ISO 80000-1：2009

Reference number ISO 80000-1:2009(E) © ISO 2009 INTERNATIONAL STANDARD ISO 80000-1 First edition 2009-11-15 Quantities and units Part 1: General Grandeurs et unités Partie 1: Généralités ISO 80000-1:2009(E) PDF disclaimer This PDF file may contain embedded typefaces. In accordance with Adobe's licensing policy, this file may be printed or viewed but shall not be edited unless the typefaces which are embedded are licensed to and installed on the computer performing the editing. In downloading this file, parties accept therein the responsibility of not infringing Adobe's licensing policy. The ISO Central Secretariat accepts no liability in this area. Adobe is a trademark of Adobe Systems Incorporated. Details of the software products used to create this PDF file can be found in the General Info relative to the file; the PDF-creation parameters were optimized for printing. Every care has been taken to ensure that the file is suitable for use by ISO member bodies. In the unlikely event that a problem relating to it is found, please inform the Central Secretariat at the address given below. COPYRIGHT PROTECTED DOCUMENT © ISO 2009 All rights reserved. Unless otherwise specified, no part of this publication may be reproduced or utilized in any form or by any means, electronic or mechanical, including photocopying and microfilm, without permission in writing from either ISO at the address below or ISO's member body in the country of the requester. ISO copyright office Case postale 56 • CH-1211 Geneva 20 Tel. + 41 22 749 01 11 Fax + 41 22 749 09 47 E-mail copyright@iso.org Web www.iso.org Published in Switzerland ii © ISO 2009 – All rights reserved ISO 80000-1:2009(E) © ISO 2009 – All rights reserved iii Contents Page Foreword ............................................................................................................................................................iv Introduction........................................................................................................................................................vi 1 Scope ......................................................................................................................................................1 2 Normative references............................................................................................................................1 3 Terms and definitions ...........................................................................................................................1 4 Quantities .............................................................................................................................................11 5 Dimensions ..........................................................................................................................................14 6 Units......................................................................................................................................................14 7 Printing rules .......................................................................................................................................22 Annex A (normative) Terms in names for physical quantities.....................................................................31 Annex B (normative) Rounding of numbers ..................................................................................................35 Annex C (normative) Logarithmic quantities and their units .......................................................................37 Annex D (informative) International organizations in the field of quantities and units.............................39 Bibliography......................................................................................................................................................41 ISO 80000-1:2009(E) iv © ISO 2009 – All rights reserved 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 2. 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. Attention is drawn to the possibility that some of the elements of ISO 80000-1 may be the subject of patent rights. ISO shall not be held responsible for identifying any or all such patent rights. ISO 80000-1 was prepared by Technical Committee ISO/TC 12, Quantities and units in co-operation with IEC/TC 25, Quantities and units. This first edition of ISO 80000-1 cancels and replaces ISO 31-0:1992 and ISO 1000:1992. It also incorporates the Amendments ISO 31-0:1992/Amd.1:1998, ISO 31-0:1992/Amd.2:2005 and ISO 1000:1992/Amd.1:1998. The major technical changes from the previous standard are the following: ⎯ the structure has been changed to emphasize that quantities come first and units then follow; ⎯ definitions in accordance with ISO/IEC Guide 99:2007 have been added; ⎯ Annexes A and B have become normative; ⎯ a new normative Annex C has been added. ISO 80000 consists of the following parts, under the general title Quantities and units: ⎯ Part 1: General ⎯ Part 2: Mathematical signs and symbols to be used in the natural sciences and technology ⎯ Part 3: Space and time ⎯ Part 4: Mechanics ⎯ Part 5: Thermodynamics ⎯ Part 7: Light ⎯ Part 8: Acoustics ⎯ Part 9: Physical chemistry and molecular physics ⎯ Part 10: Atomic and nuclear physics ⎯ Part 11: Characteristic numbers ⎯ Part 12: Solid state physics ISO 80000-1:2009(E) © ISO 2009 – All rights reserved v IEC 80000 consists of the following parts, under the general title Quantities and units: ⎯ Part 6: Electromagnetism ⎯ Part 13: Information science and technology ⎯ Part 14: Telebiometrics related to human physiology ISO 80000-1:2009(E) vi © ISO 2009 – All rights reserved Introduction 0.1 Quantities Systems of quantities and systems of units can be treated in many consistent, but different, ways. Which treatment to use is only a matter of convention. The presentation given in this International Standard is the one that is the basis for the International System of Units, the SI (from the French: Système international d’unités), adopted by the General Conference on Weights and Measures, the CGPM (from the French: Conférence générale des poids et mesures). The