ISO TR 20461-2000.pdf

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TECHNICAL
REPORT
ISO/TR
20461
First edition
2000-11-01
Determination of uncertainty for volume
measurements made using the gravimetric
method
Détermination de l'incertitude de mesure pour les mesurages
volumétriques effectués au moyen de la méthode gravimétrique
Reference number
ISO/TR 20461:2000(E)
©
ISO 2000
ISO/TR 20461:2000(E)
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ii
© ISO 2000 – All rights reserved
ISO/TR 20461:2000(E)
Contents
Page
Foreword.....................................................................................................................................................................iv
1
2
3
4
5
6
7
8
Scope ..............................................................................................................................................................1
Modelling the measurement .........................................................................................................................1
Standard uncertainty of measurement associated with the volume
V
20
.................................................4
Sensitivity coefficients..................................................................................................................................4
Standard uncertainty associated with the volume delivered by a piston-operated volumetric
apparatus........................................................................................................................................................6
Standard uncertainties of measurement .....................................................................................................7
Expanded uncertainty of measurement associated with volume
V
20
......................................................7
Example for determining the uncertainty of the measurement ................................................................7
Bibliography ..............................................................................................................................................................10
© ISO 2000 – All rights reserved
iii
ISO/TR 20461:2000(E)
Foreword
ISO (the International Organization for Standardization) is a worldwide federation of national standards bodies (ISO
member bodies). The work of preparing International Standards is normally carried out through ISO technical
committees. Each member body interested in a subject for which a technical committee has been established has
the right to be represented on that committee. International organizations, governmental and non-governmental, in
liaison with ISO, also take part in the work. ISO collaborates closely with the International Electrotechnical
Commission (IEC) on all matters of electrotechnical standardization.
International Standards are drafted in accordance with the rules given in the ISO/IEC Directives, Part 3.
The main task of technical committees is to prepare International Standards. Draft International Standards adopted
by the technical committees are circulated to the member bodies for voting. Publication as an International
Standard requires approval by at least 75 % of the member bodies casting a vote.
In exceptional circumstances, when a technical committee has collected data of a different kind from that which is
normally published as an International Standard (“state of the art”, for example), it may decide by a simple majority
vote of its participating members to publish a Technical Report. A Technical Report is entirely informative in nature
and does not have to be reviewed until the data it provides are considered to be no longer valid or useful.
Attention is drawn to the possibility that some of the elements of ISO/TR 20461 may be the subject of patent rights.
ISO shall not be held responsible for identifying any or all such patent rights.
ISO/TR 20461 was prepared by Technical Committee ISO/TC 48,
Laboratory glassware and related apparatus,
Subcommittee SC 1,
Volumetric instruments.
iv
© ISO 2000 – All rights reserved
TECHNICAL REPORT
ISO/TR 20461:2000(E)
Determination of uncertainty for volume measurements made
using the gravimetric method
1
Scope
This Technical Report gives the detailed evaluation of uncertainty for volume measurements according to the
Guide to the Expression of Uncertainty in Measurement
(GUM) [1]. It uses the gravimetric method specified in
ISO 8655-6 [2] as the reference method for calibrating piston-operated volumetric apparatus. It has been arranged
in paragraphs to facilitate direct access to different aspects of this kind of evaluation as follows:
¾
¾
¾
modelling the measurement by describing the physical equations necessary to calculate the volume using the
gravimetric method of measurement;
determination of the standard uncertainty of measurement associated with the volume
V
20
by describing the
calculation procedure according to the GUM;
determination of the sensitivity coefficients with an example of the calculation of all sensitivity coefficients by
using complete equations, approximations of equations and by giving numerical values for standard
conditions;
determination of the standard uncertainty associated with the volume delivered by a piston-operated
volumetric apparatus giving the combination of the standard uncertainty associated with the volume
V
20
measured using the gravimetric measuring system and the experimental standard deviation associated with
the volume delivered by the apparatus;
determination of the standard uncertainties of measurement with a brief insight into the calculation of
uncertainties of measuring devices according to GUM;
determination of the expanded uncertainty of measurement associated with volume
V
20
;
example of the determination of the uncertainty for volume measurements.
¾
¾
¾
¾
2
Modelling the measurement
The equation for the volume
V
20
of the delivered water at 20 °C is given by
V
20
=
m
´
Z
´
Y
with
m
=
m
2
–
m
1
–
m
E
where
m
m
1
is the balance reading of delivered water;
is the balance reading of the weighing vessel before delivery of the measured volume of water;
(2)
(1)
© ISO 2000 – All rights reserved
1

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