Difference between revisions of "International System of Units"

From WikiChem
Jump to: navigation, search
(Derived units)
(Derived units)
 
(2 intermediate revisions by the same user not shown)
Line 52: Line 52:
  
 
==Derived units==
 
==Derived units==
A derived unit is formed from a combination of base units, particularly a product of base units raised to non-zero powers: for example, the metre per second as a unit of speed. A derived unit is said to be "coherent" if there is no numerical factor other than one before product of the base units (raised, if necessary, to their different powers). For example, the metre per second squared is the coherent SI derived unit for acceleration, whereas the centimetre per second squared (better known as the [[gal]]) is not coherent because of the factor of 10<sup>-2</sup>.
+
A derived unit is formed from a combination of base units, particularly a product of base units raised to non-zero powers: for example, the metre per second ({{nowrap|m s<sup>−1</sup>}}) as a unit of [[speed]]. A derived unit is said to be "coherent" if there is no numerical factor other than one before product of the base units (raised, if necessary, to their different powers). For example, the metre per second squared ({{nowrap|m s<sup>−2</sup>}}) is the coherent SI derived unit for [[acceleration]], whereas the centimetre per second squared<ref group="note">This unit is better known as the [[gal]] (symbol: Gal).</ref> is a valid derived SI unit but is not coherent because of the factor of 10<sup>−2</sup> implied by the prefix "centi" (''[[#Multiples and submultiples|see below]]'').
  
The number of possible derived units is without limit, but certain coherent derived units have special names and symbols within the SI.
+
The number of possible derived units is without practical limit, but certain coherent derived units have special names and symbols within the SI.
 +
 
 +
{| class="wikitable"
 +
|-
 +
! Name
 +
! Symbol
 +
! Physical quantity
 +
! Definition
 +
! Notes
 +
|-
 +
| [[becquerel]] || Bq || [[activity (radionuclide)|activity]] || s<sup>−1</sup> ||
 +
|-
 +
| [[coulomb]] || C || [[electric charge]] || s A ||
 +
|-
 +
| [[farad]] || F || [[capacitance]] || m<sup>−2</sup> kg<sup>−1</sup> s<sup>4</sup> A<sup>2</sup> = C/V ||
 +
|-
 +
| [[gray]] || Gy || [[absorbed dose (ionizing radiation)|absorbed dose]] || m<sup>2</sup> s<sup>−2</sup> = J/kg ||
 +
|-
 +
| [[henry]] || H || [[inductance]] || m<sup>2</sup> kg s<sup>−2</sup> A<sup>−2</sup> = Wb/A ||
 +
|-
 +
| [[hertz]] || Hz || [[frequency]] || s<sup>−1</sup> ||
 +
|-
 +
| [[joule]] || J || [[energy]]<br/>[[work]]<br/>amount of [[heat]] || m<sup>2</sup> kg s<sup>−2</sup> = N m ||
 +
|-
 +
| [[katal]] || kat || [[catalytic activity]] || s<sup>−1</sup> mol ||
 +
|-
 +
| [[lumen]] || lm || [[luminous flux]] || cd sr = cd ||
 +
|-
 +
| [[lux]] || lx || [[illuminance]] || m<sup>−2</sup> cd = lm/m<sup>2</sup> ||
 +
|-
 +
| [[newton]] || N || [[force]] || m kg s<sup>−2</sup> ||
 +
|-
 +
| [[ohm]] || Ω || [[electric resistance]] || m<sup>2</sup> kg s<sup>−3</sup> A<sup>−2</sup> = V/A ||
 +
|-
 +
| [[pascal]] || Pa || [[pressure]]<br/>[[stress]] || m<sup>−1</sup> kg s<sup>−2</sup> = N/m<sup>2</sup> ||
 +
|-
 +
| [[siemens]] || S || [[electric conductance]] || m<sup>−2</sup> kg<sup>−1</sup> s<sup>3</sup> A<sup>2</sup> = A/V ||
 +
|-
 +
| [[sievert]] || Sv || [[dose equivalent]] || m<sup>2</sup> s<sup>−2</sup> = J/kg ||
 +
|-
 +
| [[tesla]] || T || [[magnetic flux density]] || kg s<sup>−2</sup> A<sup>−1</sup> = Wb/m<sup>2</sup> ||
 +
|-
 +
| [[volt]] || V || [[electric potential difference]]<br/>[[electromotive force]] || m<sup>2</sup> kg s<sup>−3</sup> A<sup>−1</sup> = W/A = J/C ||
 +
|-
 +
| [[watt]] || W || [[power]]<br/>[[radiant flux]] || m<sup>2</sup> kg s<sup>−3</sup> = J/s ||
 +
|-
 +
| [[weber]] || Wb || [[magnetic flux]] || m<sup>2</sup> kg s<sup>−2</sup> A<sup>−1</sup> = V s ||
 +
|-
 +
| [[degree Celsius]] || °C || [[Celsius temperature]] || K ||
 +
|-
 +
| [[radian]] || rad || [[plane angle]] || m/m = 1 ||
 +
|-
 +
| [[steradian]] || sr || [[solid angle]] || m<sup>2</sup>/m<sup>2</sup> = 1 ||
 +
|-
 +
|}
  
 
==Multiples and submultiples==
 
==Multiples and submultiples==

Latest revision as of 11:28, 23 March 2010

The International System of Units (commonly abbreviated to SI from its French name Système Internationale d'Unités) is the international system of units of measurement established under the Metre Convention. It is based on seven "base units", with a potentially limitless number of "derived units".

