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Terms and Units of Itfeasure · the International System of Units'(SI} AppendlxA Terms and Units of Itfeasure · The International System of Units'(SI} The International System of Units, abbreviated SI, as defmed in International Standard ISO 1000, is described in this appendix. International Standard ISO 1000 was approved by International Organization of Standards (ISO) Member Bodies from 30 countries including the United States. The SI consists of the following: 1. Seven base units 2. AlI the derived units 3. Two supplementary units 4. The series of approved prefixes for multiples and submultiples of units. The units which apply to optical safety, their defmitions, their symbols, and the for­ mation of multiple and submultiple units are presented in this appendix. Informa­ tion related to style, use, and format is also provided. A.l TIlE TIlREE CLASSES OF UNITS IN TIlE SI The units of the International System of Units are divided into three classes: 1. Base units 2. Derived units 3. Supplementary units. Scientifically and technical1y this classification is partially arbitrary. The 10th General Conference of Weights and Measures (1954) adopted as base units ofthe SI the units of the quantities: length, mass, time, electric current, thermodynamic temperature, amount of substance, and luminous intensity which by convention are regarded as dimensional1y independent. Associated with these quantities are seven well-defmed units. This action was taken in the interest of achieving the advantages of having a single, practical, internationally accepted system for trade, education, science, and technology. The derived units are the units of quantities that can be formed by combining base quantities and other derived quantities according to the rules of algebra. The units of these derived quantities are such that no numerical factors (factors of pro­ portionality) are introduced into the fundamental equations defming these quan­ tities. Thus the SI-composed of seven base units, a growing number of derived 929 930 Sliney and Wolbarsht TABLE A-l. SI Base and Supplementary Units Quantity Name Symbol SI base units: length meter m mass* kilogram kg time second s electric current ampere A thermodynamic temperature kelvin K amount of substance mole moI luminous intensity candela cd SI supplementary units: plane angle radian rad solid angle steradian sr ., "Weight" is the commonly used term for "mass. " units, and the supplementary units forms a coherent system of units. A coherent system of units is one in which alI derived units can be expressed as products of ratios of the base units (and, in the SI, the supplementary units) without the intro­ duction of numerical factors. Examples of derived quantities are speed, energy, and irradiance. Two other units were adopted by the Il th General Conference of Weights and Measures (1960) as supplementary units primarily because it was not agreed that the two units were either base units or derived units. The quantities involved are plane angle and solid angle, and they may be regarded as base units or as derived units. A.2 BASE UNITS OF THE SI The SI is constructed from seven base units for independent quantities plus two supplementary units for plane angle and solid angle, listed in A-l. Units for alI other quantities are derived from these nine units. In Table A-2 are listed many SI derived units with special names which were derived from the base and supplementary units in a coherent manner, which means, in brief, that they are expressed as products and ratios of the nine base and supplementary units without numerical factors. A.3 SUPPLEMENTARY UNITS At present, there are only two units, both purely geometrical, in the SI which are classified as supplementary. They are presented before derived units because they may be used in derived units. Thus, for practical purposes these supplementary units Terms and Units 931 TABLEA-2. SI Derived Units with Special Names SI Unit Quantity Expression Name Symbol in terms of other units Area square meter m2 m2 Volume cubic meter m3 m3 Frequency hertz Hz S-l Force newton N kg·m/s2 Pressure, stress pascal Pa N/m 2 Energy, work, quantity ofheat joule J N·m Power, radiant flux watt W J/s Quantity of electricity, electric charge coulomb C A·s Electric potential, potential difference, voIt V W/A electromotive force Capacitance farad F C/V Electric resistance ohm n VIA Conductance siemens S A/V Magnetic flux weber Wb V·s Magnetic flux density tesla T Wb/m 2 Inductance henry H Wb/A Luminous flux lumen lm cd ·sr Illuminance lux Ix lm/m2 Celsiust degree °c K temperature Celsius Activity (of a radionuclide)t becquerel Bq S-l Absorbed dose, specific energy imparted, gray Gy J/kg kerma, absorbed dose indext Wave number 1 permeter Iim Iim Density, mass density kilogram per kgfm3 kgfm3 cubic meter