quantities and relations among the quantities used here are those almost universally accepted for use throughout the physical sciences. They are presented in the majority of scientific textbooks today and are familiar to all scientists and technologists. NOTE For electric and magnetic units in the CGS-ESU, CGS-EMU1) and Gaussian systems, there is a difference in the systems of quantities by which they are defined. In the CGS-ESU system, the electric constant ε0 (the permittivity of vacuum) is defined to be equal to 1, i.e. of dimension one; in the CGS-EMU system, the magnetic constant µ0 (permeability of vacuum) is defined to be equal to 1, i.e. of dimension one, in contrast to those quantities in the ISQ where they are not of dimension one. The Gaussian system is related to the CGS-ESU and CGS-EMU systems and there are similar complications. In mechanics, Newton’s law of motion in its general form is written F = c⋅ma. In the old technical system, MKS2), c = 1/gn, where gn is the standard acceleration of free fall; in the ISQ, c = 1. The quantities and the relations among them are essentially infinite in number and are continually evolving as new fields of science and technology are developed. Thus, it is not possible to list all these quantities and relations in this International Standard; instead, a selection of the more commonly used quantities and the relations among them is presented. It is inevitable that some readers working in particular specialized fields may find that the quantities they are interested in using may not be listed in this International Standard or in another International Standard. However, provided that they can relate their quantities to more familiar examples that are listed, this will not prevent them from defining units for their quantities. Most of the units used to express values of quantities of interest were developed and used long before the concept of a system of quantities was developed. Nonetheless, the relations among the quantities, which are simply the equations of the physical sciences, are important, because in any system of units the relations among the units play an important role and are developed from the relations among the corresponding quantities. The system of quantities, including the relations among them the quantities used as the basis of the units of the SI, is named the International System of Quantities, denoted “ISQ”, in all languages. This name was not used in ISO 31, from which the present harmonized series has evolved. However, ISQ does appear in ISO/IEC Guide 99:2007 and in the SI Brochure [8], Edition 8:2006. In both cases, this was to ensure consistency with the new Quantities and units series that was under preparation at the time they were published; it had already been announced that the new term would be used. It should be realized, however, that ISQ is simply a convenient notation to assign to the essentially infinite and continually evolving and expanding system of quantities and equations on which all of modern science and technology rests. ISQ is a shorthand notation for the “system of quantities on which the SI is based”, which was the phrase used for this system in ISO 31. 1) CGS = centimetre-gram-second; ESU = electrostatic units; EMU = electromagnetic units. 2) MKS = metre-kilogram-second. ISO 80000-1:2009(E) © ISO 2009 – All rights reserved vii 0.2 Units A system of units is developed by first defining a set of base units for a small set of corresponding base quantities and then defining derived units as products of powers of the base units corresponding to the relations defining the derived quantities in terms of the base quantities. In this International Standard and in the SI, there are seven base quantities and seven base units. The base quantities are length, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous intensity. The corresponding base units are the metre, kilogram, second, ampere, kelvin, mole, and candela, respectively. The definitions of these base units, and their practical realization, are at the heart of the SI and are the responsibility of the advisory committees of the International Committee for Weights and Measures, the CIPM (from the French: Comité international des poids et mesures). The current definitions of the base units, and advice for their practical realization, are presented in the SI Brochure [8], published by and obtainable from the International Bureau of Weights and Measures, the BIPM (from the French: Bureau international des poids et mesures). Note that in contrast to the base units, each of which has a specific definition, the base quantities are simply chosen by convention and no attempt is made to define them otherwise then operationally. 0.3 Realizing the values of units To realize the value of a unit is to use the definition of the unit to make measurements that compare the value of some quantity of the same kind as the unit with the value of the unit. This is the essential step in making measurements of the value of any quantity in science. Realizing the values of the base units is of particular importance. Realizing the values of derived units follows in principle from realizing the base units. There may be many different ways for the practical realization of the value of a unit, and new methods may be developed as science advances. Any method consistent with the laws of physics could be used to realize any SI unit. Nonetheless, it is often helpful to review experimental methods for realizing the units, and the CIPM recommends such methods, which are presented as part of the SI Brochure. 