# Instrumental Uncertainty of Conductance Transducers for
## 4 Experimental Results
### Thermal Influence  
The experimental setup allowed applying controlled temperature steps to the conductance transducer, half-immersed in a constant water level. Figure 23 shows the obtained water and air temperature time evolutions, while Table 3 presents the average and the experimental standard deviation values of the last 30 min of each temperature step. Figure 23 shows convergent steps for both the air and water temperatures, noticing a faster evolution of the air temperature during transitions due to the higher thermal inertia of water. Each temperature step also shows high temperature stability, as seen in Table 3, for the last 30 min of each temperature step (experimental standard deviation values of 0.001 \({}^{\circ}\)C and 0.003 \({}^{\circ}\)C, respectively, for the water and the air temperatures). However, the comparison between the average values mentioned in Table 3 shows temperature differences between water and air, ranging from 0.278 \({}^{\circ}\)C up to 1.222 \({}^{\circ}\)C. Temperature differences are particularly high in the 40 \({}^{\circ}\)C temperature step, being the air temperature always higher than the water temperature. \begin{table}
\begin{tabular}{c c c c c} \hline \multirow{2}{*}{**Linear Parameter**} & **Test Position** & **Test Position** & **Test Position** & **Average** \\  & **0\({}^{\circ}\)** & **60\({}^{\circ}\)** & **120\({}^{\circ}\)** & **Position** \\ \hline Slope (mm\(\cdot\)V\({}^{-1}\)) & \(-\)29.67 \(\pm\) 0.13 & \(-\)29.79 \(\pm\) 0.15 & \(-\)29.75 \(\pm\) 0.12 & \(-\)29.74 \(\pm\) 0.13 \\ Intercept (mm) & 154.36 \(\pm\) 0.77 & 152.82 \(\pm\) 0.85 & 153.35 \(\pm\) 0.74 & 153.51 \(\pm\) 0.78 \\ Correlation factor & \(-\)0.88 & \(-\)0.87 & \(-\)0.88 & \(-\)0.88 \\ \hline \end{tabular}
\end{table} 
Table 2: Estimates and standard uncertainties of the calibration curve linear parameters related to the short-range conductance transducer. During the thermal test of the conductance transducer, the input voltage applied by the power supply was recorded and is shown in Figure 24.  
As shown in Figure 24, during the thermal test a variation of 5.4 mV was observed--corresponding to the difference between the maximum (15.0064 V) and the minimum (15.0010 V) recorded input voltage values--noticing a decreasing evolution from an initial stage to the end of the test. An abrupt decrease in the input voltage was noticed after  
Figure 23: Water and air temperature records during the thermal test. \begin{table}
\begin{tabular}{c c c c} \hline
**Temperature Set** & **Water** & **Air** & **Temperature Difference** \\
**Point/°C** & **Temperature/°C** & **Temperature/°C** & **between Air and Water/°C** \\ \hline
10 & 9.555 \(\pm\) 0.001 & 9.833 \(\pm\) 0.003 & 0.278 \\
25 & 24.567 \(\pm\) 0.001 & 24.869 \(\pm\) 0.003 & 0.302 \\
40 & 38.640 \(\pm\) 0.001 & 39.773 \(\pm\) 0.002 & 1.133 \\
25 & 24.397 \(\pm\) 0.001 & 24.872 \(\pm\) 0.003 & 0.475 \\
10 & 9.505 \(\pm\) 0.001 & 9.820 \(\pm\) 0.003 & 0.315 \\
25 & 24.528 \(\pm\) 0.001 & 24.866 \(\pm\) 0.003 & 0.338 \\
40 & 38.515 \(\pm\) 0.001 & 39.737 \(\pm\) 0.003 & 1.222 \\ \hline \end{tabular}
\end{table} 
Table 3: Average and experimental standard deviation values related to the last 30 min of the temperature testing steps. Figure 24: Input voltage of the conductance transducer during the thermal test. three hours, which can be attributed to a transient warming period of the used electrical equipment. After this, the input voltage evolution maintained its decreasing linear tendency in time, showing reduced magnitude peaks in its profile during transitions between temperature steps. This electrical signal was characterized by an approximately constant noise close to 0.2 mV, after removing the linear tendency. With respect to the output voltage of the conductance transducer, Figure 25 shows its time evolution during the performed thermal test, in addition to the previously shown air and water temperature records (in Figure 23).