Difference between revisions of "International System of Units"
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[[File:SI-units.png|right|400px|link=https://www.bipm.org/utils/common/pdf/si-brochure/SI-Brochure-9-EN.pdf]] | [[File:SI-units.png|right|400px|link=https://www.bipm.org/utils/common/pdf/si-brochure/SI-Brochure-9-EN.pdf]] | ||
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== Base quantities / SI base units == | == Base quantities / SI base units == | ||
::::» [[time]] / [[second |[second]]] | ::::» [[time]] / [[second |[second]]] | ||
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::::» [[gas constant]] | ::::» [[gas constant]] | ||
::::» [[motive unit]] | ::::» [[motive unit]] | ||
+ | ::::» [[number of entities]] | ||
== General remarks == | == General remarks == | ||
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:::: Before stating the result of a measurement, it is essential that the quantity being presented is adequately described. This may be simple, as in the case of the length of a particular steel rod, but can become more complex when higher accuracy is required and where additional parameters, such as temperature, need to be specified. | :::: Before stating the result of a measurement, it is essential that the quantity being presented is adequately described. This may be simple, as in the case of the length of a particular steel rod, but can become more complex when higher accuracy is required and where additional parameters, such as temperature, need to be specified. | ||
− | When a measurement result of a quantity is reported, the estimated value of the measurand (the quantity to be measured), and the uncertainty associated with that value, are necessary. Both are expressed in the same unit. | + | :::: When a measurement result of a quantity is reported, the estimated value of the measurand (the quantity to be measured), and the uncertainty associated with that value, are necessary. Both are expressed in the same unit. |
== Definition of the SI (p. 127) == | == Definition of the SI (p. 127) == | ||
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:::: The numerical values of the seven defining constants have no uncertainty. | :::: The numerical values of the seven defining constants have no uncertainty. | ||
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+ | == Quantity calculus (p. 147) == | ||
+ | :::: Symbols for units are treated as mathematical entities. In expressing the value of a quantity as the product of a numerical value and a unit, both the numerical value and the unit may be treated by the ordinary rules of algebra. This procedure is described as the use of quantity calculus, or the algebra of quantities. For example, the equation ''p'' = 48 kPa may equally be written as ''p''/kPa = 48. It is common practice to write the quotient of a quantity and a unit in this way for a column heading in a table, so that the entries in the table are simply numbers. | ||
+ | Suggestion: ''p''/[kPa] = 48 | ||
+ | |||
+ | |||
+ | == Quantity symbols and unit symbols (p. 149) == | ||
+ | :::: Unit symbols must not be used to provide specific information about the quantity and should never be the sole source of information on the quantity. Units are never qualified by further information about the nature of the quantity; any extra information on the nature of the quantity should be attached to the quantity symbol and not to the unit symbol. | ||
+ | Comment: Quantity calculus can be extended by providing specific information about the quantity together with the unit symbol, ''e.g.'', [kJ·mol<sup>-1</sup> O<sub>2</sub>]. | ||
+ | |||
+ | == Writing and printing of unit symbols and of numbers (p. 162) == | ||
+ | :::: Roman (upright) type, in general lower-case, is used for symbols of units; if, however, the symbols are derived from proper names, capital roman type is used. These symbols are not followed by a full stop. | ||
+ | |||
+ | :::: In numbers, the comma (French practice) or the dot (British practice) is used only to separate the integral part of numbers from the decimal part. Numbers may be divided in groups of three in order to facilitate reading; neither dots nor commas are ever inserted in the spaces between groups. | ||
Revision as of 11:16, 15 August 2019
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International System of Units
Description
The SI is a consistent system of units for use in all aspects of life, including international trade, manufacturing, security, health and safety, protection of the environment, and in the basic science that underpins all of these. The system of quantities underlying the SI and the equations relating them are based on the present description of nature and are familiar to all scientists, technologists and engineers.
The definition of the SI units is established in terms of a set of seven defining constants. The complete system of units can be derived from the fixed values of these defining constants, expressed in the units of the SI. These seven defining constants are the most fundamental feature of the definition of the entire system of units. These particular constants were chosen after having been identified as being the best choice, taking into account the previous definition of the SI, which was based on seven base units, and progress in science (p. 125).
