decagram n : 10 grams [syn: dekagram, dkg, dag]

English

Alternative spellings

• (UK) decagramme

Etymology

Greek deka ten + -gram

Noun

1. A metric measurement that weighs 10 grams. Symbol: dag.
2. A ten pointed star.

Translations

The kilogram or kilogramme (symbol: kg) is the base unit of mass in the International System of Units (known also by its French-language initials “SI”). The kilogram is defined as being equal to the mass of the International Prototype Kilogram (IPK; known also by its French-language name Le Grand K), which is almost exactly equal to the mass of one liter of water. It is the only SI base unit with an SI prefix as part of its name. It is also the only SI unit that is still defined in relation to an artifact rather than to a fundamental physical property that can be reproduced in different laboratories. In everyday usage, the mass of an object in kilograms is often referred to as its weight, although strictly speaking the weight of an object is the gravitational force on it, measured in newtons (see also Kilogram-force). Similarly, the avoirdupois pound, used in both the Imperial system and U.S. customary units, is a unit of mass and its related unit of force is the pound-force. The avoirdupois pound is defined as exactly , making one kilogram approximately equal to 2.205 avoirdupois pounds.

Many units in the SI system are defined relative to the kilogram so its stability is important. After the International Prototype Kilogram had been found to vary in mass over time, the International Committee for Weights and Measures (known also by its French-language initials CIPM) recommended in 2005 that the kilogram be redefined in terms of fundamental constants of nature.

The nature of mass

The kilogram is a unit of mass, the measurement of which corresponds to the general, everyday notion of how “heavy” something is. However, mass is actually an inertial property; that is, the tendency of an object to remain at constant velocity unless acted upon by an outside force. An object with a mass of one kilogram will accelerate at one meter per second squared (about one-tenth the acceleration due to Earth’s gravity) when acted upon by a force of one newton (symbol: N).

While the weight of matter is entirely dependent upon the strength of local gravity, the mass of matter is constant (assuming it is not traveling at a relativistic speed with respect to an observer). Accordingly, for astronauts in microgravity, no effort is required to hold objects off the cabin floor; they are “weightless.” However, since objects in microgravity still retain their mass, an astronaut must exert ten times as much force to accelerate a 10-kilogram object at the same rate as a 1-kilogram object.

History

Early definitions

See also Grave (mass) for more on the history of the kilogram.

On 7 April 1795, the gram was decreed in France to be equal to “the absolute weight of a volume of water equal to the cube of the hundredth part of the meter, at the temperature of melting ice.” Since trade and commerce typically involve items significantly more massive than one gram, and since a mass standard made of water would be inconvenient and unstable, the regulation of commerce necessitated the manufacture of a practical realization of the water-based definition of mass. Accordingly, a provisional mass standard was made as a single-piece, metallic artifact one thousand times more massive than the gram—the kilogram.

At the same time, work was commissioned to precisely determine the mass of a cubic decimeter (one liter) of water. Although the decreed definition of the kilogram specified water at 0 °C—its highly stable temperature point—the scientists in 1799 chose to redefine the standard to water’s most stable density point: the temperature at which water reaches maximum density, which was measured at the time as 4 °C. They concluded that one cubic decimeter of water at its maximum density was equal to 99.92072% of the mass of the provisional kilogram made four years earlier. That same year, 1799, an all-platinum kilogram prototype was fabricated with the objective that it would equal, as close as was scientifically feasible for the day, the mass of a cubic decimeter of water at 4 °C. The prototype was presented to the Archives of the Republic in June and on 10 December 1799, the prototype was formally ratified as the Kilogramme des Archive (Kilogram of the Archives) and the kilogram was defined as being equal to its mass. This standard stood for the next ninety years.

International Prototype Kilogram

Since 1889, the SI system defines the magnitude of the kilogram to be equal to the mass of the International Prototype Kilogram, often referred to in the professional metrology world as the “IPK”. The IPK is made of an alloy of 90% platinum and 10% iridium (by weight) and is machined into a right-circular cylinder (height = diameter) of 39.17 mm to minimize its surface area. The addition of 10% iridium improved upon the all-platinum Kilogram of the Archives by greatly increasing hardness while still retaining platinum’s many virtues: extreme resistance to oxidation, extremely high density, satisfactory electrical and thermal conductivities, and low magnetic susceptibility. The IPK and its six sister copies are stored in an environmentally monitored safe in the lower vault located in the basement of the BIPM’s House of Breteuil in Sèvres on the outskirts of Paris (see Links to photographs, below for images). Three independently controlled keys are required to open the vault. Official copies of the IPK were made available to other nations to serve as their national standards. These are compared to the IPK roughly every 50 years.

