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Fundamental Units (SI)

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Fundamental Units (SI) In the Name of God (Applied Chemistry) Dimensions & Units Introduction In science, a type of question often asked is how much? how big? In order to answer such questions it is important to have systems of measurement which are consistent and understood by all. 2 1 Introduction Inch, foot; based on human body 4000 B.C. Egypt; King’s Elbow=0.4633 m, 1.5 ft, 2 handspans, 6 hand-widths, 24 finger-thickness AD 1101 King Henry I yard (0.9144 m) from his nose to the tip of his thumb 1528 French physician J. Fernel distance between Paris and Amiens Introduction 1872, Meter (in Greek, metron to measure)- 1/10 of a millionth of the distance between the North Pole and the equator Platinum (90%)-iridium (10%) X-shaped bar kept in controlled condition in Paris39.37 in In 1960, 1,650,763.73 wave length in vacuum of the orange light given off by electrically excited krypton 86. 2 Dimensions & Units Dimension - abstract quantity (e.g. length) Dimensions are used to describe physical quantities Dimensions are independent of units Unit - a specific definition of a dimension based upon a physical reference (e.g. meter) 5 Dimensions & Units How long is the rod? Rod of unknown length Reference: Three rods of 1-m length The unknown rod is 3 m long. unit number The number is meaningless without the unit! 3 System of Units A system of units is described by: a set of fundamental dimensions from which all other dimensions may be derived, and a set of base units. A dimension is a property that can be measured such as distance, time, temperature, speed. A unit is a basic division of a measured quantity and it enables to say how much of the quantity we have 10 miles, 2 hours etc. In most systems, length (distance), weight, and time are fundamental quantities; or as has been now accepted as better in science and engineering, the substitution of mass for weight, as a better more 7basic parameter. System of Units Imperial System of Units USCS (U.S. Customary System of Units) SI (The International System of Units) AES (American Engineering) systems of units 4 System of Units Both imperial units and US customary units derive from earlier English units. Imperial units were mostly used in the British Commonwealth and the former British Empire but in most Commonwealth countries they have been largely supplanted by the metric system. 9 System of Units US customary units, however, are still the main system of measurement in the United States. The U.S. customary units have common roots with the imperial units, which were used in the British Empire. Many U.S. units are virtually identical to their imperial counterparts, but the U.S. customary system developed from English units in use before the imperial system was standardized in 1824, and there are several numerical differences from the imperial system. 10 5 System of Units The International System of Units (abbreviated SI from French: Système international d'unités) is the modern form of the metric system and is generally a system of units of measurement devised around seven base units and the convenience of the number ten France in 1840 legislated official adoption of the metric system and made its use be mandatory In U.S., in 1866, the metric system was made legal, but its use was not compulsory 11 Absolute and Gravitational Unit Systems Absolute system Dimensions used are not affected by gravity Fundamental dimensions L,T,M Gravitational System Widely used used in engineering Fundamental dimensions L,T,F 6 The International System of Units (SI) Fundamental Dimension Base Unit length [L] meter (m) mass [M] kilogram (kg) time [T] second (s) electric current [A] ampere (A) absolute temperature [q] kelvin (K) luminous intensity [l] candela (cd) amount of substance [n] mole (mol) Supplementary SI Dimensions Supplementary Dimension Base Unit plane angle radian (rad) solid angle steradian (sr) 7 Fundamental Units (SI) Mass (kilogram): “a cylinder of platinum-iridium alloy maintained under vacuum conditions by the International Bureau of Weights and Measures in Paris” Fundamental Units (SI) Time(second): “the duration of 9,192,631,770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the cesium-133 atom” 8 Fundamental Units (SI) Length or Distance (meter): “the length of the path traveled by light in vacuum during a time interval of 1/299792458 seconds” photon Laser 1 m t = 0 s t = 1/299792458 s Fundamental Units (SI) Electric Current (ampere): “that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross section, and placed one meter apart in a vacuum,would produce between these conductors a force equal to 2 × 10-7 newtons per meter of length” 9 Fundamental Units (SI) Temperature (kelvin): The kelvin unit is 1/273.16 of the temperature interval from absolutezero to the triple point of water. Water Phase Diagram Pressure Temperature 273.16 K Fundamental Units (SI) Amount of Substance (mole): “the amount of a substance that contains as many elementary entities as there are atoms in 0.012 kilograms of carbon 12” 10 Fundamental Units (SI) Light or Luminous Intensity (candela): “the candela is the luminous intensity of a source that emits monochromatic radiation of frequency 540 × 1012 Hz and that has a radiant intensity of 1/683 watt per steradian.“ Supplementary Units (SI) Plane Angle (Radian): “the plane angle between two radii of a circle which cut off on the circumference an arc equal in length to the radius: 11 Supplementary Units (SI) Solid Angle (Steradian): “the solid angle which, having its vertex in the center of a sphere cuts off an area of the surface of the sphere equal to that of a square with sides of length equal to the radius of the sphere” The International System of Units (SI) Prefix Decimal Multiplier Symbol Atto 10-18 a Femto 10-15 f pico 10-12 p nano 10-9 n micro 10-6 m milli 10-3 m centi 10-2 c deci 10-1 d 12 The International System of Units (SI) Prefix Decimal Multiplier Symbol deka 10+1 da hecto 10+2 h kilo 10+3 k mega 10+6 M Giga 10+9 G Tera 10+12 T Peta 10+15 P exa 10+18 E U.S. Customary System of Units (USCS) Fundamental Dimension Base Unit length [L] foot (ft) force [F] pound (lb) time [T] second (sec) Derived Dimension Unit Definition 2 2 mass [FT /L] slug lbf sec /ft 13 American Engineering System of Units (AES) Fundamenal Dimension Base Unit length [L] foot (ft) mass [m] pound (lbm) force [F] pound (lbf) time [T] second (sec) electric charge [Q] coulomb (C) absolute temperature [q degree Rankine (oR) luminous intensity [l] candela (cd) amount of substance [n] mole (mol) 27 SI System of Units Force = (mass) (acceleration) F=ma W=mg 14 SI System of Units: Force Force = ma kg m s 2 = Newton = N SI System of Units: Work/Energy Work/ Energy = Force X Distance = N.m kg.m 2 s 2 = Joule = J 15 SI System of Units: Power Power = Work / Time N m Joule J s s s kg m 2 s 3 = Watt = W SI System of Units: Stress/Pressure Pressure = Force / Area N kg m / s 2 m 2 m 2 kg m s 2 = Pascal = Pa 16 Temperature Scale vs Temperature Interval 212oF 32oF DT = 212oF - 32oF=180 oF Scale Interval Temperature Conversion Temperature Scale oF 1.8o C 32 oR 1.8K 1 1 o C o F 32 K o R 1.8 1.8 Temperature Interval Conversion Factors 1.8 o F 1.8 oR 1 o F 1 o C F o C K o R K 17 Length Name of unit Symbol Definition Relation to SI units angstrom Å ≡ 1×10 10 m ≡ 0.1 nm foot (International) ft ≡ 1/3 yd ≡ 0.3048 m ≡ 12 inches ≡ 0.3048 m inch (International) in ≡ 1/36 yd ≡ 1/12 ft ≡ 0.0254 m 1 meter (SI base unit) m ≡ Distance light travels in ⁄299792458 of ≡ 1 m a second in vacuum. micron µ ≡ 1×10 6 m mile (international) mi ≡ 80 chains ≡ 5280 ft ≡ 1760 yd ≡ 1609.344 m nanometer nm ≡ 1×10 9 m ≡ 1×10 9 m nautical mile NM; mi ≡ 1852 m ≡ 1852 m (international) quarter ≡ ¼ yd = 0.2286 m picometer pm ≡ 1×10 12 m yard (International) yd ≡ 0.9144 m ≡ 3 ft ≡ 36 in ≡ 0.9144 m 35 Area Name of unit Symbol Definition Relation to SI units acre (international) ac ≡ 1 ch × 10 ch = ≡ 4 046.856 4224 m2 4840 sq yd square (roofing) ≡ 10 ft × 10 ft = 9.290 304 m2 square foot sq ft ≡ 1 ft × 1 ft ≡ 9.290 304×10 2 m2 square inch sq in ≡ 1 in × 1 in ≡ 6.4516×10 4 m2 square kilometre km2 ≡ 1 km × 1 km = 106 m2 square metre (SI unit) m2 ≡ 1 m × 1 m = 1 m2 square mile sq mi ≡ 1 mi × 1 mi = 2.589 988 110 336×106 m2 square yard sq yd ≡ 1 yd × 1 yd ≡ 0.836 127 36 m2 (International) 36 18 Volume Name of unit Symbol Definition Relation to SI units barrel (Imperial) bl (Imp) ≡ 36 gal (Imp) = 0.163 659 24 m3 barrel (petroleum) bl; bbl ≡ 42 gal (US) = 0.158 987 294 928 m3 barrel (U.S. fluid) fl bl (US) ≡ 31½ gal (US) = 0.119 240 471 196 m3 cubic foot cu ft ≡ 1 ft × 1 ft × 1 ft ≡ 0.028 316 846 592 m3 cubic inch cu in ≡ 1 in × 1 in × 1 in ≡ 16.387 064×10 6 m3 cubic metre (SI unit) m3 ≡ 1 m × 1 m × 1 m ≡ 1 m3 cubic mile cu mi ≡ 1 mi × 1 mi × 1 mi ≡ 4 168 181 825.440 579 584 m3 cubic yard cu yd ≡ 27 cu ft ≡ 0.764 554 857 984 m3 37 Volume Name of unit Symbol Definition Relation to SI units cup (metric) c ≡ 250.0×10 6 m3 = 250.0×10 6 m3 drop (metric) ≡ 1/20 mL = 50.0×10 9 m3 gallon (Imperial) gal (Imp) ≡ 4.546 09 L ≡ 4.546 09×10 3 m3 gallon (U.S.
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