Kilogram

The kilogram or kilogramme, (symbol: kg) is the SI base unit of mass. A gram is defined as one thousandth of a kilogram. Conversion of units describes equivalent units of mass in other systems.

Multiples

SI prefixes are used to name multiples and subdivisions of the kilogram. The most commonly used ones are:

tonne 

1 000 kilograms (strictly speaking, this should be named megagram, but the name is less commonly used) (not to be confused with non-metric ton units)

gram 

1/1 000 kilogram

milligram 

1 thousandth of a gram = 1 millionth of a kilogram

microgram 

1 millionth of a gram = 1/10^-9 kilogram

Definition

The kilogram is the only one of the SI units which is still defined in relation to an artifact rather than to fundamental physical properties. It is also the only base unit that employs one of the prefixes.

The kilogram was originally defined as the mass of one litre of pure water at a temperature of 4 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 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 is considered to have a mass which is 50 micrograms larger than a kilogram. This perspective is counterintuitive and defeats the purpose of a standard unit of mass, since the standard should not change arbitrarily over time.

The gram

The gram or gramme, symbol g, is a unit of mass, and is defined in the SI system of units as one one-thousandth of a kilogram (i.e., 1 × 10⁻³ kg). One ounce avoirdupois is 28.34952 grams (see Conversion of units of mass).

Although the gram is not an SI base unit, it is a submultiple of the kilogram, which is a base unit. In SI, gram is also the root to which SI prefixes are applied. However, the gram is a base unit of the older cgs system of measurement, a system which is no longer widely used. The gram is an essential measurement unit in scientific endeavors worldwide.

A gram was originally defined as the weight of one cubic centimeter of water at its densest. This occurs at a temperature near four degrees Celsius. However, its definition was changed to the mass of a metal artifact in the eighteenth century.

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 approach attempts at defining the kilogram by a fixed count of silicon atoms. As a practical realization, a sphere will be used where the size is measured by interferometry.
• The ion accumulation approach involves accumulation of gold atoms and measuring the electrical current required to neutralise them.

Fundamental-constant approaches

• The Watt balance uses the current balance that formerly was 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.
• 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 (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.)

Orders of magnitude

• A yottagram (symbol: Yg) is 10²⁴ g
• A zettagram (symbol: Zg) is 10²¹ g. This is equal to one million trillion kilograms.
• An exagram (symbol: Eg) is equal to 10¹⁸ grams.
• A petagram (symbol: Pg) is 10¹⁵ g
• A teragram (symbol: Tg) is 10¹² g
• The gigagram, with symbol Gg, is equal to 1,000,000 kg, or 1,000 t. It rarely has any practical application.
• A centigram (symbol cg) is 1/100 of a gram.
• The milligram (symbol mg) is defined as 10⁻⁶ kg. It is used for stating the masses of small objects. A grain of sand might be close in mass to a milligram. Laboratory scientists frequently measure masses in milligrams. Substances found in small amounts, such as sodium in food, and doses of pharmaceuticals, such as aspirin, are generally measured in milligrams.
  • One milligram is the weight of 1 mm³ of water (a cube of size 1 mm × 1 mm × 1 mm).
  • See 1 E-6 kg for comparisons.
• The microgram (symbol µg, sometimes mcg) is defined as 1 µg = 10⁻⁹ kg. See 1 E-9 kg for comparisons.
• The nanogram (symbol ng) is defined as 1 × 10⁻¹² kilogram
• The picogram (symbol pg) defined as 1 × 10⁻¹⁵ kilogram
• The femtogram (symbol fg) defined as 1 × 10⁻¹⁸ kilogram
• An attogram (symbol ag) is 10⁻¹⁸ gram. In 2004, a research team at Cornell University made a detector using NEMS cantilevers with sub-attogram sensitivity.
• A zeptogram (symbol zg) is 10⁻²⁴ kilograms
• A yoctogram (symbol yg) equals 1 × 10⁻²⁴ grams. It 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 atomic mass unit = 1.660 54 yg
  • Although the amu is often convenient as a unit, one may sometimes want to use yoctograms to relate easily to other SI values.
  • Mass of an electron: 0.000 91 yg
  • Mass of a proton : 1.672 6 yg
  • Mass of a neutron: 1.674 9 yg

See also

• orders of magnitude (mass) for comparisons with other masses

External links

• 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
• More on the Avogadro project
• Conversion: Units of Weight
• Le Bureau International des Poids et Mesures
• Attogram Detection
• World's most sensitive scales weigh a zeptogram, by New Scientist.com
• Scales tip with tiniest mass yet, by BBC News Online

See also: Kilogram, 1880s, 1889, 1 E-2 m, 1 E-3 kg, 1 E-6 kg, 1 E-9 kg, 1 E3 kg, 1 E8 s, 2004