Physical bases of freezing point measurement using ... - Boschung

Proceedings of the 9 th SIRWEC Conference 15-17 March 1998, Luleå, Sweden 282
eopt , which is rather weak, is represented in figure 7.
e opt [mm]
0.16
0.14
0.12
0.10
0.08
0.06
0.04
0.02
0.00
Figure 7 : dependence of eopt on s.
0 10 20 30 40
s [g/m 2 ]
Knowing e and Ts, the salt content can be calculated by :
cT ( s)
⋅ e
s =
ν
( cT ( ) )
where c(Ts) is approximated by the following polynomial :
s
, (13)
−63−42−2 cT ( ) =−6. 211⋅10 ⋅T −4. 637 ⋅10 ⋅T −1807 . ⋅10 ⋅T
s s s
4.3 Accuracy of the measurement of the freezing temperature
s
. (14)
While the accuracy of the measurement of Ts by an active probe is mostly given by the
accuracy ΔT of the sensor which measures the temperature during the cooling, the one of a
passive probe is dependent of the function T = T( x , x , x , K, x , K , x ) used to compute
s s 1 2 3 i n
the freezing temperature. In that case, the absolute error is given by :
ΔT
s ≅
i=
1
n
Ts
∑ x
∂
∂
i
Δ x , (15)
where the xi are the different variables which are measured and Δxi their absolute errors. In
other words, the accuracy of a passive probe is a sum of errors depending of the different
parameters themselves and their absolute error. If for instance a passive probe is able to
measure the salt concentration and the thickness of the solution, it can be understood that
errors on c and e (due to the measurements themselves, pollutants, etc.) will affect the
i