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4.4.2 Substitution Weighing
The double substitution method shown in Figure 3 requires four
weighing operations for each substitution cycle. For both loading
cases – "Pycnometer with reference fluid" and "Pycnometer with
reference fluid and test specimen" – n
each case. The cycle difference for the cycle j in the first loading
case is:
corresponding to the following in the second loading case:
P1 and P2 identify the measurement values which result from
the Pycnometer weighing operations. S1 and S2 identify the
corresponding measurement values for the reference weights.
If the drift of the balance under load is constant and the time
intervals between the weighing operations are the same, the
cycle differences provide the drift-adjusted measurement results
for the difference in mass between the Pycnometer and the
reference weights.
The mean cycle differences are:
and
The corrected weight values from the equations:
and
result from the mean cycle differences and the mass values
m
and m
of the reference weights, as well as their densities
R0
R1
p
and p
.
R0
R1
Note:
The following influences are to 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 the substitution reference weights
Further information is available in the manual.
10
cycles are measured in
w
4.5 Further Influences on the Test Specimen's Density Value
4.5.1 Air Density
The air density is determined by the following parameters:
Pressure p , temperature t and relative humidity hrel. The CIPM
formula applies, which under the climate conditions in the
laboratory can be approximately represented by:
Note:
Do not disregard uncertainties related to air density. Refer to the
manual for information concerning the treatment of uncertainty
analysis.
4.5.2 Fluid Density
The fluid density p is generally determined by temperature
measurement. The following formula applies in the case of
water:
Note:
The influence of temperature changes on the fluid density can
be ignored in the uncertainty analysis, as its contribution is very
small in comparison with other influences.
4.5.3 Fill Volume
The fill volume of the Pycnometer depends on its temperature.
If the fill volume is known at a temperature of 20°C, the volume
at a different temperature t can be determined with the aid of
thermal expansion coefficient γ.
V(t) = V (20°C)(1+γ(t –20°C))
The expansion coefficient of the Pycnometer material
is γ = 210.10
–6
–1
K
.
Note:
Even small fluctuations in reference fluid temperature, in
thermal equilibrium, cause comparatively large changes in the
fill volume. For this reason emphasis must be placed on the most
accurate temperature measurement at various thermometer
insertion depths. Further information is available in the manual.
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