\pm\) 11 & 379 \(\pm\) 26 & 58,500 \(\pm\) 2290 & 273 \(\pm\) 19 \\
575 & 307 \(\pm\) 12 & 392 \(\pm\) 27 & 65,920 \(\pm\) 2580 & 278 \(\pm\) 19 \\
600 & 326 \(\pm\) 13 & 406 \(\pm\) 28 & 73,850 \(\pm\) 2890 & 283 \(\pm\) 20 \\
625 & 342 \(\pm\) 13 & 419 \(\pm\) 29 & 82,200 \(\pm\) 3220 & 288 \(\pm\) 20 \\
650 & 357 \(\pm\) 14 & 433 \(\pm\) 30 & 90,960 \(\pm\) 3570 & 293 \(\pm\) 20 \\
675 & 370 \(\pm\) 15 & 447 \(\pm\) 31 & 100,050 \(\pm\) 3920 & 299 \(\pm\) 21 \\ \hline \end{tabular}
\end{table} 
Table 7: Thermodynamic functions of compounds of NdNa\({}_{2}\)NiMnO\({}_{5}\) and NdK\({}_{2}\)NiMnO\({}_{5}\). The provided data represent the results of calculations for heat capacity \(\rm C^{0}_{p}(T)\), entropy \(\rm S^{0}(T)\), enthalpy change \(\rm H^{0}(T)-H^{0}(298.15)\), and the function \(\rm\Phi^{xx}(T)\) within the temperature range of 298.15-675 K. Let us consider the key conclusions drawn from these data. At heat capacity \(\rm C^{0}_{p}(T)\), for both compounds, \(\rm C^{0}_{p}(T)\) increases with rising temperature, which is typical for solids. The \(\rm C^{0}_{p}(T)\) value for NdNa\({}_{2}\)NiMnO\({}_{5}\) shows minor fluctuations (phase transition temperature at 423 K) but generally rises with temperature, reaching up to 408 \(\pm\) 20 J/(mol\(\cdot\)K) at 675 K. In contrast, NdK\({}_{2}\)NiMnO\({}_{5}\) exhibits a sharp increase at 423 K (524 \(\pm\) 25 J/(mol\(\cdot\)K)). These jumps likely indicate a second-order phase transition. The entropy \(\rm S^{0}(T)\) increases with temperature for both compounds, reflecting the growing disorder in the system as it is heated. The initial values at 298.15 K are 239 \(\pm\) 7 J/(mol\(\cdot\)K) for NdNa\({}_{2}\)NiMnO\({}_{5}\) and 264 \(\pm\) 8 J/(mol\(\cdot\)K) for NdK\({}_{2}\)NiMnO\({}_{5}\). The enthalpy change \(\rm H^{0}(T)-H^{0}(298.15)\) increases with rising temperature, as expected, since the system absorbs energy during heating. The values of \(\rm H^{0}(T)-H^{0}(298.15)\) for NdK\({}_{2}\)NiMnO\({}_{5}\) grow faster compared to NdNa\({}_{2}\)NiMnO\({}_{5}\). The values of the function \(\rm\Phi^{xx}(T)\) also increase with rising temperature, indicating changes in the thermodynamic stability or reactivity of the compounds.