Section: 1 | International System of Units (SI) |
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John R. Rumble, ed., CRC Handbook of Chemistry and Physics, 102nd Edition (Internet Version 2021), CRC Press/Taylor & Francis, Boca Raton, FL.
If a specific table is cited, use the format: "Physical Constants of Organic Compounds," in CRC Handbook of Chemistry and Physics, 102nd Edition (Internet Version 2021), John R. Rumble, ed., CRC Press/Taylor & Francis, Boca Raton, FL.

INTERNATIONAL SYSTEM OF UNITS (SI)

The International Bureau of Weights and Measures (BIPM) was established by Article 1 of the Metre Convention, which was signed on May 20, 1875. BIPM is charged with providing the basis for a single, coherent system of measurements to be used throughout the world and operates under the authority of the International Committee of Weights and Measures (CIPM). In 1960, the 11th General Conference on Weights and Measures (CGPM) formally defined and established the International System of Units (SI). Since then, the SI has been periodically updated to take into account advances in science and the need for measurements in new domains.

In 2018, the 26th CGPM (2019) decided that the SI would be based on the fixed numerical values of a set of seven defining constants from which the definitions of the seven base units of the SI would be deduced. This major change was made to allow anchoring of the SI to specific experimental realizations of measurable quantities and to remove the base units from dependence on physical artifacts. The change has been taking place over a number of years, and its completion was made possible by realization of the base unit kilogram separate from its previous physical artifact as stored at BIPM in Sevres, France. This discussion of the the newly constituted SI is based on more complete documentation in References 1 and 2. Because of the importance of the SI in science, much of the discussion below is taken verbatim from these references.

The core of the SI is the seven base units for physical quantities as shown in Table 1.

TABLE 1. SI Base Units



Base quantityNameSymbol
lengthmeterm
masskilogramkg
timeseconds
electric currentampereA
thermodynamic temperaturekelvinK
amount of substancemolemol
luminous intensitycandelacd


As of May 20, 2019, the SI is the system of units in which the base units are now defined by the seven fundamental constants given in Table 2. More complete discussions of these constants and their experimental realizations can be found in References 1 and 2.

TABLE 2. Fundamental Constants Used to Define the SI



Fundamental constantSymbolValue
Unperturbed ground-state hyperfine transition frequency of the cesium 133 atom 133CsΔνCs9 192 631 770 Hz
Speed of light in vacuumc299 792 458 m s-1
Planck constanth6.626 070 15 × 10-34 J s
Elementary chargee1.602 176 634 × 10-19 C
Boltzmann constantk1.380 649 × 10-23 J K-1
Avogadro constantNA6.022 140 76 × 1023 mol-1
Luminous efficacy of monochromatic radiation of frequency 540 × 1012 HzKcd683 lm W-1


The hertz, joule, coulomb, lumen, and watt are related to the units second, meter, kilogram, ampere, kelvin, mole, and candela as follows in Table 3. (Note sr is steradian.) 

TABLE 3. Relationship of Important Units to the Basic SI Units



Unit nameSymbolRelationship
hertzHzs-1
jouleJkg m2 s-2
coulombCA s
lumenlmcd m2 m-2 = cd sr
wattWkg m2 s-3


Table 4 provides the definitions of the base quantities. The defintions replace older definitions as discussed in detail in References 1 and 2. These definitions 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 because the product of the numerical value and the unit has to equal the value of the constant, which is invariant. The defining constants have been chosen such that, when taken together, their units cover all of the units of the SI. In general, there is no one-to-one correspondence between the defining constants and the SI base units, except for the cesium frequency ΔνCs and the Avogadro constant NA. Any SI unit is a product of powers of these seven constants and a dimensionless factor. 

TABLE 4. Definitions of the SI Base Units as Adopted by BIPM in 2019

ampere: The ampere, symbol A, is the SI unit of electric current. It is defined by taking the fixed numerical value of the elementary charge e to be 1.602 176 634 × 10-19 when expressed in the unit C, which is equal to A s, where the second is defined in terms of ΔνCs
candela: The candela, symbol cd, is the SI unit of luminous intensity in a given direction. It is defined by taking the fixed numerical value of the luminous efficacy of monochromatic radiation of frequency 540 × 1012 Hz, Kcd, to be 683, when expressed in the unit lm W-1, which is equal to cd sr W-1, or cd sr kg-1 m-1 s3, where the kilogram, meter, and second are defined in terms of h, c, and ΔνCs.
kelvin: The kelvin, symbol K, is the SI unit of thermodynamic temperature. It is defined by taking the fixed numerical value of the Boltzmann constant k to be 1.380 649 × 10-23 when expressed in the unit J K-1, which is equal to kg m2 s-2 K-1, where the kilogram, meter, and second are defined in terms of h, c, and ΔνCs. 
kilogram: The kilogram, symbol kg, is the SI unit of mass. It is defined by taking the fixed numerical value of the Planck constant h to be 6.626 070 15 × 10-34 when expressed in the unit J s, which is equal to kg m2 s-1, where the meter and second are defined in terms of c and ΔνCs.
meter: The meter, symbol m, is the SI unit of length. It is defined by taking the fixed numerical value of the speed of light in vacuum c to be 299 792 458 when expressed in the unit m s-1, where the second is defined in terms of the cesium frequency ΔνCs.
mole:

