# Assessment of Lightweight Concrete Thermal Properties at Elevated Temperatures
## 3 Results and Discussion
### Specific Heat  
In this research work, two techniques were used to measure specific heat. In both cases, temperature was an influential parameter that affected the specific heat of LWCs. The measured values of specific heat for LWC are higher than those specified in Eurocodes 2 and 4.  
The DSC technique provides graphs of specific heat against temperature. Upward peaks indicate endothermic reactions such as vaporization, as shown in Figure 7. However, with the MTPS technique, the specific heat is calculated using a constant value of density. By not taking into account the variation in density (loss of mass), endothermic reactions such as vaporization are not measured. To compare the two techniques, the loss of mass should be measured to provide an adjusted density as a function of temperature. Finally, Equation (4) should be modified to include this adjustment.  
To analyze this, after increasing the temperature, the loss of mass was measured using a single-point cell in all the MTPS tests, and the variation in density was calculated. The data were statistically analyzed to generate correlations between the loss of mass and the increase in temperature. The mathematical equation formed through regression analysis is generalized as follows, Equations (8)-(10):  
\[\Delta m(T)=-0.0002\times T+a\quad 20\leq T\leq 50\ ^{\circ}\mathrm{C} \tag{8}\]  
\[\Delta m(T)=-0.00092\times T+b\quad 50<T\leq 110\ ^{\circ}\mathrm{C} \tag{9}\]  
\[\Delta m(T)=\Delta m(T=110\ ^{\circ}\mathrm{C})\quad 110<T\leq 160\ ^{\circ} \mathrm{C} \tag{10}\]  
where \(\Delta m(T)\) represents the loss of mass in kg, \(T\) is the temperature in \({}^{\circ}\mathrm{C}\), and \(a\) and \(b\) are constants in kg and kg/\({}^{\circ}\mathrm{C}\), respectively.  
The constants for each LWC, along with the corresponding coefficient of correlation (R\({}^{2}\)), are summarized in Table 6. The coefficient of correlation R\({}^{2}\) for all the LWCs studied was more than 0.90, indicating a good correlation between the experimental and calculated data.  
Finally, density is calculated as the loss of mass by volume of each sample as a function of temperature. This calculated density is used to determine specific heat, using Equation (4). Figure 8 shows the variation in specific heat in the range of 20-160 \({}^{\circ}\mathrm{C}\) for the three LWCs studied. Good agreement is found between the calculated and DSC experimental values of specific heat. The modified values of specific heat, plotted with dots, show an increase in specific heat with temperature. The two grey dashed lines represent an error of \(\pm\)8%. Therefore, the modified specific heat is accurate and able to follow the real behavior of LWCs.  
\begin{table}
\begin{tabular}{c c c c} \hline \hline
**Type of LWC** & **Coefficients** & **R\({}^{2}\)** \\ \hline \multirow{2}{*}{LWC-1} & a & 0.99 & 0.99 \\  & b & 0.9 & 0.9 \\ \hline \multirow{2}{*}{LWC-2} & a & 0.98 & 0.98 \\  & b & 0.91 & 0.91 \\ \hline \multirow{2}{*}{LWC-3} & a & 0.97 & 0.97 \\  & b & 0.94 & 0.94 \\ \hline \hline \end{tabular}
\end{table}
Table 6: Coefficients of the fitted curves for loss of mass.