INTERNATIONAL SYSTEM OF UNITS (SI) 1 SIbaseunits Table1givesthesevenbasequantities,assumedtobemutuallyindependent,onwhichtheSIis founded;andthenamesandsymbolsoftheirrespectiveunits,called``SIbaseunits.' ' Definitionsof theSIbaseunitsaregiveninAppendixA.ThekelvinanditssymbolKarealsousedtoexpressthe valueofatemperatureintervaloratemperaturedifference. Table1.SIbaseunits SIbaseunit Basequantity Name Symbol length meter m mass kilogram kg time second s electriccurrent ampere A thermodynamictemperature kelvin K amountofsubstance mole mol luminousintensity candela cd 2 SIderiived units Derivedunitsareexpressedalgebraicallyintermsofbaseunitsorotherderivedunits(including theradianandsteradianwhicharethetwosupplementaryunits– seeSec.3).Thesymbolsfor derivedunitsareobtainedbymeansofthemathematicaloperationsofmultiplicationanddivision. Forexample,thederivedunitforthederivedquantitymolarmass(massdividedbyamountofsub- stance)isthekilogrampermole,symbolkg/mol.Additionalexamplesofderivedunitsexpressedin termsofSIbaseunitsaregiveninTable2. Table2.ExamplesofSIderivedunitsexpressedintermsofSIbaseunits SIderivedunit Derivedquantity Name Symbol area squaremeter m2 volume cubicmeter m3 speed,velocity meterpersecond m/s acceleration meterpersecondsquared m/s2 wavenumber reciprocalmeter m21 massdensity(density) kilogrampercubicmeter kg/m3 specificvolume cubicmeterperkilogram m3/kg currentdensity amperepersquaremeter A/m2 magneticfieldstrength amperepermeter A/m amount-of-substanceconcentration (concentration) molepercubicmeter mol/m3 luminance candelapersquaremeter cd/m2 2.1 SIde rived units withspecial namesandsymbols CertainSIderivedunitshavespecialnamesandsymbols;thesearegiveninTables3aand3b. AsdiscussedinSec.3,theradianandsteradian,whicharethetwosupplementaryunits,are includedinTable3a. INTERNATIONAL SYSTEM OF UNITS (SI) (continued) Table3a.SIderivedunitswithspecialnamesandsymbols,includingtheradianandsteradian SIderivedunit Expression Expression Derivedquantity Specialname Specialsymbol interms interms ofother ofSIbase SIunits units planeangle radian rad m?m21 =1 solidangle steradian sr m2 ?m22 =1 frequency hertz Hz s21 force newton N m?kg?s22 pressure,stress pascal Pa N/m2 m21 ?kg?s22 energy,work,quantity ofheat joule J N?mm2 ?kg?s22 power,radiantflux watt W J/s m2 ?kg?s23 electriccharge, quantityofelectricity coulomb C s?A electricpotential, potentialdifference, electromotiveforce volt V W/A m2 ?kg?s23 ?A21 capacitance farad F C/V m22 ?kg21 ?s4 ?A2 electricresistance ohm V V/A m2 ?kg?s23 ?A22 electricconductance siemens S A/V m22 ?kg21 ?s3 ?A2 magneticflux weber Wb V?sm2 ?kg?s22 ?A21 magneticfluxdensity tesla T Wb/m2 kg?s22 ?A21 inductance henry H Wb/A m2 ?kg?s22 ?A22 Celsiustemperature(a) degreeCelsius 8CK luminousflux lumen lm cd?sr cd?sr(b) illuminance lux lx lm/m2 m22 ?cd?sr(b) (a) SeeSec.2.1.1. (b) Thesteradian(sr)isnotanSIbaseunit.However,inphotometrythesteradian(sr)ismaintainedinexpressions forunits(seeSec.3). Table3b.SIderivedunitswithspecialnamesandsymbolsadmittedforreasonsofsafeguardinghumanhealth(a) SIderivedunit Derivedquantity Special Special Expressioninterms Expressioninterms name symbol ofotherSIunits ofSIbaseunits activity(ofa radionuclide) becquerel Bq s21 absorbeddose, specificenergy (imparted),kerma gray Gy J/kg m2 ?s22 doseequivalent,ambientdose equivalent,directionaldose equivalent,personaldose equivalent,equivalentdose sievert Sv J/kg m2 ?s22 (a) Thederivedquantitiestobeexpressedinthegrayandthesieverthavebeenrevisedinaccordancewiththe recommendationsoftheInternationalCommissiononRadiationUnitsandMeasurements(ICRU). 