# Cryogenic System for FTIR Analysis of Hydrocarbon Fuels at Low Temperature and Atmospheric Pressure
## 3 Results  
### Uncertainty Assessment  
The objective of this assessment is to determine the combined and expanded uncertainties of temperature measurements in the experimental setup as well as the accuracy of band wavenumbers in recording IR spectra of hydrocarbon substances at temperatures down to 80 K and atmospheric pressure. A spectrometer with a diffuse reflection attachment was used as a measuring instrument, the error analysis of which is carried out during the recording and analyzing of infrared spectra. The assessment of the combined uncertainty of spectral measurements takes into account the following sources: (1) spectral resolution (\(U_{t}\)), the indicator that is responsible for the ability of device to distinguish peaks; (2) instrument error, which means the calibration error of the spectrometer (\(U_{l}\)); (3) digital noise/baseline instability (\(U_{n}\)), namely the noise and instability impact to the result; (4) deviation of peak position approximation (\(U_{a}\)), which occurs when the peak is being smoothed. According to the GUM, total standard uncertainty is defined by the root sum square (RSS), which is the combination of all uncertainty sources' contributions:  
\[\Delta U=\sqrt{U_{r}^{2}+U_{l}^{2}+U_{n}^{2}+U_{a}^{2}} \tag{1}\]  
Taking into account all these uncertainties and having performed all the calculations, we present uncertainty contributions in Table 1.  
Thus, the expanded uncertainty in determining the positions of absorption bands in the IR spectra obtained with the spectrometer is \(\pm\)0.936 cm\({}^{-1}\) at a 95% confidence level. This uncertainty must be taken into account when interpreting the spectra. As for temperature, the measurement device is a thermocouple attached to a PID controller, the uncertainty of which is under investigation. Thermocouple uncertainty assessment consists of determining contributions of the following sources: (1) thermocouple voltage (\(Y_{v}\)), the quantity, signaling about deviation of voltage measuring; (2) contact thermal resistance (\(Y_{c}\)), the deviation of temperature measuring, occurring based on a material's resistance to heating/cooling on the contact point; (3) temperature gradient in bar (\(Y_{g}\)), namely the deviation due to temperature distribution across the copper bar; (4) PID controller fluctuation (\(Y_{f}\)), the instrument error. \[\Delta Y=\sqrt{Y_{v}^{2}+Y_{c}^{2}+Y_{g}^{2}+Y_{f}^{2}} \tag{2}\]  
Having calculated all errors and deviations, we present temperature measurement uncertainty budget in Table 2. \begin{table}
\begin{tabular}{p{11.4 pt} p{11.4 pt} p{11.4 pt} p{11.4 pt} p{11.4 pt} p{11.4 pt} p{11.4 pt} p{11.4 pt}} \hline \hline \multirow{2}{*}{**J\(\Psi\)**} & \multirow{2}{*}{**Uncertainty Source**} & \multirow{2}{*}{**Type**} & \multirow{2}{*}{**Units**} & \multicolumn{2}{c}{**Standard**} & \multirow{2}{*}{**Distribution**} & \multicolumn{1}{p{11.4 pt}}{**Standard Uncertainty**} & \multicolumn{1}{p{11.4 pt}}{**Sensitivity Coefficient**} & \multicolumn{1}{p{11.4 pt}}{**Uncertainty Contribution, K**} \\ \cline{5-8}  & & & & & **Error** & & **Uncertainty** & **Coefficient** & **Contribution, cm\({}^{-1}\)** \\ \hline
1. & Spectral resolution & B & cm\({}^{-1}\) & \(\pm\)0.125 & Rectangular & \(\frac{\pm 0.125}{\sqrt{3}}\) & 1 & \(\pm\)0.072 \\ \hline
2. & Instrument error & B & cm\({}^{-1}\) & \(\pm\)0.500 & Rectangular & \(\frac{\pm 0.5}{\sqrt{3}}\) & 1 & \(\pm\)0.289 \\ \hline
3. & Digital noise/ baseline instability & A & cm\({}^{-1}\) & \(\pm\)0.200 & Normal & \(\pm\)0.2 & 1 & \(\pm\)0.200 \\ \hline
4. & Deviation of peak position approximation & A & cm\({}^{-1}\) & \(\pm\)0.300 & Normal & \(\pm\)0.3 & 1 & \(\pm\)0.300 \\ \hline  & & \multicolumn{3}{c}{Total standard uncertainty} & & & & \(\pm\)0.468 \\ \hline  & & \multicolumn{3}{c}{Expanded uncertainty} & & & & \(\pm\)0.936 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Uncertainty budget of spectra analysis.