Abbreviation: SI
Reference: Bureau International des Poids et Mesures (2019) The International System of Units (SI). 9th edition:117-216 ISBN 978-92-822-2272-0. - »Open Access pdf«
Contents
- 1 Description
- 2 Base quantities / SI base units
- 3 Fundamental relationships
- 4 General remarks
- 5 Defining the unit of a quantity (p. 127)
- 6 Definition of the SI (p. 127)
- 7 Quantity calculus (p. 147)
- 8 Quantity symbols and unit symbols (p. 149)
- 9 Writing and printing of unit symbols and of numbers (p. 162)
Base quantities / SI base units
- » time / [second]
- » length / [meter]
- » mass / [kilogram]
- » electric current / [ampere]
- » thermodynamic temperature / [kelvin]
- » amount of substance / [mole]
- » luminous intensity / [candela]
Fundamental relationships
General remarks
- Since 'small spelling variations occur in the language of the English speaking countries (for instance, "metre" and "meter", "litre" and "liter")' (p. 124), a decision should be taken for consistent spelling in a document. The English text of the SI brochure follows the style "metre" and "litre". It is found that in the scientific literature the spelling style "meter" and "liter" prevails even in European journals. Below are direct quotes from the SI brochure (with reference to the page number in the 9th edition), implementing corresponding changes in spelling style.
Defining the unit of a quantity (p. 127)
- The value of a quantity is generally expressed as the product of a number and a unit. The unit is simply a particular example of the quantity concerned which is used as a reference, and the number is the ratio of the value of the quantity to the unit.
- For a particular quantity different units may be used. For example, the value of the speed ‘’v’’ of a particle may be expressed as v = 25 m/s or v = 90 km/h, where meter per second and kilometer per hour are alternative units for the same value of the quantity speed.
- Before stating the result of a measurement, it is essential that the quantity being presented is adequately described. This may be simple, as in the case of the length of a particular steel rod, but can become more complex when higher accuracy is required and where additional parameters, such as temperature, need to be specified.
- When a measurement result of a quantity is reported, the estimated value of the measurand (the quantity to be measured), and the uncertainty associated with that value, are necessary. Both are expressed in the same unit.
Definition of the SI (p. 127)
- As for any quantity, the value of a fundamental constant can be expressed as the product of a number and a unit.
- The definitions below specify the exact numerical value of each constant when its value is expressed in the corresponding SI unit. By fixing the exact numerical value the unit becomes defined, since the product of the numerical value and the unit has to equal the value of the constant, which is postulated to be invariant.
- The seven constants are chosen in such a way that any unit of the SI can be written either through a defining constant itself or through products or quotients of defining constants.
- The International System of Units, the SI, is the system of units in which
- the unperturbed ground state hyperfine transition frequency of the caesium 133 atom ∆ν_{Cs} is 9 192 631 770 Hz,
- the speed of light in vacuum c is 299 792 458 m/s,
- the Planck constant h is 6.626 070 15 × 10^{−34} J s,
- the elementary charge e is 1.602 176 634 × 10^{−19} C x^{-1},
- the Boltzmann constant k is 1.380 649 × 10^{−23} J x^{-1} K^{-1},
- the Avogadro constant NA is 6.022 140 76 × 10^{23} x mol^{−1},
- the luminous efficacy of monochromatic radiation of frequency 540 × 1012 Hz, K_{cd}, is 683 lm/W,
- where the hertz, joule, coulomb, lumen, and watt, with unit symbols Hz, J, C, lm, and W, respectively, are related to the units second, meter, kilogram, ampere, kelvin, mole, and candela, with unit symbols s, m, kg, A, K, mol, and cd, respectively, according to Hz = s^{–1}, J = kg m^{2} s^{–2}, C = A s, lm = cd m^{2} m^{–2} = cd sr, and W = kg m^{2} s^{–3}.
- The numerical values of the seven defining constants have no uncertainty.
Quantity calculus (p. 147)
- Symbols for units are treated as mathematical entities. In expressing the value of a quantity as the product of a numerical value and a unit, both the numerical value and the unit may be treated by the ordinary rules of algebra. This procedure is described as the use of quantity calculus, or the algebra of quantities. For example, the equation p = 48 kPa may equally be written as p/kPa = 48. It is common practice to write the quotient of a quantity and a unit in this way for a column heading in a table, so that the entries in the table are simply numbers.
Suggestion: p/[kPa] = 48
Quantity symbols and unit symbols (p. 149)
- Unit symbols must not be used to provide specific information about the quantity and should never be the sole source of information on the quantity. Units are never qualified by further information about the nature of the quantity; any extra information on the nature of the quantity should be attached to the quantity symbol and not to the unit symbol.
Comment: Quantity calculus can be extended by providing specific information about the quantity together with the unit symbol, e.g., [kJ·mol^{-1} O_{2}].
Writing and printing of unit symbols and of numbers (p. 162)
- Roman (upright) type, in general lower-case, is used for symbols of units; if, however, the symbols are derived from proper names, capital roman type is used. These symbols are not followed by a full stop.
- In numbers, the comma (French practice) or the dot (British practice) is used only to separate the integral part of numbers from the decimal part. Numbers may be divided in groups of three in order to facilitate reading; neither dots nor commas are ever inserted in the spaces between groups.
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