The IPK is one of three cylinders made in 1879. In 1883, it was found to be indistinguishable from the mass of the Kilogram of the Archives made eighty-four years prior, and was formally ratified as the kilogram by the 1st CGPM in 1889. This small, 25 ppm difference, and the fact that the mass of the IPK was indistinguishable from the mass of the Kilogram of the Archives, speak volumes of the scientists’ skills over years ago when making their measurements of water’s properties and in manufacturing the Kilogram of the Archives.

Stability of the International Prototype Kilogram

The stability of the IPK is crucial because the kilogram underpins much of the SI system of measurement as it is currently defined and structured. For instance, the newton is defined as the force necessary to accelerate the kilogram by one meter per second squared. If the mass of the IPK were to change slightly, so too must the newton by a proportional degree. In turn, the pascal, the SI unit of pressure, is defined in terms of the newton. This chain of dependency follows to many other SI units of measure. For instance, the joule, the SI unit of energy, is defined as that expended when a force of one newton acts through one meter. Next to be affected is the SI unit of power, the watt, which is one joule per second. The ampere too is defined relative to the newton, and ultimately, the kilogram. With the magnitude of the primary units of electricity thus determined by the kilogram, so too follow many others; namely, the coulomb, volt, tesla, and weber. Even units used in the measure of light would be affected. The candela—following the change in the watt—would in turn affect the lumen and lux.

Because the magnitude of many of the units comprising the SI system of measurement is ultimately defined by the mass of a -year-old, golf ball-size piece of metal, the quality of the IPK must be diligently protected in order to preserve the integrity of the SI system. Yet, in spite of the best stewardship, the IPK has likely already lost  µg relative to the average mass of the worldwide ensemble of prototypes since the third periodic verification  years ago. Further, the world’s national metrology labs must wait for the fourth periodic verification to confirm whether the historical trends persisted.

Fortunately, definitions of the SI units are quite different from their practical realizations. For instance, the meter is defined as the distance light travels in a vacuum during a time interval of of a second. However, the meter’s practical realization typically takes the form of a helium-neon laser, and the meter’s length is delineated—not defined—as wavelengths of light from this laser. Now suppose that the official measurement of the second was found to have drifted by a few parts per billion (it is actually exquisitely stable). There would be no automatic effect on the meter because the second—and thus the meter’s length—is abstracted via the laser comprising the meter’s practical realization. Scientists performing meter calibrations would simply continue to measure out the same number of laser wavelengths until an agreement was reached to do otherwise. The same is true with regard to the real-world dependency on the kilogram: if the mass of the IPK was found to have changed slightly, there would be no automatic effect upon the other units of measure because their practical realizations provide an insulating layer of abstraction. Any discrepancy would eventually have to be reconciled though because the virtue of the SI system is its precise mathematical and logical harmony amongst its units. If the IPK’s value were definitively proven to have changed, one solution would be to simply redefine the kilogram as being equal to the mass of the IPK plus an offset value, similarly to what is currently done with its replicas; e.g., “the kilogram is equal to the mass of the IPK + 42 ppb.”

The long-term solution to this problem, however, is to liberate the SI system’s dependency on the IPK by developing a practical realization of the kilogram that can be reproduced in different laboratories by following a written specification. The units of measure in such a practical realization would have their magnitudes precisely defined and expressed in terms of fundamental physical constants. While major portions of the SI system would still be based on the kilogram, the kilogram would in turn be based on invariant, universal constants of nature. While this is a worthwhile objective and much work towards that end is ongoing, no alternative has achieved the uncertainty of a couple parts in 108 (~20 µg) required to improve upon the IPK. However, as of April 2007, the NIST’s implementation of the watt balance was approaching this goal, with a demonstrated uncertainty of 36 µg. See Watt balance, below.

