21 thg 9, 2014

HỆ ĐƠN VỊ


Scien tists have adopted the metric system to simplify their calculations and promote communication across national boundaries. However, there have been two ideas as to which metric units should be preferred in science. Scientists working in laboratories, dealing with small quantities and distances, preferred to measure distance in centimeters and mass in grams. Scientists and engineers working in larger contexts preferred larger units: meters for distance and kilograms for mass. Everyone agreed that units of other quantities such as force, pressure, work, power, and so on should be related in a simple way to the basic units, but which basic units should be used?


The result was two clusterings of metric units in science and engineering. One cluster, based on the centimeter, the gram, and the second, is called the CGS system. The other, based on the meter, kilogram, and second, is called the MKS system.
When we say, for example, that the dyne is the CGS unit of force, this determines its definition: it is the force which accelerates a mass of one gram at the rate of one centimeter per second per second. The MKS unit of force, the newton, is the force which accelerates a mass of one kilogram at the rate of one meter per second per second. The ratio between a CGS unit and the corresponding MKS unit is usually a power of 10. A newton accelerates a mass 1000 times greater than a dyne does, and it does so at a rate 100 times greater, so there are 100 000 = 105 dynes in a newton.
The CGS system was introduced formally by the British Association for the Advancement of Science in 1874. It found almost immediate favor with working scientists, and it was the system most commonly used in scientific work for many years. Meanwhile, the further development of the metric system was based on meter and kilogram standards created and distributed in 1889 by the International Bureau of Weights and Measures (BIPM). During the 20th century, metric units based on the meter and kilogram--the MKS units--were used more and more in commercial transactions, engineering, and other practical areas. By 1950 there was some discomfort among users of metric units, because the need to translate between CGS and MKS units went against the metric ideal of a universal measuring system. In other words, a choice needed to be made.
In 1954, the Tenth General Conference on Weights and Measures (CGPM) adopted the meter, kilogram, second, ampere, degree Kelvin, and candela as the basic units for all international weights and measures, and in 1960 the Eleventh General Conference adopted the name International System of Units (SI) for this collection of units. (The "degree Kelvin" became the kelvin in 1967.) In effect, these decisions gave the central core of the MKS system preference over the CGS system. Although some of the CGS units remain in use for a variety of purposes, they are being replaced gradually by the SI units selected from the MKS system.
Following is a table of CGS units with their SI equivalents. Note that in some cases there is more than one name for the same unit. The CGS electromagnetic and electrostatic units are not included in this table, except for those which have special names.


CGS unit  measuringSI equivalent 
barye (ba)pressure0.1 pascal (Pa)
biot (Bi)electric current10 amperes (A)
calorie (cal)heat energy4.1868 joule (J)
darcypermeability0.98692 x 10-12 square meter (m2)
debye (D)electric dipole moment3.33564 x 10-30 coulomb meter (C·m)
dyne (dyn)force10-5 newton (N)
emumagnetic dipole moment0.001 ampere square meter (A·m2)
ergwork, energy10-7 joule (J)
franklin (Fr)electric charge3.3356 x 10-10 coulomb (C)
galileo (Gal)acceleration0.01 meter per second squared (m·s-2)
gauss (G)magnetic flux density10-4 tesla (T)
gilbert (Gi)magnetomotive force0.795 775 ampere-turns (A)
kayser (K)wave number100 per meter (m-1)
lambert (Lb)luminance3183.099 candelas per square meter (cd·m-2)
langleyheat transmission41.84 kilojoules per square meter (kJ·m-2)
line (li)magnetic flux10-8 weber (Wb)
maxwell (Mx)magnetic flux10-8 weber (Wb)
oersted (Oe)magnetic field strength
79.577 472 ampere-turns per meter (A·m-1)
phot (ph)illumination104 lux (lx)
poise (P)dynamic viscosity0.1 pascal second (Pa·s)
stilb (sb)luminance104 candelas per square meter (cd·m-2)
stokes (St)kinematic viscosity10-4 square meters per second (m2·s-1)
unit polemagnetic flux1.256 637 x 10-7 weber (Wb)

