# Electro-Thermal Properties of Carbon-Fiber-Reinforced Mortar Prisms
## 4 Experimental Results
\begin{table}
\begin{tabular}{c c c c c c c c c c} \hline \hline
**Sample** & \multicolumn{2}{c}{**1**} & \multicolumn{2}{c}{**2**} & \multicolumn{2}{c}{**3**} & \multicolumn{2}{c}{**Applied**} & \multicolumn{1}{c}{**Dynamic**} \\ \hline
**Side** & **a (\(\Omega\))** & **b (\(\Omega\))** & **a (\(\Omega\))** & **b (\(\Omega\))** & **a (\(\Omega\))** & **b (\(\Omega\))** & **Average** (\(\Omega\))** & **(Voltage(\(\Omega\))**)** & **Dynamic** \\ \hline
**Prism** & **Average (\(\Omega\))** & & **Average (\(\Omega\))** & & **Average (\(\Omega\))** & & **(\(\Omega\))** & **Current(\(A\))** & **(Temp. Incre.)** \\ \hline
0.5\%(\(\Omega\)) & 16.7 & 28 & 24 & 24 & 12 & 22 & 21.12 & 30.25 & 22.87 \\  & 22.35 & & & 24 & & 17 & & (26.3, 1.15) & (119.71) \\ \hline
1.0\%(\(\Omega\)) & 8.3 & 7.5 & 6 & 6.8 & 5.1 & 8.5 & 7.0 & 29.92 & 6.18 \\  & 7.9 & & & 6.4 & & 6.8 & 6.8 & (13.6, 2.2) & (117.24) \\ \hline
1.5\%(\(\Omega\)) & 5.4 & 4.9 & 6.5 & 4.8 & 5.2 & 5.0 & 5.3 & 30.0 & 5.21 \\  & 5.15 & & & 5.65 & & 5.1 & 5.1 & (12.5, 2.4) & (127.22) \\ \hline
2.0\%(\(\Omega\)) & 5.1 & 4.2 & 4.4 & 4.8 & 3.7 & 4.3 & 4.42 & 29.97 & 2.19 \\  & 4.65 & & & 4.6 & & 4.0 & & (8.1, 3.7) & (137.83) \\ \hline \hline \end{tabular}
\end{table} 
Table 2: Measured and calculated resistances of prisms of 4 different percentages. Figure 4 shows the full frame thermal image of a piece of a 1.0% prism to specify the surface area for determining the average temperature and the lines to show the heat diffusion/temperature distribution patterns of the different percentage prisms. The total resolution of the image is 640 \(\times\) 480, but the surface area of the piece is approximately 444 \(\times\) 222 pixels. The trace of the discarded conductive gel electrode is also shown in the middle of the prism. The vertically aligned rectangle in this trace represents the location of the minimum volume defined by the 5 mm width electrodes. Since the 222 pixels correspond to 40 mm, the width of the rectangle corresponds to 28 (\(-\)222 \(\times\) 5/40) pixels. When there is no heat diffusion, the electric power will heat the volume, which works as the heat source defined above. Thus, the expected temperature increments predicted by Equation (3) will be 119.71\({}^{\circ}\), 117.24\({}^{\circ}\), 127.22\({}^{\circ}\) and 137.83\({}^{\circ}\) for the 0.5%, 1.0%, 1.5% and 2.0% prisms, respectively, when the weight and the applied electric power differences of each percentage prism from other prisms as shown in Tables 1 and 2 are considered. However, in practice, the temperature increase will be much lower than the value given above due to the fact that (1) the heat source has higher volume than the minimum one, (2) the heated volume will radiate the heat to the surrounding space through radiation and convection, and (3) some heat from the volume will be diffused to the neighbors. Due to this diffusion and the electrical paths formed outside of the volume, the temperatures of the volume surrounding the minimum volume will also increase. As the prism temperature increases, the prism's overall resistance can decrease. The increasing temperature will induce the prism to expand. The expansion of the prism will cause stronger squeezing of the fibers in it. This squeezing will force the fibers to contact/connect themselves more tightly. This tightened contact/connection will reduce overall resistance of the prism, which will be reduced even further as the fiber amount increases. This could be the reason why the heated state resistance of the 2.0% prism is reduced to a half of its unheated state resistance. However, this decreased resistance could revert to its unheated value when the prism is cooled. Since the presence of the minimum volume is hardly identified due to thermal diffusion, the accurate estimation of the electric power deposited to the volume will not  
Figure 4: Position of lines and surfaces for measuring temperature increments. The temperature distribution is less than 25\({}^{\circ}\). The prism surface is in the 23\({}^{\circ}\) range. be possible.