Proposed future definitions

In the following section, wherever numeric equalities are shown in ‘concise form’—such as —the two digits between the parentheses denotes the uncertainty at 1σ standard deviation (68% confidence level) in the two least significant digits of the significand.

The kilogram is the only SI unit that is still defined in relation to an artifact. Note that the meter was also once defined as an artifact (a single platinum-iridium bar with two marks on it). However, it was eventually redefined in terms of invariant, fundamental constants of nature that are delineated via practical realizations (apparatus) that can be reproduced in different laboratories by following a written specification. Today, physicists are investigating various approaches to do the same with the kilogram. Some of the approaches are fundamentally very different from each other. Some are based on equipment and procedures that enable the reproducible production of new, kilogram-mass prototypes on demand (albeit with extraordinary effort) using measurement techniques and material properties that are ultimately based on, or traceable to, fundamental constants. Others are devices that measure either the acceleration or weight of hand-tuned, kilogram test masses and which express their magnitudes in electrical terms via special components that permit traceability to fundamental constants. Measuring the weight of test masses requires the precise measurement of the strength of gravity in laboratories. All approaches would precisely fix one or more constants of nature at a defined value. These different approaches are as follows:

Atom-counting approaches

Carbon-12

Though not offering a practical realization, this definition would precisely define the magnitude of the kilogram in terms of a certain number of carbon-12 atoms. Carbon-12 is an isotope of carbon. The mole is currently defined as “the quantity of entities (elementary particles like atoms or molecules) equal to the number of atoms in 12 grams of carbon-12.” Thus, the current definition of the mole requires that (83⅓) moles of 12C has a mass of precisely one kilogram. The number of atoms in a mole, a quantity known as the Avogadro constant, is an experimentally determined value that is currently measured as being atoms (2006 CODATA value). This new definition of the kilogram proposes to fix the Avogadro constant at precisely and the kilogram would be defined as “the mass equal to that of 83⅓ ·  atoms of 12C.”

Currently, the uncertainty in the Avogadro constant is determined by the uncertainty in the measured mass of 12C atoms (a relative standard uncertainty of 50 parts per billion at this time). By fixing the Avogadro constant, the practical effect of this proposal would be that the precise magnitude of the kilogram would be subject to future refinement as improved measurements of the mass of 12C atoms become available; electronic realizations of the kilogram would be recalibrated as required. In an electronic definition of the kilogram, 83⅓ moles of 12C would—by definition—continue to have a mass of precisely one kilogram and the Avogadro constant would continue to have uncertainty in its precise value.

A variation on a 12C-based definition proposes to define the Avogadro constant as being precisely 84,446,8863 (≈) atoms. An imaginary realization of a 12-gram mass prototype would be a cube of 12C atoms measuring precisely 84,446,886 atoms across on a side. With this proposal, the kilogram would be defined as “the mass equal to 84,446,8863 × 83⅓ atoms of 12C.” The value 84,446,886 was chosen because it has a special property; its cube (the proposed new value for the Avogadro constant) is evenly divisible by twelve. Thus with this definition of the kilogram, there would be an integer number of atoms in one gram of 12C: 50,184,508,190,229,061,679,538 atoms.

Avogadro project

This approach would define the kilogram as “the mass which would be accelerated at precisely when subjected to the per-meter force between two straight parallel conductors of infinite length, of negligible circular cross section, placed 1 meter apart in vacuum, through which flow a constant current of (6,241,509,647,120,417,390) elementary charges per second”.

Effectively, this would define the kilogram as a derivative of the ampere, rather than present relationship, which defines the ampere as a derivative of the kilogram. This redefinition of the kilogram would result from fixing the elementary charge (e) to be precisely coulomb (from the current 2006 CODATA value of ), which effectively defines the coulomb as being the sum of 6,241,509,647,120,417,390 elementary charges. It would necessarily follow that the ampere then becomes an electrical current of this same quantity of elementary charges per second.

The virtue of a practical realization based upon this definition is that unlike the watt balance and other scale-based methods, all of which require the careful characterization of gravity in the laboratory, this method delineates the magnitude of the kilogram directly in the very terms that define the nature of mass: acceleration due to an applied force. Unfortunately, it is extremely difficult to develop a practical realization based upon accelerating masses. Experiments over a period of years in Japan with a superconducting, 30-gram mass supported by diamagnetic levitation never achieved an uncertainty better than ten parts per million. Magnetic hysteresis was one of the limiting issues. Other groups are continuing this line of research using different techniques to levitate the mass.

