Kilogram

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Kilogram
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“Kg” redirects here. For other uses, see Kg (disambiguation).

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 Kilogram. 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. The mass of the kilogram is almost exactly equal to that of one liter of water.

The avoirdupois pound, the unit of mass in both the Imperial system and U.S. customary units, is defined as exactly 0.453 592 37 kg, which is to say, one kilogram is approximately equal to 2.205 avoirdupois pounds.

While the weight of objects are often given in kilograms, the kilogram is, in the strict scientific sense, a unit of mass. The equivalent unit of weight is the kilogram-force, which is a deprecated unit. Similarly, ever since the 1893 redefinition of the pound in terms of the kilogram, the pound too is a measure of mass and its related unit of weight is the pound-force.
Shown above is a computer-generated image of the International Prototype Kilogram (“IPK”). The IPK is the kilogram. It sits next to an inch-based ruler for scale. The IPK is made of a platinum-iridium alloy and is stored in a vault at the BIPM in Sèvres, France. To view a photograph of the actual IPK, click this link to an NIST Web page.
Shown above is a computer-generated image of the International Prototype Kilogram (“IPK”). The IPK is the kilogram. It sits next to an inch-based ruler for scale. The IPK is made of a platinum-iridium alloy and is stored in a vault at the BIPM in Sèvres, France. To view a photograph of the actual IPK, click this link to an NIST Web page.
Contents
[hide]

* 1 The nature of mass
* 2 SI multiples
* 3 History
o 3.1 Early definitions
o 3.2 International Prototype Kilogram
o 3.3 The gram
* 4 Stability of the International Prototype Kilogram
* 5 Proposed future definitions
o 5.1 Atom-counting approaches
o 5.2 Fundamental-constant approaches
o 5.3 CIPM Recommendation 1 (CI-2005)
* 6 Mass vs. weight
o 6.1 The distinction between the two
o 6.2 The unit of weight: kilogram-force
o 6.3 Converting mass to force
o 6.4 Buoyancy and “conventional mass”
o 6.5 Types of scales and what they measure
* 7 See also
* 8 References
* 9 External links

[edit] The nature of mass

The kilogram is a unit of mass, which corresponds to the intuitive idea of “how much matter there is in an object.” Mass is 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/second² (about one-tenth the acceleration of Earth’s gravity) when acted upon (pushed by) a force of one newton (symbol: N).

While the weight of matter is entirely dependent upon the strength of gravity, the mass of matter is constant (assuming it is not traveling at a relativistic velocity with respect to an observer). Accordingly, astronauts in microgravity exert no effort to lift loose objects inside their spacecraft since those objects are hovering. However, since objects in microgravity still retain their mass, a 100-kilogram object accelerates at only one-hundredth the rate of a 1-kilogram object when an astronaut pushes on them with equal force.

[edit] SI multiples

Because multiple SI prefixes may not be used, SI prefixes are used with the gram, not the kilogram.[1] For instance, one-millionth of a kilogram is 1 mg (one milligram), not 1 µkg (one microkilogram). The most common prefixed forms of gram are shown in bold text in the table below.[2]
Submultiples Multiples
Factor Name Symbol Factor Name Symbol
100 gram g
10−1 decigram dg 101 decagram dag
10−2 centigram cg 102 hectogram hg
10−3 milligram mg 103 kilogram kg
10−6 microgram µg 106 megagram Mg
10−9 nanogram ng 109 gigagram Gg
10−12 picogram pg 1012 teragram Tg
10−15 femtogram fg 1015 petagram Pg
10−18 attogram ag 1018 exagram Eg
10−21 zeptogram zg 1021 zettagram Zg
10−24 yoctogram yg 1024 yottagram Yg

When the Greek lowercase ‘µ’ (mu) in the symbol of microgram is typographically unavailable, it is occasionally replaced by Latin lowercase ‘u’. Other informal abbreviations like ‘mcg’ (confusingly also used to designate the obsolete term “millicentigram,” which is equal to 10 µg) may also be encountered, particularly in pharmaceutical labeling.

[edit] History

[edit] Early definitions

On 7 April 1795, the gram was decreed in France to be equal to “the absolute weight of a volume of pure water equal to a cube of one hundredth of a meter, and to the temperature of the melting ice.”[3] The regulation of trade and commerce required a practical reference standard in addition to the definition based on fundamental physical properties. Accordingly, a provisional kilogram standard was made as single-piece, metallic reference standard one thousand times more massive than the gram.

In addition to this provisional kilogram standard, work was commissioned to determine precisely how massive a cubic decimeter (now defined as one liter) of water is. Although the decreed definition of the kilogram specified water at 0 °C — a highly stable temperature point — the scientists chose to redefine the standard and perform their measurements at the most stable density point: the temperature at which water reaches maximum density, which was measured at the time as 4 °C.[4] 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 earlier that year.[5] Four years later in 1799, an all-platinum standard, the “Kilogramme des Archives,” was fabricated with the objective that it would equal, as close as was scientifically feasible for the day, to the mass of cubic decimeter of water at 4 °C. The kilogram was defined to be equal to the mass of the Kilogramme des Archives and this standard stood for the next ninety years.