Nguồn: http://www.unc.edu/~rowlett/units/cgsmks.html

The seven SI base units

NameSymbolMeasureCurrent (2005) formal definition[1]Historical origin / justificationDimension
symbol
metremlength"The metre is the length of the path travelled by light in vacuum during a time interval of 1  299792458 of a second."
17th CGPM (1983, Resolution 1, CR, 97)
 10,000,000 of the distance from the Earth's equator to the North Pole measured on the circumference throughParis.L
kilogramkgmass"The kilogram is the unit of mass; it is equal to the mass of the international prototype of the kilogram."
3rd CGPM (1901, CR, 70)
The mass of one litre of water. A litre is one thousandth of a cubic metre.M
secondstime"The second is the duration of 9192631770 periods of the radiation corresponding to the transition between the two hyperfine levels of the ground state of the caesium 133 atom."
13th CGPM (1967/68, Resolution 1; CR, 103)
"This definition refers to a caesium atom at rest at a temperature of 0 K."
(Added by CIPM in 1997)
The day is divided in 24 hours, each hour divided in 60 minutes, each minute divided in 60 seconds.
A second is 1  (24 × 60 × 60) of the day
T
ampereAelectric current"The ampere is that constant current which, if maintained in two straight parallel conductors of infinite length, of negligible circular cross-section, and placed 1 metre apart in vacuum, would produce between these conductors a force equal to 2 × 10−7 newton per metre of length."
9th CGPM (1948)
The original "International Ampere" was defined electrochemically as the current required to deposit 1.118 milligrams of silver per second from a solution of silver nitrate. Compared to the SI ampere, the difference is 0.015%.I
kelvinKthermodynamic temperature"The kelvin, unit of thermodynamic temperature, is the fraction 1  273.16of the thermodynamic temperature of the triple point of water."
13th CGPM (1967/68, Resolution 4; CR, 104)
"This definition refers to water having the isotopic composition defined exactly by the following amount of substance ratios: 0.000 155 76 mole of 2H per mole of 1H, 0.000 379 9 mole of 17O per mole of 16O, and0.002 005 2 mole of 18O per mole of 16O."
(Added by CIPM in 2005)
The Celsius scale: the Kelvin scale uses the degree Celsius for its unit increment, but is a thermodynamic scale (0 K is absolute zero).Θ
molemolamount of substance"1. The mole is the amount of substance of a system which contains as many elementary entities as there are atoms in 0.012 kilogram of carbon 12; its symbol is 'mol.'
2. When the mole is used, the elementary entities must be specified and may be atoms, molecules, ions, electrons, other particles, or specified groups of such particles."
14th CGPM (1971, Resolution 3; CR, 78)
"In this definition, it is understood that unbound atoms of carbon 12, at rest and in their ground state, are referred to."
(Added by CIPM in 1980)
Atomic weight or molecular weight divided by the molar mass constant, 1 g/mol.N
candelacdluminous intensity"The candela is the luminous intensity, in a given direction, of a source that emits monochromatic radiation of frequency 540×1012 hertz and that has a radiant intensity in that direction of 1/683 watt per steradian."
16th CGPM (1979, Resolution 3; CR, 100)
The candlepower, which is based on the light emitted from a burning candle of standard properties.J
Nguồn: http://en.wikipedia.org/wiki/SI_base_unit

SI derived units

Other quantities, called derived quantities, are defined in terms of the seven base quantities via a system of quantity equations. The SI derived units for these derived quantities are obtained from these equations and the seven SI base units. Examples of such SI derived units are given in Table 2, where it should be noted that the symbol 1 for quantities of dimension 1 such as mass fraction is generally omitted.


Table 2.  Examples of SI derived units

SI derived unit
Derived quantityNameSymbol
areasquare meterm2
volumecubic meterm3
speed, velocitymeter per secondm/s
accelerationmeter per second squared  m/s2
wave numberreciprocal meterm-1
mass densitykilogram per cubic meterkg/m3
specific volumecubic meter per kilogramm3/kg
current densityampere per square meterA/m2
magnetic field strength  ampere per meterA/m
amount-of-substance concentrationmole per cubic metermol/m3
luminancecandela per square metercd/m2
mass fractionkilogram per kilogram, which may be represented by the number 1kg/kg = 1




For ease of understanding and convenience, 22 SI derived units have been given special names and symbols, as shown in Table 3.