2.1.1DegreeCelsiusInadditiontothequantitythermodynamictemperature(symbolT), expressedintheunitkelvin,useisalsomadeofthequantityCelsiustemperature (symbolt)definedbytheequation t=T2T0 , whereT0 =273.15Kbydefinition.ToexpressCelsiustemperature,theunitdegreeCelsius,symbol 8C,whichisequalinmagnitudetotheunitkelvin,isused;inthiscase,``degreeCelsius' ' isaspecial nameusedinplaceof``kelvin.' ' AnintervalordifferenceofCelsiustemperaturecan,however,be expressed in the unit kelvin as well as in the unit degree Celsius. (Note that the thermodynamic temperatureT0 is exactly 0.01 K below the thermodynamic temperature of the triple point of water.) INTERNATIONAL SYSTEM OF UNITS (SI) (continued) 2.2 UseofSIderivedunitswithspecialnamesandsymbols ExamplesofSIderivedunitsthatcanbeexpressedwiththeaidofSIderivedunitshaving specialnamesandsymbols(includingtheradianandsteradian)aregiveninTable4. Table4.ExamplesofSIderivedunitsexpressedwiththeaidofSIderivedunitshavingspecialnamesandsymbols SIderivedunit Expression Derivedquantity Name Symbol intermsof SIbaseunits angularvelocity radianpersecond rad/s m?m21 ?s21 =s21 angularacceleration radianpersecondsquared rad/s2 m?m21 ?s22 =s22 dynamicviscosity pascalsecond Pa?sm21 ?kg?s21 momentofforce newtonmeter N?mm2 ?kg?s22 surfacetension newtonpermeter N/m kg?s22 heatfluxdensity, irradiance wattpersquaremeter W/m2 kg?s23 radiantintensity wattpersteradian W/sr m2 ?kg?s23 ?sr21(a) radiance wattpersquare metersteradian W/(m2 ?sr) kg?s23 ?sr21(a) heatcapacity,entropy jouleperkelvin J/K m2 ?kg?s22 ?K21 specificheatcapacity, jouleperkilogram specificentropy kelvin J/(kg?K) m2 ?s22 ?K21 specificenergy jouleperkilogram J/kg m2 ?s22 thermalconductivity wattpermeterkelvin W/(m?K) m?kg?s23 ?K21 energydensity joulepercubicmeter J/m3 m21 ?kg?s22 electricfieldstrength voltpermeter V/m m?kg?s23 ?A21 electricchargedensity coulombpercubicmeter C/m3 m23 ?s?A electricfluxdensity coulombpersquaremeter C/m2 m22 ?s?A permittivity faradpermeter F/m m23 ?kg21 ?s4 ?A2 permeability henrypermeter H/m m?kg?s22 ?A22 molarenergy joulepermole J/mol m2 ?kg?s22 ?mol21 molarentropy,molar heatcapacity joulepermolekelvin J/(mol?K) m2 ?kg?s22 ?K21 ?mol21 exposure(xandgrays) coulombperkilogram C/kg kg21 ?s?A absorbeddoserate graypersecond Gy/s m2 ?s23 (a) Thesteradian(sr)isnotanSIbaseunit.However,inradiometrythesteradian(sr)ismaintainedinexpressions forunits(seeSec.3). TheadvantagesofusingthespecialnamesandsymbolsofSIderivedunitsareapparentinTable 4.Consider,forexample,thequantitymolarentropy:theunitJ/(mol?K)isobviouslymoreeasily understoodthanitsSIbase-unitequivalent,m2 ?kg?s22 ?K21 ?mol21.Nevertheless,itshould alwaysberecognizedthatthespecialnamesandsymbolsexistforconvenience;eithertheformin whichspecialnamesorsymbolsareusedforcertaincombinationsofunitsortheforminwhichthey