The definitions of the base units and other fundamental aspects of the system are approved by the General Conference on Weights and Measures (CGPM), a diplomatic conference which meets every four years, based on recommendations from the International Committee for Weights and Measures (CIPM). The CIPM is also charged with agreeing many of the technical details of the system, such as the methods of realization of units and other details of conventional measurement techniques.

Base units

Unit name Unit symbol Physical quantity Notes
metre m length
kilogram kg mass
second s time
ampere A electric current
kelvin K thermodynamic temperature
candela cd luminous intensity
mole mol amount of substance

The six original base units were selected in 1956 by the 9th CGPM (the mole was added in 1972). They represent a conventional choice: the choice made in the International System of Units is not the only possible choice of base units, nor is there any physical significance that the ampere was chosen as the base for electromagnetic units rather than, e.g., the coulomb.

The inclusion of the candela as a base unit is for both historical and practical reasons. There is an obvious technical need to classify many everyday light sources on the basis of their effect on the human eye. This is acheived by multiplying the radient intensity (measured in watts per steradian) by a standard luminosity function that models the response of the human eye: the result is the candela, which is also the base for a series of other luminosity units.

Derived units

A derived unit is formed from a combination of base units, particularly a product of base units raised to non-zero powers: for example, the metre per second (m s−1) as a unit of speed. A derived unit is said to be "coherent" if there is no numerical factor other than one before product of the base units (raised, if necessary, to their different powers). For example, the metre per second squared (m s−2) is the coherent SI derived unit for acceleration, whereas the centimetre per second squared[note 1] is a valid derived SI unit but is not coherent because of the factor of 10−2 implied by the prefix "centi" (see below).

The number of possible derived units is without practical limit, but certain coherent derived units have special names and symbols within the SI.

Name Symbol Physical quantity Definition Notes
becquerel Bq activity s−1
coulomb C electric charge s A
farad F capacitance m−2 kg−1 s4 A2 = C/V
gray Gy absorbed dose m2 s−2 = J/kg
henry H inductance m2 kg s−2 A−2 = Wb/A
hertz Hz frequency s−1
joule J energy
work
amount of heat
m2 kg s−2 = N m
katal kat catalytic activity s−1 mol
lumen lm luminous flux cd sr = cd
lux lx illuminance m−2 cd = lm/m2
newton N force m kg s−2
ohm Ω electric resistance m2 kg s−3 A−2 = V/A
pascal Pa pressure
stress
m−1 kg s−2 = N/m2
siemens S electric conductance m−2 kg−1 s3 A2 = A/V
sievert Sv dose equivalent m2 s−2 = J/kg
tesla T magnetic flux density kg s−2 A−1 = Wb/m2
volt V electric potential difference
electromotive force
m2 kg s−3 A−1 = W/A = J/C
watt W power
radiant flux
m2 kg s−3 = J/s
weber Wb magnetic flux m2 kg s−2 A−1 = V s
degree Celsius °C Celsius temperature K
radian rad plane angle m/m = 1
steradian sr solid angle m2/m2 = 1

Multiples and submultiples

Multiples   Submultiples
Symbol Prefix     Prefix Symbol
da deca 101 10−1 deci d
h hecto 102 10−2 centi c
k kilo 103 10−3 milli m
M mega 106 10−6 micro µ
G giga 109 10−9 nano n
T tera 1012 10−12 pico p
P peta 1015 10−15 femto f
E exa 1018 10−18 atto a
Z zetta 1021 10−21 zepto z
Y yotta 1024 10−24 yocto y

Units used with the SI

There are several sets of units which are not SI units but which have some degree of acceptance for use with the International System of Units.

Common units with exact conversion factors

Name Symbol Physical
quantity
Value Notes
minute min time 1 min = 60 s
hour h time 1 h = 60 min = 3600 s
day d time 1 d = 86 400 s
degree ° plane angle 1° = (π/180) rad
minute plane angle 1′ = (1/60)° = (π/10 800) rad
second plane angle 1″ = (1/60)′ = (π/648 000) rad
hectare ha area 1 ha = 1 hm2 = 0.01 km2 = 104 m2
litre L, l volume 1 L = 1 l = 1 dm3 = 103 cm3 = 10−3 m3 [note 2]
tonne t mass 1 t = 1000 kg

Units with empirical conversion factors

Name Symbol Physical
quantity
Value Notes
electronvolt eV energy 1 eV = 1.602 176 487(40) × 10−19 J [1]
dalton Da mass 1 Da = 1 u = 1.660 538 782(83) × 10−27 kg [1]
atomic mass unit u
astronomical unit ua length 1 ua = 149 597 870 700(3) m [2][3][4]
[note 3]

Notes and references

Notes

  1. This unit is better known as the gal (symbol: Gal).
  2. The spelling "liter" and the symbol L are mandatory in the U.S. interpretation of the SI.
  3. There are several different symbols for the astronomical unit, including ua, au, AU and A.

References

External links

Error creating thumbnail: Unable to save thumbnail to destination
This page is currently licensed under the Creative Commons Attribution 3.0 Unported license and any later versions of that license.