Luminance candela per cd/m2 cd/m 2 square meter Optical flux density, irradiance watt per W/m 2 W/m 2 square meter Energy density joule per cubic J/m 3 J/m 3 meter Radiant intensity watt per W/sr W/sr steradian Radiance watt per square W/(m 2 ·sr) W/(m2 ·sr) meter steradian t In addition to the thermodynamic temperature (symbol T), expressed in kelvins (see Table A-l), use is also made of Celsius temperature (symbol t) defined by the equation: t = T - Te where Te 273.15 K by definition. The unit "degree Celsius" is equal to the unit "kelvin, " but "degree Celsius" is a special name in place of "kelvin" for expressing Celsius temperature. A tem­ perature interval or a Celsius temperature difference can be expressed in degrees, Celsius as well as in kelvins. 932 Sliney and Wolbarsht TABLE A-3. SI Units Used with the SI Expression Expression Quantity Name Symbol in terms of In terms of other units SIunits Time minute min 60s Time hour h 60min 3600 s Time day d 24h 86400 s Plane ang1e degree o (1T/180) rad Plane ang1e minute (1/60t (1T/I0 800) rad Plane ang1e second " (1/60)' (1T /648 000) rad The radian and steradian are defined in International Standard ISO 1000 as follows: 1. radian. The radian is the plane angle between two radii of a circle which cut off an the circumference an arc equal in length ta the radius. 2. steradian. The steradian is the solid angle which, having its vertex in the center of a sphere, cuts off an area of the surface of the sphere equal ta that of a square with sides of length equal ta the radius of the sphere. O The use of degree (symbol ) and its decimal submultiples is permissible when use of the radian is not convenient. Solid angle always should be expressed in steradians. TABLEA-4. SI PreflXes Multiplication Factors PrefIX SISymbol 1 000 000 000 000 000 000 = 1018 exa E 1 000 000 000 000 000 = 1015 peta P 1 000 000 000 000 = 1012 tera T 1 000 000 000 = 109 giga G 1 000 000 = 106 mega M 1 000 = 103 kilo k 100 = 102 hecto* h 10= 101 deka* da 0.1 10-1 deci* d 0.01 10-2 centi* c 0.001 10-3 milli m 10'-6 0.000 001 micro J.l 0.000 000 001 10-9 nano n 0.000 000 000 001 10-12 pica p 0.000 000 000 000 001 10-15 femto f 0.000 000 000 000 000 001 10-18 atto a * To be avoided where possible. Terms and Units 933 Table A-5. elE Radiometric and Photometric Tenns in Four Languages. Symbol English French Gernum Russian Qe Radiant energy energie rayonnante Strahlungsmenge JHepI'HH HJrry'leHHH <Pe, Pe Radiant Flux, or flux energetique Strahlungsfluss IIOTOK H31IyqeHHH Radiant power Ee Irradiance eclairement Bestrahlungsst'ărke JHepr eT H'IeCKaH {mergetique OCBemeHHOCTb Re Radiant Exposure exposition Bestrahlung JHepreTH'leCKaH energetique JKCII03HUHH Le Radiance luminance Strahldichte JHepreTH'leCKaH energetique HpKOCTb le Radiant Intensity intensite energetique Strahlstiirke JHepreTH'leCKaH CHlIa CBeTa Qv Quantity of Ught quantite de lumiere Uchtmenge CBeTOBOH IIOTOK <Pv, Pv Luminous Flux fluxlumineux Uchtstrom CBeTOBOH JHeprHH Ev lliuminance eclairement lumineuse Beleuchtungssiărke OCBemeHHOCTb Hv Ught Exposure exposition lumineuse Belichtung JKCII03HUHH Lv Luminance luminancelumineuse Leuchtdichte HpKOCTb Iv Luminous intensite lumineuse Uchtstiirke CHlIa CBeTa Intensity 934 Sliney and Wolbarsht BASE UNITS DERIVED UNITS WITH SPECIAL NAMES kilogram ----- ..Y IJIkg) pIICII MASS --~Gy ABSORBEO OOSE PRESSURE. t STRESS meter ENERGV. WORK. b....... lt::'\ (li,) h• .., <?11/sl OU=6ANTITVOF HEAT ~ Hz , ACTlYITV second /' (OF IONIZING FREOUENCV , RAOIATION SOURCE) I " I WJIt W,) ------------__ J_______ W coulomb (A's) .'rld (CIV) C F POWER. HEAT FLOW RATE ampere kelvin ElECTROMDTlVE rdq,;;' FORCE ICelsius THE RMOOVNAMIC TEMPERATURE I °c I candela CELSIUS 1 ----------.... I I 1 TEMPERATURE I MAGNETIC 15 IL t->C____ qK- 273. .J1 FLUX FLUX 1 DENSITV I I I radian r:::-1 I L...:!.J m2 ____ J PLANE ANGlE steradian LUMINDUS FLUX IUUMINANCE SOLID ANGlE SOLID LlNES INDICATE MULTlPLlCATION BROKEN LlNES DIVISION L-.._________ '-- ____--'-- ___ -._---.--__________--1 Figure A-l. Relationships of SI Units with Names. Diagram courtesy National Bureau of Standards. Terms and Units 935 A.4 CONYERSION FACTORS AND CONSTANTS A.4.1 Usefui Physicai Constants Acceleration due to gravity g = 9.81 m/s BoItzmann constant k 1.381 X 10-23 J/K Charge of an electron e 1.602 X 10-19 A·s Impedance of free space Zo =.;;;re;; = 376.7 n Maximum spectral Iuminous efficacy Km = 6831m/W Permeability of free space Ilo 1.257 X 10-6 Y's/A'm) Permittivity of free space Eo = 8.854 X 10-12 A'S(Y'm) P1anck constant h = 6.626 X 10-34 J·s lst Radiation constant CI = 2rrhc2 = 3.741832 X 1O-16W/m2 2nd Radiation constant C2 = hc/k = 0.014388 m·K Stefan-BoItzmann constant a = 5.67032 X 10-8 W'm2 ·K4 Ye10city of Iight in vacuum c = 2.998 X 10 8 m/s A.4.2 Usefu1 Mathematical Constants rr = 3.14159
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