Kilogram

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

A kilogram is equivalent to 2.205 avoirdupois Avoirdupois pounds in the United States customary system that is still used in the United States, although usage is officially discouraged and the metric system is the preferred system of use.

Definition[]

The kilogram was originally defined as the mass of one litre of pure water at a temperature of 3.98 degrees Celsius and standard atmospheric pressure. This definition was hard to realize accurately, partially because the density of water depends ever-so-slightly on the pressure, and pressure units include mass as a factor, introducing a circular dependency in the definition of the kilogram.

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). For more details see history at [2]

The gram[]

The gram or gramme is the term to which SI prefixes are applied.

The gram was 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[]

The Avogadro [3] approach attempts to define the kilogram as a fixed number of silicon [4] atoms. As a practical realization, a sphere would be used and its size would be measured by interferometry [5].
The ion accumulation approach involves accumulation of gold atoms and measuring the electrical current required to neutralise them.

Fundamental-constant approaches[]

The kilogram is the base unit of mass, equal to 1 097 769 238 499 215 084 016 780 676 223 m_e electron mass units.

where m_e = 9.109382616 x10 -³¹Kg

The Watt balance [6] uses the current balance that was formerly used to define the ampere to relate the kilogram to a value for Planck's constant [7], based on the definitions of the volt and the ohm. Just as the meter was redefined to fix the speed of light to an exact value, this would have the effect of fixing Planck's constant to an exact value. A possible definition would be:

The kilogram is the mass of a body at rest whose equivalent energy corresponds to a frequency of exactly [(299792458)²/6626069311] × 10⁴³ Hz.

The levitated superconductor approach relates the kilogram to electrical quantities by levitating a superconducting body in a magnetic field generated by a superconducting coil, and measuring the electrical current required in the coil.
Since the values of the Josephson (CIPM (1988) Recommendation 1, PV 56; 19) and [[von Klitzing constant [8] (CIPM (1988), Recommendation 2, PV 56; 20) constants have been given conventional values, it is possible to combine these values (K_J ≡ 4.835 979×10¹⁴ Hz/V and R_K ≡ 2.581 280 7×10⁴ Ω) with the definition of the ampere to define the kilogram as follows:

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 6.241 509 629 152 65×10¹⁸ elementary charges per second.

Link with weight[]

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 980.665 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 gee, 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

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 (or tonne)	Mg	10⁻⁶	microgram	µg or (unofficial) mcg*
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

* Warning!: mcg is often used because the µ symbol may be unavailable; however, this is misleading and dangerous (if not wrong) because, in SI, mcg means millicentigram, not microgram.

External links[]

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