## 3 Methods
### Models of Radial and Flat Diffusion Based on Fick's Laws
#### 3.3.2 Model Based on the Laws of Liquid Evaporation
On the other hand, Figure 10 represents p\({}_{\rm v10}\) versus p\({}_{\rm s10}\) for the working temperature range. It can be seen as  
\[\rm{P}_{\rm v10}=0.0196\ P_{\rm s10} \tag{27}\]  
with a correlation coefficient of R\({}^{2}\) = 0.96. The proposed model is as follows:  
\[\rm{G}=K^{\prime}\ \frac{A\ M_{Hg}\ P_{v10}}{R\ T} \tag{28}\]  
Figure 10: Hg vapor pressure p\({}_{\rm v10}\) versus Hg saturation vapor pressure p\({}_{\rm s10}\)Validation of the Model Based on the Laws of Liquid Evaporation. \begin{table}
\begin{tabular}{c c c c c c c} \hline \hline \(\rm\Theta\) (\({}^{\circ}\)C) & **T (K)** & **C\({}_{\rm 10}\) (ng/m\({}^{3}\))** & **C\({}_{\rm 10}\) (mol/m\({}^{3}\))** & **P\({}_{\rm v10}\) (Pa)** & **P\({}_{\rm s10}\) (Pa)** & **P\({}_{\rm v10}\)/P\({}_{\rm s10}\)** \\ \hline
29 & 302 & 58,488 & 2.92 \(\times\) 10\({}^{-7}\) & 7.32 \(\times\) 10\({}^{-4}\) & 3.55 \(\times\) 10\({}^{-1}\) & 0.00206 \\
30 & 303 & 50,000 & 2.49 \(\times\) 10\({}^{-7}\) & 6.28 \(\times\) 10\({}^{-4}\) & 3.85 \(\times\) 10\({}^{-1}\) & 0.00163 \\
6.5 & 279.5 & 15,827 & 7.89 \(\times\) 10\({}^{-8}\) & 1.83 \(\times\) 10\({}^{-4}\) & 4.95 \(\times\) 10\({}^{-2}\) & 0.00371 \\
7.5 & 280.5 & 12,028 & 6.00 \(\times\) 10\({}^{-8}\) & 1.40 \(\times\) 10\({}^{-4}\) & 5.43 \(\times\) 10\({}^{-2}\) & 0.00257 \\
12.5 & 285.5 & 16,024 & 7.99 \(\times\) 10\({}^{-8}\) & 1.90 \(\times\) 10\({}^{-4}\) & 8.62 \(\times\) 10\({}^{-2}\) & 0.00220 \\
10.5 & 283.5 & 14,757 & 7.36 \(\times\) 10\({}^{-8}\) & 1.73 \(\times\) 10\({}^{-4}\) & 7.18 \(\times\) 10\({}^{-2}\) & 0.00241 \\
4 & 277 & 6512 & 3.25 \(\times\) 10\({}^{-8}\) & 7.48 \(\times\) 10\({}^{-5}\) & 3.89 \(\times\) 10\({}^{-2}\) & 0.00192 \\
11 & 284 & 15,945 & 7.95 \(\times\) 10\({}^{-8}\) & 1.88 \(\times\) 10\({}^{-4}\) & 7.52 \(\times\) 10\({}^{-2}\) & 0.00250 \\
14 & 287 & 12,089 & 6.03 \(\times\) 10\({}^{-8}\) & 1.44 \(\times\) 10\({}^{-4}\) & 9.87 \(\times\) 10\({}^{-2}\) & 0.00146 \\
14.5 & 287.5 & 25,500 & 1.27 \(\times\) 10\({}^{-7}\) & 3.04 \(\times\) 10\({}^{-4}\) & 1.03 \(\times\) 10\({}^{-1}\) & 0.00294 \\
24 & 297 & 48,397 & 2.41 \(\times\) 10\({}^{-7}\) & 5.96 \(\times\) 10\({}^{-4}\) & 2.35 \(\times\) 10\({}^{-1}\) & 0.00254 \\
21 & 294 & 29,518 & 1.47 \(\times\) 10\({}^{-7}\) & 3.60 \(\times\) 10\({}^{-4}\) & 1.82 \(\times\) 10\({}^{-1}\) & 0.00197 \\
13.5 & 279.5 & 8890 & 4.43 \(\times\) 10\({}^{-8}\) & 1.06 \(\times\) 10\({}^{-4}\) & 9.44 \(\times\) 10\({}^{-2}\) & 0.00112 \\
3.5 & 276.5 & 11,011 & 5.49 \(\times\) 10\({}^{-8}\) & 1.26 \(\times\) 10\({}^{-4}\) & 3.71 \(\times\) 10\({}^{-2}\) & 0.00340 \\
6 & 302 & 10,589 & 5.28 \(\times\) 10\({}^{-8}\) & 1.23 \(\times\) 10\({}^{-4}\) & 4.95 \(\times\) 10\({}^{-2}\) & 0.00248 \\ \hline \hline \end{tabular}
\end{table} 
Table 3: Hg vapor and saturation pressures estimated from the concentration C\({}_{\rm 10}\). which, in our case, is applied with the following parameter values: K\({}^{\prime}\) = 8.49 \(\times\) 10\({}^{-7}\); A = \(\pi\)\(\times\) 10\({}^{2}\) = 314 m\({}^{2}\); M\({}_{\rm{Hg}}\) = 200.56 g/mol: R = 8.3411 J/mol K and p\({}_{\rm{v10}}\)= 0.00196 \(\times\) p\({}_{\rm{s10}}\) = 0.00196 \(\times\) 10\({}^{(10.184-3210.29)}\)/T) leaving the expression of G as a function of temperature:  
\[\rm{G}=1.260\cdot 10^{-5}\frac{10^{(10.184-3210.29)}}{T} \tag{29}\]  
Figure 11 shows the value of G calculated in this manner along with G values estimated previously from the actual concentration data measured at point 9. It is verified that the model is capable of representing the phenomenon and predicting the emission rate with sufficient accuracy. On the other hand, the model can be used to estimate the concentration of gaseous mercury in the air above the debris C\({}_{10}\):  
\[\rm{C}_{10}=\frac{M_{\rm{Hg}}\,P_{\rm{v10}}}{R\,T} \tag{30}\]  
As can be seen in Figure 12, the model is also useful for the estimation of the gaseous Hg concentration at the focus. Figure 11: Emission Rate vs. temperature values derived from measurements (dots) and calculated with evaporation liquid model (line).