Kilogram
For other uses of 'kg' see kg (disambiguation) |
The U.S. National Prototype Kilogram, which currently serves as the nation's primary standard for measuring mass. It was assigned to the United States in 1889 and is periodically recertified and traceable to the primary international standard, "The Kilogram," held at the Bureau International des Poids et Mesures (BIPM) near Paris. The international prototype, made of platinum-iridium, is kept at the BIPM under conditions specified by the 1st CGPM in 1889. |
The
kilogram or
kilogramme, (symbol:
kg) is the
SI base unit of
mass. It is defined as being equal to the mass of the international prototype of the kilogram.
It is the only SI base unit that employs a prefix
[http://www.bipm.org/en/si/history-si/name_kg.html], and the only SI unit that is still defined in relation to an
artifact rather than to a fundamental physical property.
A kilogram is approximately equivalent to 2.205
avoirdupois pounds in the
Imperial system and the customary system of weights and measures used in the
United States.
The kilogram was
originally defined as the mass of one
litre of pure
water at
standard atmospheric pressure and at the
temperature at which water has its maximum density (3.98 degrees
Celsius). This definition was hard to realize accurately, partially because the density of water depends slightly on the pressure, and pressure units include mass as a factor, introducing a
circular dependency in the definition.
To avoid these problems, the kilogram was redefined as
precisely the mass of a particular
standard mass created to approximate the original definition. Since
1889, the
SI system defines the unit to be equal to the mass of the
international prototype of the kilogram, which is made from an
alloy of
platinum and
iridium of
39 mm height and diameter, and is kept at the
Bureau International des Poids et Mesures (International Bureau of Weights and Measures). Official copies of the prototype kilogram are made available as national prototypes, which are compared to the Paris prototype (
"Le Grand Kilo") roughly every
10 years. The international prototype kilogram was made in the
1880s.
By definition, the error in the repeatability of the current definition is exactly zero; however, in the usual sense of the word, it can be regarded as of the order of 2 micrograms. This is found by comparing the official standard with its official copies, which are made of roughly the same materials and kept under the same conditions. There is no reason to believe that the official standard is any more or less stable than its official copies, thus giving a way to estimate its stability. This procedure is performed roughly once every forty years.
The international prototype of the kilogram seems to have lost about 50 micrograms in the last 100 years, and the reason for the loss is still unknown (reported in
Der Spiegel, 2003 #26). The observed variation in the prototype has intensified the search for a new definition of the kilogram. It is accurate to state that any object in the universe (other than the reference metal in France) that had a mass of 1 kilogram 100 years ago, and has not changed since then, now has a mass of 1.000 000 050 kg. This perspective is counterintuitive and defeats the purpose of a standard unit of mass, since the standard should not change arbitrarily over time. The philosopher
Saul Kripke elaborated on the philosophical implications of this kind of problem, referring, however, to the then-current definition of the
metre in terms of an artifact, a choice which was later dropped.
The
gram or
gramme is the term to which
SI prefixes are applied.
The reason the base unit of mass has a prefix is historic. Originally, the decimal system of units was commissioned by Louis XVI and in the original plans, the kilogram was supposed to be called the grave. A gramme was simply an alternative name for a thousandth of a grave, and a tonne for 1000 graves. However, the metric system didn't come in effect until after the
French Revolution. At that time, the name "grave" had become politically incorrect, since it is an alternative word for the title "
count" (cognate with the British "markgrave" and the German "Graf"), and nobility titles were not considered compatible with the notion of
égalité.
The gram was also the base unit of the older
CGS system of measurement, a system which is no longer widely used.
There is an ongoing effort to introduce a new definition for the kilogram by way of fundamental or atomic constants. The proposals being worked on are:
Atom-counting approaches
* The
Avogadro approach attempts to define the kilogram as a fixed number of
silicon atoms. As a practical realization, a
sphere would be used and its size would be measured by
interferometry.
* The
ion accumulation approach involves accumulation of
gold atoms and measuring the electrical current required to neutralise them.
Fundamental-constant approaches
In a similar manner that the
metre was redefined to fix the
speed of light to an exact value of 299792458 m/s, there are proposals to redefine the kilogram in such a way to fix other
physical constants of nature to exact values.
*
Electron mass:
The kilogram is the base unit of mass, equal to 1 097 769 238 499 215 084 016 780 676 223
electron mass units.:This would have the effect of defining the electron mass to be
me = 9.1093826 kg. This is consistent with the current 2002
CODATA value for the electron mass which is 9.1093826 ± 0.0000016 kg.
*
Planck's constant: The
Watt balance uses the
current balance that was formerly used to define the
ampere to relate the kilogram to a value for Planck's constant, based on the definitions of the
volt and the
ohm. Using the Watt balance, a possible definition for the kilogram would be:
The kilogram is the mass of a body at rest whose equivalent energy corresponds to a frequency of exactly (299792458)
2/66260693 Hz.: This would have the effect of defining Planck's constant to be
h = 6.6260693
J s. This is consistent with the current 2002 CODATA value for Planck's constant which is 6.6260693 ± 0.0000011 J s.
