# Instrumental Uncertainty of Conductance Transducers for
## 4 Experimental Results
### Thermal Influence
The corresponding average and experimental standard deviation values of both the input and output voltage are mentioned in Table 4, considering the last 30 min of the temperature testing steps. Figure 25 shows convergent output voltage values for each temperature step, with the exception of the 40 \({}^{\circ}\)C temperature step, where an increasing linear (long-term) tendency is observed. This voltage behavior can be justified by: (i) the high temperature environment increases water electrolysis and polarization effects in the metallic electrodes, which are reflected in a higher electrical current and, therefore, in a higher output voltage; (ii) a more significant thermal vertical stratification of the water temperature (with the contribution of the high magnitude--above 1 \({}^{\circ}\)C--temperature difference between water and air temperature at the 40 \({}^{\circ}\)C testing step), making the application of the horizontal electrode less effective in the compensation of water resistivity variation by the thermal effect, noticing that this compensation electrode is located in a lower region of the conductance transducer. \begin{table}
\begin{tabular}{c c c} \hline \hline
**Temperature Set Point/\({}^{C}\)C** & **Input Voltage/V** & **Output Voltage/V** \\ \hline
10 & 15.0039 \(\pm\) 0.0001 & 6.4377 \(\pm\) 0.0008 \\
25 & 15.0037 \(\pm\) 0.0002 & 6.5177 \(\pm\) 0.0013 \\
40 & 15.0030 \(\pm\) 0.0002 & 6.5610 \(\pm\) 0.0007 \\
25 & 15.0026 \(\pm\) 0.0001 & 6.5244 \(\pm\) 0.0009 \\
10 & 15.0028 \(\pm\) 0.0002 & 6.4417 \(\pm\) 0.0012 \\
25 & 15.0026 \(\pm\) 0.0002 & 6.5283 \(\pm\) 0.0008 \\
40 & 15.0016 \(\pm\) 0.0002 & 6.5778 \(\pm\) 0.0008 \\ \hline \hline \end{tabular}
\end{table} 
Table 4: Input and output average voltage and experimental standard deviation values related to the last 30 min of the temperature testing steps. Figure 25: Output voltage of the conductance sensor during the thermal test. A transient voltage behavior is noticed in the beginning of each temperature step, similar to the transient thermal behavior of the air and water temperatures. Short-term stationary regimes, related to the last 30 min of the temperature testing steps, are characterized by an electrical stability of the output voltage equal or below 1.3 mV. Both Figure 25 and Table 4 show that a temperature decrease originates a decrease in the output voltage and reciprocally, reflecting a higher or lower electrical current between the vertical electrodes, assuming that variations in the water resistivity are properly compensated by the horizontal electrode. Output voltage reversibility is also noticed in each temperature step, namely, 4.0 mV at 10 \({}^{\circ}\)C, 10.6 mV at 25 \({}^{\circ}\)C and 16.8 mV at 40 \({}^{\circ}\)C (obtained from the output voltage values shown in Table 4 and expressed in absolute values), therefore, showing an increasing magnitude tendency with the temperature increase. This voltage behavior can be originated by an increasing and cumulative effect of water electrolysis in the transducer. Using the average calibration linear parameters of the thermal tested conductance transducer (see Table 2, in Section 4.2.2), the output voltage profile can be converted to water level values, and a profile can be obtained, relative to the initial water level. A graphical representation of the calculated values is presented in Figure 26, while Table 5 shows the dimensional conversion of Table 4.  
The relative variation of the water level during the thermal test varied between a maximum value of 2.102 mm for the first 10 \({}^{\circ}\)C temperature step, and a minimum value of \(-2.077\) mm for the last 40 \({}^{\circ}\)C temperature step. The above mentioned voltage stability