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Kilogram

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File:Kilogram.jpg
The U.S. National Prototype Kilogram, which currently serves as the primary standard for measuring mass in the U.S. 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 kilogram or kilogramme (symbol: kg) is the SI base unit of mass. It is defined as the mass of the international prototype kilogram. One kilogram is almost exactly the mass of one litre of water. When the context is clear, it is often referred to in short form as a kilo.

The kilogram is the only SI base unit that employs a prefix,[1] and the only SI unit that is still defined in relation to an artifact rather than to a fundamental physical property.

The pound, being defined as exactly 453.59237 grams, results in the kilogram being approximately equivalent to 2.205 avoirdupois pounds[2] in the Imperial system and the customary system of weights and measures used in the United States.

History

The kilogram was originally defined as one thousand times "the absolute weight of a volume of pure water equal to the cube of the hundredth part of a metre, and at the temperature of melting ice",[3] and later as the mass of one litre of pure water at standard atmospheric pressure and at the temperature at which water has its maximum density (277.13 K, 3.98 °C). [citation needed] 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.

International prototype

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 90% platinum and 10% iridium (by weight) and machined into a right-circular cylinder (height = diameter) of 39 mm. The international prototype is kept at the Bureau International des Poids et Mesures (International Bureau of Weights and Measures) in Sèvres on the outskirts of Paris. Official copies of the prototype kilogram are made available as national prototypes, which are compared to the Paris prototype ("Le Grand Kilo") roughly every 40 years. The international prototype is one of three cylinders made in 1879. In 1883, it was found to be indistinguishable from the mass of the kilogram standard at the time, and formally ratified as the kilogram by the 1st CGPM in 1889.[4]

By definition, the error in the repeatability of the current definition is exactly zero; however, any changes in the standard over time can be found by comparing the official standard to its official copies. Because the official copies and the official standard are made of roughly the same materials and kept under the same conditions, comparing the relative masses between standards over time estimates the stability of the standard. 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.[5] The observed variation in the prototype has intensified the search for a new definition of the kilogram.

The gram

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 of France 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, properly named milligrave, and a tonne was an alternative name for 1000 graves, properly named kilograve. 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 margrave 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.

Proposed future definitions

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

  • One Avogadro approach attempts to define the kilogram as a fixed number of silicon atoms of the same isotope. Silicon is the element of choice because the process of creating monocrystalline silicon is well-known. As a practical realization the monocrystaline rod would be cut and polished into a sphere, the weight of which would be measured using three different approaches in development by several different institutes. The sizes of the best spheres would be measured by interferometry. As the crystalline structure of the monocrystal is known, the number of atoms in this one kilogram could be estimated.[6]
  • 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 299,792,458 m/s, there are proposals to redefine the kilogram in such a way to fix other physical constants of nature to exact values.

  • 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 (2997924582/66260693)×1041 Hz.
This would have the effect of defining Planck's constant to be h = 6.6260693×10−34 J s. This is consistent with the current 2002 CODATA value for Planck's constant which is 6.6260693×10−34 ± 0.0000011×10−34 J s.
  • Avogadro constant: The kilogram is the mass of exactly (6.0221415×1023/0.012) unbound carbon-12 atoms at rest and in their ground state.
This would have the effect of defining Avogadro's number to be NA = 6.0221415×1023 elementary entities per mole and, consequently, a simpler and concise definition for the mole. This is consistent with the current 2002 CODATA value for the Avogadro constant which is 6.0221415×1023 ± 0.0000010×1023 mol-1.
  • 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 = 9.1093826×10−31 kg. This is consistent with the current 2002 CODATA value for the electron mass which is 9.1093826×10−31 ± 0.0000016×10−31 kg.
  • Elementary charge: The kilogram is the mass which would be accelerated at precisely 2×10−7 m/s2 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 = 1.60217653×10−19 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 1.60217653×10−19 ± 0.00000014×10−19 C.

CIPM RECOMMENDATION 1 (CI-2005)

CIPM RECOMMENDATION 1 (CI-2005):[7] 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 9.8 newtons (the SI unit of force). A value of 9.80665 m/s² (980.665 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.
  • Although the unified atomic mass unit (1 / Avogadro's number g ) is often convenient as a unit, one may sometimes want to use yoctograms to relate easily to other SI values:
    • Unified atomic mass unit = 1.6605 × 10−27 kg or 1.6605 yg
    • Mass of a free electron = 9.1094 × 10-31 kg or 0.0009 yg
    • Mass of a free proton = 1.6726 × 10−27 kg or 1.6726 yg
    • Mass of a free neutron = 1.6749 × 10−27 kg or 1.6749 yg

SI multiples

Multiple Name Symbol Multiple Name Symbol
100 gram g      
101 decagram dag 10–1 decigram dg
102 hectogram hg 10–2 centigram cg
103 kilogram kg 10–3 milligram mg
106 megagram Mg 10–6 microgram µg
109 gigagram Gg 10–9 nanogram ng
1012 teragram Tg 10–12 picogram pg
1015 petagram Pg 10–15 femtogram fg
1018 exagram Eg 10–18 attogram ag
1021 zettagram Zg 10–21 zeptogram zg
1024 yottagram Yg 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' [citation needed], 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 (1000 kg) is also more commonly known as the (metric) tonne (t), also spelled ton (the long ton is a measure of 2240 lb, whereas the short ton is 2000 lb). 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.

See also

References

  1. ^ http://www.bipm.org/en/si/history-si/name_kg.html
  2. ^ One pound avoirdupois is defined as precisely 0.453 592 37 kg. Thus, one kilogram is approximately equal to 2.204 622 6218 lbs.
  3. ^ http://smdsi.quartier-rural.org/histoire/18germ_3.htm
  4. ^ New Techniques in the Manufacture of Platinum-Iridium Mass Standards, T. J. Quinn, Platinum Metals Rev., 1986, 30, (2), Pg. 74 – 79
  5. ^ Reported in Der Spiegel, 2003 #26
  6. ^ Reuters (June 15, 2007). "Scientists grinding 'perfect' spheres". Cable News Network. Retrieved 2007-06-15. {{cite news}}: |last= has generic name (help); Cite has empty unknown parameter: |coauthors= (help)
  7. ^ http://www.bipm.fr/utils/common/pdf/CIPM2005.zip
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