Editing Precision Thermocouple Based Temperature Measurement System (section)

=== 4.2. Linear Fitting and Extraction of the Seebeck Coefficient ===

To extract the Seebeck coefficient, a linear regression was carried out on the averaged Vout versus ΔT data from each run, using the relationship Vout = S·ΔT, where the gradient S corresponds to the Seebeck coefficient. Before fitting, any data points that deviated noticeably from the general linear trend were removed, since keeping them in was found to skew the fit and inflate the residual error without reflecting the true behaviour of the pellet. The reliability of each fit was then checked using the coefficient of determination (R²).

The R² values across the four runs came out between 0.949 and 0.994, which indicates that the linear model described the data well in all cases. Reading the slope values directly from the fitted lines shown in Figures 1 through 4:

{| class="wikitable"
! Graph !! Slope (μV/K) !! R²
|-
| Graph 1 || 0.900 ± 0.039 || 0.994
|-
| Graph 2 || 1.066 ± 0.123 || 0.949
|-
| Graph 3 || 0.933 ± 0.071 || 0.978
|-
| Graph 4 || 0.836 ± 0.067 || 0.963
|}

The mean Seebeck coefficient extracted across the four runs is S = −0.934 ± 0.094 μV/K. The negative sign reflects the consistently negative output voltage observed throughout all measurements, confirming that electrons are the dominant charge carriers and that the undoped ZnO pellet behaves as an n-type semiconductor.The ± 0.094 μV/K uncertainty represents one standard deviation across the four runs and captures the variation that came with reapplying the silver paste contacts between each run.