arenotusediscorrect.Forexample,becauseofthedescriptivevalueimplicitinthecompound-unit form,communicationissometimesfacilitatedifmagneticflux(seeTable3a)isexpressedinterms ofthevoltsecond(V?s)insteadoftheweber(Wb). Tables3a,3b,and4alsoshowthatthevaluesofseveraldifferentquantitiesareexpressedinthe sameSIunit.Forexample,thejouleperkelvin(J/K)istheSIunitforheatcapacityaswellasfor entropy.Thusthenameoftheunitisnotsufficienttodefinethequantitymeasured. Aderivedunitcanoftenbeexpressedinseveraldifferentwaysthroughtheuseofbaseunitsand derivedunitswithspecialnames.Inpractice,withcertainquantities,preferenceisgiventousing certainunitswithspecialnames,orcombinationsofunits,tofacilitatethedistinctionbetweenquan- titieswhosevalueshaveidenticalexpressionsintermsofSIbaseunits.Forexample,theSIunitof frequencyisspecifiedasthehertz(Hz)ratherthanthereciprocalsecond(s21),andtheSIunitof momentofforceisspecifiedasthenewtonmeter(N?m)ratherthanthejoule(J). INTERNATIONAL SYSTEM OF UNITS (SI) (continued) Similarly,inthefieldofionizingradiation,theSIunitofactivityisdesignatedasthebecquerel (Bq)ratherthanthereciprocalsecond(s21),andtheSIunitsofabsorbeddoseanddoseequivalent aredesignatedasthegray(Gy)andthesievert(Sv),respectively,ratherthanthejouleperkilogram (J/kg). 3 SIsupplementaryunits Aspreviouslystated,therearetwounitsinthisclass:theradian,symbolrad,theSIunitofthe quantityplaneangle;andthesteradian,symbolsr,theSIunitofthequantitysolidangle.Definitions oftheseunitsaregiveninAppendixA. The SI supplementary units are now interpreted as so-called dimensionless derived units for which the CGPM allows the freedom of using or not using them in expressions for SI derived units.3 Thus the radian and steradian are not given in a separate table but have been included in Table 3a together with other derived units with special names and symbols (seeSec.2.1). This interpretation of the supplementary units implies that plane angle and solid angle are considered derived quantities of dimension one (so-called dimensionless quantities), each of which has the whichhastheunitone,symbol1,asitscoherentSIunit.However,inpractice,whenoneexpresses thevaluesofderivedquantitiesinvolvingplaneangleorsolidangle,itoftenaidsunderstandingifthe specialnames(orsymbols)``radian' ' (rad)or``steradian' ' (sr)areusedinplaceofthenumber1.For example,althoughvaluesofthederivedquantityangularvelocity(planeangledividedbytime)may beexpressedintheunits21,suchvaluesareusuallyexpressedintheunitrad/s. Becausetheradianandsteradianarenowviewedasso-calleddimensionlessderivedunits,the ConsultativeCommitteeforUnits(CCU, Comité Consultatif des Unités) of the CIPM as result of a 1993 request it received from ISO/TC12, recommended to the CIPM that it request the CGPM to abolish the class of supplementary units as a separate class in the SI. The CIPM accepted the CCU recommendation, and if the abolishment is approved by the CGPM as is likely (the question will be on the agenda of the 20th CGPM, October 1995), the SI will consist of only two classes of units: base units and derived units, with the radian and steradian subsumed into the class of derived units of the SI. (The option of using or not using them in expressions for SI