0.4 Arrangement of the tables In parts 3 to 14 of this International Standard, the quantities and relations among them, which are a subset of the ISQ, are given on the left-hand pages, and the units of the SI (and some other units) are given on the right-hand pages. Some additional quantities and units are also given on the left-hand and right-hand pages, respectively. The item numbers of quantities are written pp-nn.s (pp, part number; nn, running number in the part, respectively; s, sub-number). The item numbers of units are written pp-nn.l (pp, part number; nn, running number in the part, respectively; l, sub-letter). INTERNATIONAL STANDARD ISO 80000-1:2009(E) © ISO 2009 – All rights reserved 1 Quantities and units Part 1: General 1 Scope ISO 80000-1 gives general information and definitions concerning quantities, systems of quantities, units, quantity and unit symbols, and coherent unit systems, especially the International System of Quantities, ISQ, and the International System of Units, SI. The principles laid down in ISO 80000-1 are intended for general use within the various fields of science and technology, and as an introduction to other parts of this International Standard. Ordinal quantities and nominal properties are outside the scope of ISO 80000-1. 2 Normative references The following referenced documents are indispensable for the application of this document. For dated references, only the edition cited applies. For undated references, the latest edition of the referenced document (including any amendments) applies. ISO/IEC Guide 99:2007, International vocabulary of metrology — Basic and general concepts and associated terms (VIM) 3 Terms and definitions For the purposes of this document, the following terms and definitions apply. NOTE The content in this clause is essentially the same as in ISO/IEC Guide 99:2007. Some notes and examples are modified. 3.1 quantity property of a phenomenon, body, or substance, where the property has a magnitude that can be expressed by means of a number and a reference ISO 80000-1:2009(E) 2 © ISO 2009 – All rights reserved NOTE 1 The generic concept ‘quantity’ can be divided into several levels of specific concepts, as shown in the following table. The left hand side of the table shows specific concepts under ‘quantity’. These are generic concepts for the individual quantities in the right hand column. radius, r radius of circle A, rA or r(A) length, l wavelength, λ wavelength of the sodium D radiation, λD or λ(Na; D) kinetic energy, T kinetic energy of particle i in a given system, Ti energy, E heat, Q heat of vaporization of sample i of water, Qi electric charge, Q electric charge of the proton, e electric resistance, R electric resistance of resistor i in a given circuit, Ri amount-of-substance concentration of entity B, cB amount-of-substance concentration of ethanol in wine sample i, ci(C2H5OH) number concentration of entity B, CB number concentration of erythrocytes in blood sample i, C(Erys; Bi) Rockwell C hardness (150 kg load), HRC(150 kg) Rockwell C hardness of steel sample i, HRCi(150 kg) NOTE 2 A reference can be a measurement unit, a measurement procedure, a reference material, or a combination of such. For magnitude of a quantity, see 3.19. NOTE 3 Symbols for quantities are given in the ISO 80000 and IEC 80000 series, Quantities and units. The symbols for quantities are written in italics. A given symbol can indicate different quantities. NOTE 4 A quantity as defined here is a scalar. However, a vector or a tensor, the components of which are quantities, is also considered to be a quantity. NOTE 5 The concept ’quantity’ may be generically divided into, e.g. ‘physical quantity’, ‘chemical quantity’, and ‘biological quantity’, or ‘base quantity’ and ‘derived quantity’. NOTE 6 Adapted from ISO/IEC Guide 99:2007, definition 1.1, in which there is an additional note. 3.2 kind of quantity aspect common to mutually comparable quantities NOTE 1 Kind of quantity is often shortened to “kind”, e.g. in quantities of the same kind. NOTE 2 The division of the concept ‘quantity’ into several kinds is to some extent arbitrary. EXAMPLE 1 The quantities diameter, circumference, and wavelength are generally considered to be quantities of the same kind, namely, of the kind of quantity called length. EXAMPLE 2 The quantities heat, kinetic energy, and potential energy are generally considered to be quantities of the same kind, namely, of the kind of quantity called energy. NOTE 3 Quantities of the same kind within a given system of quantities have the same quantity dimension. However, quantities of the same dimension are not necessarily of the same kind. EXAMPLE The quantities moment of force and energy are, by convention, not regarded as being of the same kind, although they have the same dimension. Similarly for heat capacity and entropy, as well as for number of entities, relative permeability, and mass fraction. NOTE 4 In English, the terms for quantities in the left half of the table in 3.1, Note 1, are often used for the corresponding ‘kinds of quantity’. In French, the term “nature” is only used in expressions such as “grandeurs de même nature” (in English, “quantities of the same kind”). ISO 80000-1:2009(E) © ISO 2009 – All rights reserved 3 NOTE 5 Adapted from ISO/IEC Guide 99:2007, definition 1.2, in which “kind” appears as an admitted term. Note 1 has been added. 3.3 system of quantities set of quantities together with a set of non-contradictory equations relating those quantities NOTE 1 Ordinal quantities (see 3.26), such as Rockwell C hardness, and nominal properties (see 3.30), such as colour of light, are usually not considered to be part of a system of quantities because they are related to other quantities through empirical relations only. NOTE 2 Adapted from ISO/IEC Guide 99:2007, definition 1.3, in which Note 1 is different. 3.4 base quantity quantity in a conventionally chosen subset of a given system of quantities, where no quantity in the subset can be expressed in terms of the other quantities within that subset NOTE 1 The subset mentioned in the definition is termed the “set of base quantities”. EXAMPLE The set of base quantities in the International System of Quantities (ISQ) is given in 3.6. NOTE 2 Base quantities are referred to as being mutually independent since a base quantity cannot be expressed as a product of powers of the other base quantities. NOTE 3 ‘Number of entities’ can be regarded as a base quantity in any system of quantities. NOTE 4 Adapted from ISO/IEC Guide 99:2007, definition 1.4, in which the definition is slightly different. 3.5 derived quantity quantity, in a system of quantities, defined in terms of the ba