[edit] 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 comprises 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.[6] The IPK and some of its official copies are stored in an environmentally-monitored vault in the basement of the BIPM’s House of Breteuil in Sèvres on the outskirts of Paris. 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 40 years.

The IPK is one of three cylinders made in 1879. In 1883, it was found to be indistinguishable from the mass of the Kilogramme des Archives made eight-four years prior, and formally ratified as the kilogram by the 1st CGPM in 1889.[6] Modern measurements of the density of purified water that has a carefully controlled isotopic composition (known as Vienna Standard Mean Ocean Water) show that a cubic decimeter (one liter) of water at its point of maximum density, 3.984 °C, has a mass that is 25.05 parts per million less than the kilogram.[7] Given this small, 25 ppm difference, and the fact that the mass of the IPK was indistinguishable from the mass of the Kilogramme des Archives, speaks volumes of the scientists’ skills in 1795–1799 when making their measurements of water’s properties and in manufacturing the Kilogramme des Archives.

[edit] 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.

[edit] Stability of the International Prototype Kilogram

By definition, the error in the measured value of the IPK’s mass is exactly zero; the IPK is the kilogram. However, any changes in the IPK’s mass over time can be detected by comparing its mass to that of its official copies stored throughout the world, a process called “periodic verification.” For instance, the U.S. owns three kilogram replicas, two of which, K4 and K20, are from the original batch of 40 replicas of the IPK delivered in 1884. The K4 replica was designated as the primary national standard of mass for the U.S. Because the official copies are made of precisely the same alloy as the IPK and are stored under similar conditions, periodic verifications using a large number of replicas—especially, the national primary standards, which are rarely used—can convincingly demonstrate the stability of the IPK. The last set of verifications reveals that the IPK lost between about 30 and 50 micrograms over the last 100 years. The precise reason for the loss is unknown but is believed to involve surface effects and differences in the techniques used to clean them—a process that includes steam cleaning and lightly rubbing with chemical-soaked chamois. The IPK’s mass change prompted research into improved methods to obtain a smooth surface finish on newly manufactured replicas and has intensified the search for a new definition of the kilogram.[8]

[edit] Proposed future definitions

In the following section, wherever numeric equalities are shown in concise form — such as 1.854 87(14) × 1043 — the two digits between the parentheses denotes the uncertainty (the standard deviation at 68.27% confidence level) in the two least significant digits of the mantissa.

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:

[edit] 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 ultra-pure monocrystalline silicon is well-known (because of its use in the semiconductor industry). 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.[9]
* The ion accumulation approach involves accumulation of gold atoms and measuring the electrical current required to neutralise them.

[edit] 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 (299,792,458²/66,260,693) × 1041 Hz.

This would have the effect of defining Planck's constant to be h = 6.626 0693 × 10–34 J s (from the 2002 CODATA value for Planck's constant of 6.626 0693(11) × 10–34 J•s).

* Avogadro constant: The kilogram is the mass of exactly (6.022 1415 × 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 = 6.022 1415 × 1023 elementary entities per mole and, consequently, a simpler and concise definition for the mole (from the 2002 CODATA value for the Avogadro constant of 6.022 1415(10) × 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 = 9.109 3826 × 10–31 kg (from the 2002 CODATA value for the electron mass of 9.109 3826(16) × 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-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 1.602 176 487 × 10–19 coulomb (from the current 2006 CODATA value of 1.602 176 487(40) × 10–19), 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 careful characterization of the gravity at any given laboratory, this definition specifies the kilogram in terms of true acceleration of a mass.

[edit] CIPM Recommendation 1 (CI-2005)

CIPM Recommendation 1 (CI-2005):[10] 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 practical realizations 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;

[edit] Mass vs. weight

[edit] The distinction between the two

As previously stated, the kilogram is a unit of mass, which is an inertial property. Inertia is the property one senses when they rest a bowling ball on a level, smooth surface and forcefully push on it horizontally to accelerate it. Unless relativistic effects apply, mass is an unchanging, universal property of matter that is unaffected by gravity. Weight on the other hand, is a property of matter that is entirely dependent upon the strength of gravity. For instance, an astronaut’s weight on the Moon is one-sixth of that on the Earth whereas his mass has changed little during the trip.

In scientific and engineering contexts, the terms “mass” and “weight” are rigidly defined as separate measures in order to enforce clarity and precision. In everyday use, given that all masses on Earth have weight,[11] “weight” often serves to describe both properties, its meaning being dependent upon context. For example, the “net weight” of retail products in the U.S., which may be given in both pounds and kilograms, refers to mass. Conversely, the “load index” rating on automobile tires (see Tire code), which specifies the maximum structural load for a tire in kilograms, actually refers to weight; that is, the force due to gravity.