*
Elementary charge:
The kilogram is the mass which would be accelerated at precisely 2 m/s
2 if subjected to the per metre force between two straight parallel conductors of infinite length, of negligible circular cross section, placed 1 metre apart in vacuum, through which flow a constant current of exactly 6 241 509 479 607 717 888
elementary charges per second. :This redefinition of the kilogram has the effect of fixing the
elementary charge to be
e = 1.60217653
C and would result in a functionally equivalent definition for the
coulomb as being the sum of exactly 6 241 509 479 607 717 888 elementary charges and the
ampere as being the electrical current of exactly 6 241 509 479 607 717 888 elementary charges per second. This is consistent the current 2002 CODATA value for the elementary charge which is 1.60217653 ± 0.00000014 C.
CIPM RECOMMENDATION 1 (CI-2005)
CIPM RECOMMENDATION 1 (CI-2005)
[http://www.bipm.fr/utils/common/pdf/CIPM2005.zip]:Preparative steps towards new definitions of the kilogram, the
ampere, the
kelvin and the
mole in terms of fundamental constants
The International Committee for Weights and Measures (CIPM),
*approve in principle the preparation of new definitions and mises en pratique of the kilogram, the ampere and the kelvin so that if the results of experimental measurements over the next few years are indeed acceptable, all having been agreed with the various Consultative Committees and other relevant bodies, the CIPM can prepare proposals to be put to Member States of the Metre Convention in time for possible adoption by the 24th
CGPM in 2011;
*give consideration to the possibility of redefining, at the same time, the mole in terms of a fixed value of the Avogadro constant;
*prepare a Draft Resolution that may be put to the 23rd
CGPM in 2007 to alert Member States to these activities;
When the weight of an object is given in kilograms, the property intended is almost always mass. Occasionally the gravitational force on an object is given in "kilograms", but the unit used is not a true kilogram: it is the deprecated kilogram-force (kgf), also known as the
kilopond (kp). An object of mass 1 kg at the surface of the
Earth will be subjected to a gravitational force of approximately 9.80665
newtons (the SI unit of force). Note that the factor of 980.765 cm/s² (as the CGPM defined it, when cgs systems were the primary systems used) is only an agreed-upon conventional value (3rd CGPM (1901), CR 70) whose purpose is to define grams force. The local gravitational acceleration
g varies with latitude and altitude and location on the Earth, so before this conventional value was agreed upon, the gram-force was only an ill-defined unit. (See also
g, a standard measure of gravitational acceleration.)
Examples
* Attogram: a research team at
Cornell University made a detector using
NEMS cantilevers with sub-attogram sensitivity.
*Yoctogram: can be used for masses of
nucleons,
atoms and
molecules. It is a little large for light particles, but yocto- is the last official prefix in the sequence.
**The coefficient is close to the reciprocal of
Avogadro's number: 1
unified atomic mass unit = 1.66054 yg
** Although the unified atomic mass unit is often convenient as a unit, one may sometimes want to use yoctograms to relate easily to other SI values.
**Mass of a free
electron: 0.00091 yg
**Mass of a free
proton : 1.6726 yg
**Mass of a free
neutron: 1.6749 yg
| Multiple | Name | Symbol | | Multiple | Name | Symbol | | 100 | gram | | | |
| 101 | decagram | 10"1 | decigram | dg |
| 102 | hectogram | 10"2 | centigram | cg |
| 103 | kilogram | 10"3 | milligram | mg |
| 106 | megagram | 10"6 | microgram | µg |
| 109 | gigagram | 10"9 | nanogram | ng |
| 1012 | teragram | 10"12 | picogram | pg |
| 1015 | petagram | 10"15 | femtogram | fg |
| 1018 | exagram | 10"18 | attogram | ag |
| 1021 | zettagram | 10"21 | zeptogram | zg |
| 1024 | yottagram | 10"24 | yoctogram | yg |
When the Greek small letter
mu ('µ') in the symbol of
microgram is technically unavailable it should be replaced by Latin small letter 'u', but other informal abbreviations like 'mcg' (confusingly also used to designate the obsolete term "millicentigram", equal to 10 µg) can also be encountered in practice. In the pharmaceutical industry, 'mcg' is used in the place of 'µg' to designate "microgram." The decagram is alternatively spelled 'dekagram'.
The megagram (1000kg) is also more commonly known as the
(metric) tonne (t), incorrectly spelled
ton (the UK ton is an obsolete measure of 2240lb, whereas the US ton is 2000lb). The unit tonne is accepted to be used with the SI and may take the same prefixes, see also
metre-tonne-second system of units.
*
Orders of magnitude (mass) for comparisons with other masses
*
Metric system*
SI*
National Physical Laboratory FAQ on kilogram definition, the need for a new definition, and some alternatives*
Conversion Calculator for Units of MASS (& Weight)*
More on the NIST Watt Balance*
Redefinition of the kilogram: a decision whose time has come*
More on the Avogadro project*
Conversion: Units of Weight*
International Bureau of Weights and Measures (BIPM)*
Attogram Detection*
World's most sensitive scales weigh a zeptogram, by New Scientist.com*
Scales tip with tiniest mass yet, by BBC News Onlinezh-yue:千克