Table 3.  SI derived units with special names and symbols

SI derived unit
Derived quantityNameSymbol  Expression 
in terms of 
other SI units
Expression
in terms of
SI base units
plane angleradian (a)rad  -m·m-1 = 1 (b)
solid anglesteradian (a)sr (c)  -m2·m-2 = 1 (b)
frequencyhertzHz  -s-1
forcenewtonN  -m·kg·s-2
pressure, stresspascalPaN/m2m-1·kg·s-2
energy, work, quantity of heat  jouleJN·mm2·kg·s-2
power, radiant fluxwattWJ/sm2·kg·s-3
electric charge, quantity of electricitycoulombC  -s·A
electric potential difference,
electromotive force
voltVW/Am2·kg·s-3·A-1
capacitancefaradFC/Vm-2·kg-1·s4·A2
electric resistanceohmOmegaV/Am2·kg·s-3·A-2
electric conductancesiemensSA/Vm-2·kg-1·s3·A2
magnetic fluxweberWbV·sm2·kg·s-2·A-1
magnetic flux densityteslaTWb/m2kg·s-2·A-1
inductancehenryHWb/Am2·kg·s-2·A-2
Celsius temperaturedegree Celsius°C  -K
luminous fluxlumenlmcd·sr (c)m2·m-2·cd = cd
illuminanceluxlxlm/m2m2·m-4·cd = m-2·cd
activity (of a radionuclide)becquerelBq  -s-1
absorbed dose, specific energy (imparted), kermagrayGyJ/kgm2·s-2
dose equivalent (d)sievertSvJ/kgm2·s-2
catalytic activitykatalkats-1·mol
(a) The radian and steradian may be used advantageously in expressions for derived units to distinguish between quantities of a different nature but of the same dimension; some examples are given in Table 4.
(b) In practice, the symbols rad and sr are used where appropriate, but the derived unit "1" is generally omitted.
(c) In photometry, the unit name steradian and the unit symbol sr are usually retained in expressions for derived units.
(d) Other quantities expressed in sieverts are ambient dose equivalent, directional dose equivalent, personal dose equivalent, and organ equivalent dose.

For a graphical illustration of how the 22 derived units with special names and symbols given in Table 3 are related to the seven SI base units, seerelationships among SI units.
    Note on degree Celsius. The derived unit in Table 3 with the special name degree Celsius and special symbol °C deserves comment. Because of the way temperature scales used to be defined, it remains common practice to express a thermodynamic temperature, symbol T, in terms of its difference from the reference temperature T= 273.15 K, the ice point. This temperature difference is called a Celsius temperature, symbol t, and is defined by the quantity equation
    tTT0.
    The unit of Celsius temperature is the degree Celsius, symbol °C. The numerical value of a Celsius temperature expressed in degrees Celsius is given by
    t/°C = T/K - 273.15.
    It follows from the definition of t that the degree Celsius is equal in magnitude to the kelvin, which in turn implies that the numerical value of a given temperature difference or temperature interval whose value is expressed in the unit degree Celsius (°C) is equal to the numerical value of the same difference or interval when its value is expressed in the unit kelvin (K). Thus, temperature differences or temperature intervals may be expressed in either the degree Celsius or the kelvin using the same numerical value. For example, the Celsius temperature difference Deltat and the thermodynamic temperature difference DeltaT between the melting point of gallium and the triple point of water may be written as Deltat = 29.7546 °C = DeltaT = 29.7546 K.
     
The special names and symbols of the 22 SI derived units with special names and symbols given in Table 3 may themselves be included in the names and symbols of other SI derived units, as shown in Table 4.

Table 4.  Examples of SI derived units whose names and symbols include SI derived units with special names and symbols
SI derived unit
Derived quantityNameSymbol
dynamic viscositypascal secondPa·s
moment of forcenewton meterN·m
surface tensionnewton per meterN/m
angular velocityradian per secondrad/s
angular accelerationradian per second squaredrad/s2
heat flux density, irradiancewatt per square meterW/m2
heat capacity, entropyjoule per kelvinJ/K
specific heat capacity, specific entropyjoule per kilogram kelvinJ/(kg·K)
specific energyjoule per kilogramJ/kg
thermal conductivitywatt per meter kelvinW/(m·K)
energy densityjoule per cubic meterJ/m3
electric field strengthvolt per meterV/m
electric charge densitycoulomb per cubic meterC/m3
electric flux densitycoulomb per square meterC/m2
permittivityfarad per meterF/m
permeabilityhenry per meterH/m
molar energyjoule per moleJ/mol
molar entropy, molar heat capacityjoule per mole kelvinJ/(mol·K)
exposure (x and gamma rays)coulomb per kilogramC/kg
absorbed dose rategray per secondGy/s
radiant intensitywatt per steradianW/sr
radiancewatt per square meter steradianW/(m2·sr)
catalytic (activity) concentrationkatal per cubic meterkat/m3
Nguôn: http://physics.nist.gov/cuu/Units/units.html

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