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The meanings of the variables specified in this equation
are as follows:
– The mass of the test specimen m
The mass value of the test specimen. It is sufficient, however,
to use the nominal value m
t0
– The density p
of the reference fluid during weighing without
0
the test specimen. The exact density value is dependent on the
temperature. This must be determined as accurately as possible.
– The density p
of the reference fluid during weighing with the
1
test specimen. The high accuracy of the temperature measure-
ment in the Pycnometer is also critical in this case.
– The weight value difference I
This depends on the balance used. It results from the weight
values I
with and I
without the test specimen. The balance
1
0
characteristics and the standard deviation must satisfy the high
requirements of accurate density determination.
– The deviations of the weight values from linearity ∆ I
The maximum deviations are given by the manufacturer in the
technical specification for the balance. These deviations do not
change over time; however they may differ from balance to
balance. The linearity deviations are not significant if the substi-
tution method is selected. Please refer to the manual concerning
linearity deviations if the absolute method is to be carried out.
– The air densities p
and p
a0
a1
The calibration of the balance's sensitivity and weighing with
the Pycnometer must take place with the air density as constant
as possible. Therefore, weighing should take place immediately
after calibration. If higher accuracy is required, the air density
should be re-determined at the beginning of the two weighing
sequences. The air density is determined by measuring air
pressure, temperature and relative humidity.
– The density p
:
a0j
This is the density of the calibration weight for the sensitivity
of the balance. A stainless steel reference weight as provided by
the manufacturer of the balance is generally used. If the density
value is not available to a greater accuracy, p
can be used. In any case, the uncertainty of the calibration
weight density must be dealt with in the uncertainty analysis.
– Fill volumes V
and V
:
0
1
Even when the Pycnometer is filled as accurately as possible with
the reference fluid, in the case of different temperatures the fill
volumes are not exactly the same due to the thermal expansion
of the Pycnometer container. The requirement for high accuracy
when determining temperature is also important for this reason.
– Fill quantity correction value ∆ m :
The Pycnometer is designed in such a way that the fill accuracy
achieved is always as accurate as possible. Nevertheless small
deviations may arise. For example, remaining air bubbles cause
deviations in the fill quantity. The fill quantity correction value
is only considered in relation to the uncertainty analysis, while
∆ m = 0 is used to calculate the density of the test specimen.
:
t
as an approximation.
– I
:
1
0
and ∆ I
0
:
= 8000 kgm
ref
4.4 Determining the Weight Values
4.4.1 Absolute Weighing Method
By following the method described in Figure 2, a series of n
measurement values, w
loading the balance. In addition, the drift values ∆ w
for each measurement value are obtained as a result of the zero
point drift check. The following two weight values result from
these values:
and
If the characteristics of the balance are known, linearity
deviations ∆ I
and ∆I1 result from the values for I
0
:
These are then used to correct the weight values (see manual).
1
Otherwise the following are used:
∆ I
= 0
0
∆ I
= 0.
1
Note:
The following influences must be taken into account when
carrying out the uncertainty analysis for the weighing process:
– Random influences represented by Type A – uncertainty of the
weighing process – resulting from the standard deviations
– Eccentric load positioning
– Rounding errors
– Uncertainty of characteristics
Further information is available in the manual.
–3
and w
, is obtained for both cases of
0 i
1 i
0 i
and I
0
w
and ∆ w
1 i
.
1
9
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