SI multiples

Because SI prefixes may not be concatenated (serially linked) within the name or symbol for a unit of measure, SI prefixes are used with the gram, not the kilogram, which already has a prefix as part of its name. For instance, one-millionth of a kilogram is 1 mg (one milligram), not 1 µkg (one microkilogram).

• When the Greek lowercase “µ” (mu) in the symbol of microgram is typographically unavailable, it is occasionally—although not properly—replaced by Latin lowercase “u”.
• The microgram is often abbreviated “mcg”, particularly in pharmaceutical and nutritional supplement labeling, to avoid confusion since the “µ” prefix is not well recognized outside of technical disciplines. Note however, that the abbreviation “mcg”, is also the symbol for an obsolete CGS unit of measure known as the “millicentigram”, which is equal to 10 µg.
• The unit name “megagram” is rarely used, and even then, typically only in technical fields in contexts where especially rigorous consistency with the units of measure is desired. For most purposes, the unit “tonne” is instead used. The tonne and its symbol, t, were adopted by the CIPM in 1879. It is a non-SI unit accepted by the BIPM for use with the SI. In English speaking countries it is usually called “metric ton”. Note also that the unit name “megatonne” or “megaton” (Mt) is often used in general-interest literature on greenhouse gas emissions whereas the equivalent value in scientific papers on the subject is often the “teragram” (Tg).

Glossary

• Abstracted: Isolated and its effect changed in form, often simplified or made more accessible in the process.
• Artifact: A human-made object used as a comparative standard in the measurement of a physical quantity.
• Check standard:

1. A standard body’s backup replica of the International Prototype Kilogram (IPK).
2. A secondary kilogram mass standard used as a stand-in for the primary standard during routine calibrations.

• Definition: A formal, specific, and exact specification.
• Delineation: The physical means used to mark a boundary or express the magnitude of an entity.
• Disseminate: To widely distribute the magnitude of a unit of measure, typically via replicas and transfer standards.
• IPK: Abbreviation of “International Prototype Kilogram” (CG image), the artifact which has a mass defined as precisely one kilogram.
• Magnitude: The extent or numeric value of a property
• National prototype: A replica of the IPK possessed by a nation.
• Practical realization: An artifact or readily reproducible apparatus to conveniently delineate the magnitude of a unit of measure.
• Primary national standard:

1. A replica of the IPK possessed by a nation
2. The least used replica of the IPK when a nation possesses more than one.

• Prototype:

1. A human-made object that serves as the defining comparative standard in the measurement of a physical quantity.
2. A human-made object that serves as the comparative standard in the measurement of a physical quantity.
3. The IPK and any of its replicas

• Replica: An official copy of the IPK.
• Sister copy: One of six official copies of the IPK that are stored in the same safe as the IPK and are used as check standards by the BIPM.
• Transfer standard: An artifact or apparatus that reproduces the magnitude of a unit of measure in a different, usually more practical, form.

See also

• Inertia
• International System of Units (SI)
• International Bureau of Weights and Measures (BIPM)
• International Committee for Weights and Measures (CIPM)
• General Conference on Weights and Measures (CGPM)
• Gram
• Grave (orig. name of the kilogram, history of)
• Gravimetry
• Kilogram-force
• Metric system
• Mass
• Mass versus weight
• National Institute of Standards and Technology (NIST)
• Newton
• SI base units
• Standard gravity
• Tonne (metric ton)
• Watt balance
• Weight

Notes

External links

• National Institute of Standards and Technology (NIST): NIST Improves Accuracy of ‘Watt Balance’ Method for Defining the Kilogram
• The U.K.’s National Physical Laboratory (NPL): An overview of the problems with an artifact-based kilogram
• NPL: Avogadro Project
• NPL: NPL watt balance
• Metrology in France: Watt balance
• Australian National Measurement Institute: Redefining the kilogram through the Avogadro constant
• International Bureau of Weights and Measures (BIPM): Home page
• NZZ Folio: What a kilogram really weighs
• NPL: What are the differences between mass, weight, force and load?
• BBC: Getting the measure of a kilogram