Environmental Engineering Reference
In-Depth Information
Ta b l e 4 . 1 1
Comparison between the reference and the LCR-evaluated values of
ε
s
,forthe
reference materials (at 20.0
◦
C). Experimental uncertainty is also reported
material
reference
bibliographic
averaged
experimental
value
reference
evaluated
uncertainty
value
chloroform
4
.
82
±
0
.
02
[2, 11]
4.81
0.02
.
±
.
ethyl acetate
6
04
0
02
[3, 11]
6.04
0.02
1,1,1-trichloroethane
7
.
20
±
0
.
10
[3, 11]
7.42
0.04
were performed only on three Cole-Cole parameters, the accuracy of the final results
was enhanced.
Also in this case, TDR measurements were repeated ten times for each type of
oil; for each measurement, the minimization routine was performed and the corre-
sponding values of
were evaluated. The minimization procedure over
the Cole-Cole parameters was performed on the 0-1 GHz frequency range; in fact,
this frequency range was found to adequately include the major dielectric response
of oils.
Ten different types of vegetable oils were considered: in particular, four olive
oils with different acidity values (ranging from 0.3% to 4.0%) and six other kinds
of vegetable oils (i.e., peanut, sunflower, corn, castor, various seed, and soybean).
Table 4.12 summarizes the Cole-Cole parameters for the ten oils (each set of
parameters was calculated as the average of ten repetitions), and the correspond-
ing standard deviation (
ε
∞
,
f
r
and
β
). The obtained results for the Cole-Cole parameters
of the considered vegetable oils are in good agreement with the few data available
in the literature [10, 19, 23]. It is worth noting that, for the results obtained for oils,
the standard deviation was reported (rather than the experimental uncertainty), so as
to provide an indicator of the metrological performance of the method, when used
without performing a series of repeated measurements.
As expected, from Table 4.12, it is apparent that
σ
s
change slightly
among the different oils. Conversely,
f
r
seems to change significantly between one
type of oil and another. To better evidence this trend, for each oil, Fig. 4.15 shows
the expanded uncertainty range
β
,
ε
∞
,and
ε
is the standard deviation cor-
responding to the Gaussian probability distribution (which, in turn, was verified
through the
±
2
.
26
σ
;where
σ
-square test). The expanded uncertainty was evaluated considering the
t
-distribution of Student, and 2.26 is the
t
-score that corresponds to a confidence
level of 95% and to nine degrees of freedom [16]. On the basis of the obtained
results, the proposed technique can be useful for quality monitoring of oils: for ex-
ample, by measuring the relaxation frequency, it might be possible to discriminate
different kinds of oil. Additionally, using the averaged relaxation frequency as a
reference value (i.e., the expected value that the considered oil should exhibit), any
deviation may be associated with the possible presence of adulterants.
χ
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