The mole, symbol mol, is the SI unit of amount of substance. One mole contains exactly 6.022 140 76 × 1023 elementary entities. This number is the fixed numerical value of the Avogadro constant, NA, when expressed in the unit mol-1 and is called the Avogadro number. The amount of substance, symbol n, of a system is a measure of the number of specified elementary entities. An elementary entity may be an atom, a molecule, an ion, an electron, any other particles, or specified group of particles.

second: The second, symbol s, is the SI unit of time. It is defined by taking the fixed numerical value of the cesium frequency ΔνCs, the unperturbed ground-state hyperfine transition frequency of the cesium 133 atom (133Cs), to be 9 192 631 770 when expressed in the unit Hz, which is equal to s-1.

 

SI derived units

Derived units are units that may be expressed in terms of base units by means of the mathematical symbols of multiplication and division (and, in the case of °C, subtraction). Certain derived units have been given special names and symbols, and these special names and symbols may themselves be used in combination with those for base and other derived units to express the units of other quantities. Table 5 lists some examples of derived units expressed directly in terms of base units.

TABLE 5. Examples of SI Derived Units



Physical quantityNameSymbol
areasquare meterm2
volumecubic meterm3
speed, velocitymeter per secondm s-1
accelerationmeter per second squaredm s-2
wave numberreciprocal meterm-1
density, mass densitykilogram per cubic meterkg m-3
specific volumecubic meter per kilogramm3 kg-1
current densityampere per square meterA m-2
magnetic field strengthampere per meterA m-1
concentration (of amount of substance)mole per cubic metermol m-3
luminancecandela per square metercd m-2
refractive index(the number) one1a

  • aThe symbol “1” (for the number "one") is generally omitted in combination with a numerical value.


For convenience, certain derived units, which are listed in Table 6, have been given special names and symbols. These names and symbols may themselves be used to express other derived units. The special names and symbols are a compact form for the expression of units that are used frequently. The final column shows how the SI units concerned may be expressed in terms of SI base units. In this column, factors such as m0, kg0 …, which are all equal to 1, are not shown explicitly.

TABLE 6. SI Derived Units with Special Names and Symbols



Physical quantityNameSymbolOther SI unitsSI base units
Continued on next page...
plane angleradian(a)radm · m-1 = 1(b)
solid anglesteradian(a)sr(c)m2 · m-2 = 1(b)
frequencyhertzHzs-1
forcenewtonNm · kg · s-2
pressure, stresspascalPaN m-2m-1 · kg · s-2
energy, work, quantity of heatjouleJN · mm2 · kg · s-2
power, radiant fluxwattWJ s-1m2 · kg · s-3
electric charge, quantity of electricitycoulombCs · A
electric potential difference, electromotive forcevoltVW A-1m2 · kg · s-3 · A-1
capacitancefaradFC V-1m-2 · kg-1 · s4 · A2
electric resistanceohmΩV A-1m2 · kg · s-3 · A-2
electric conductancesiemensSA V-1m-2 · kg-1 · s3 · A2
magnetic fluxweberWbV · sm2 · kg · s-2 · A-1
magnetic flux densityteslaTWb m-2kg · s-2 · A-1
inductancehenryHWb A-1m2 · kg · s-2 · A-2
Celsius temperaturedegree Celsius(d)°CK
luminous fluxlumenlmcd · sr(c)m2 · m–2 · cd = cd
illuminanceluxlxlm m-2m2 · m–4 · cd = m–2 · cd
activity (of a radionuclide)becquerelBqs-1

  • (a)The radian and steradian may be used with advantage in expressions for derived units to distinguish between quantities of different nature but the same dimension. Some examples of their use in forming derived units are given in the next table.
  • (b)In practice, the symbols rad and sr are used where appropriate, but the derived unit “1” is generally omitted in combination with a numerical value.
  • (c)In photometry, the name steradian and the symbol sr are usually retained in expressions for units.
  • (d)It is common practice to express a thermodynamic temperature, symbol T, in terms of its difference from the reference temperature T0 = 273.15 K. The numerical value of a Celsius temperature t expressed in degrees Celsius is given by t/°C = T/K-273.15. The unit °C may be used in combination with SI prefixes, e.g., millidegree Celsius, m°C. Note that there should never be a space between the ° sign and the letter C, and that the symbol for kelvin is K, not °K.


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