[edit] The unit of weight: kilogram-force

When an object's gravitational force—weight— is expressed in kilograms, the unit of measure is not a true kilogram; it is the deprecated kilogram-force (kgf or kg-f), also known as the kilopond (kp), which is a non-SI unit of force that serves very practically as a unit of weight. All objects on Earth are subject to a gravitational acceleration of approximately 9.8 m/s². The CGPM (also known as the “General Conference on Weights and Measures”) fixed the value of standard gravity at precisely 9.80665 m/s² so that disciplines such as metrology would have a standard value for converting units of defined mass into defined forces and pressures. In fact, the kilogram-force is defined as precisely 9.80665 newtons. As a practical matter, gravitational acceleration (symbol: g) varies with latitude and elevation; these variations are typically a few tenths of a percent.

Since masses are rarely measured to an uncertainty of better than one percent, it is technically just as valid to state that a one-kilogram object on Earth has a weight of one kilogram-force as it is to state that it has a mass of one kilogram. Accordingly, it may correctly be assumed that when someone speaks or writes of a “weight” in kilograms, they are referring to the gravitational load of the kilogram and the proper “kilogram-force” is implied.

[edit] Converting mass to force

Unlike laypeople, professionals in virtually all SI-unit-using engineering and scientific disciplines involving accelerations and kinetic energies rigorously maintain the distinctions between mass, force, and weight, as well as their respective units of measure. Engineers in disciplines involving weight loading, such as structural engineering, first convert loads due to objects like concrete and automobiles—which are always tallied in kilograms—to newtons before continuing with their calculations. Primarily, this is because material properties like elastic modulus are quite properly measured and published in terms of newtons and pascals (which is a unit of pressure derived from the newton). Kilograms are converted to newtons by multiplying by 9.8, 9.81, or 9.80665. Note that the highest-precision figure would likely result in false precision if the final product was expressed to six significant digits since loads in kilograms are rarely known with such accuracy and local gravity is rarely identical to standard gravity.

[edit] Buoyancy and “conventional mass”

The masses of objects are relatively invariant whereas their weights vary slightly with changes in barometric pressure, such as with changes in weather and altitude. This is because objects have volume and therefore have a buoyant effect in air. Buoyancy—a force that counters gravity’s—reduces the weight of all objects. Further, objects with precisely the same mass but with different densities displace different volumes and therefore have different buoyancies and weights. Normally, the effect of air buoyancy is too small to be of any consequence in normal day-to-day activities.[12] In metrology however, where mass standards are calibrated with extreme accuracy, buoyancy is a significant effect so air density is precisely accounted for during calibration.

Given the extremely high cost of platinum-iridium mass standards, high-quality “working” standards are made of special stainless steel alloys, which occupy greater volume than those made of platinum-iridium. For convenience, a standard value of buoyancy relative to stainless steel was developed for metrology work and this results in term called “conventional mass.”[13] Conventional mass is defined as follows: “For a mass at 20 °C, ‘conventional mass’ is the mass of a reference standard of density 8000 kg/m³ which it balances in air with a density of 1.2 kg/m³.” The effect is a small one, 150 ppm for stainless steel mass standards, but the appropriate corrections are made during the calibration of all precision mass standards so they have the true mass indicated on them. In routine laboratory use however, the reading on a precision scale when a stainless steel standard is placed upon it is actually its conventional mass; that is, its true mass minus buoyancy. Also, any object compared to a stainless steel mass standard has its conventional mass measured; that is, its true mass minus some degree of buoyancy.

The effect of buoyancy invalidates the standard answer to the childhood riddle of “Which weights more, a ton of lead or a ton of aluminum?” The correct answer is “Lead weighs more, by 327 grams-force.”[14]

[edit] Types of scales and what they measure

It’s notable at a purely technical level, that whenever someone stands on a balance-beam scale at a doctor’s office, they are really and truly having their mass measured. Excluding buoyancy, which affects all types of scales in fluids, balance-beam scales compare the mass on the platform with those of the sliding counterweights on the beams; gravity serves only as the force-generating mechanism that allows the needle to diverge from the “balanced” (null) point. On scales such as these, gravity can vary in strength without affecting the reading. Conversely, whenever someone steps onto a spring-based or digital load cell-based scale, they are technically having their weight measured notwithstanding that the displayed units of measure are in kilograms. On force-measuring instruments such as these, variations in gravity will affect the reading.

[edit] See also

* Orders of magnitude (mass) for comparisons with other masses
* Metric system
* SI

[edit] References

1. ^ NIST: SI prefixes (link to Web site).
2. ^ Criteria: A total of ≥250,000 Google hits on both the U.S. spelling (-gram) and the U.K./International spelling (-gramme).
3. ^ Decree relating to the weights and measurements
4. ^ Citation: L'Histoire Du Mètre, La Détermination De L'Unité De Poids, link to Web site here.
5. ^ Citation: History of the kilogram
6. ^ a b New Techniques in the Manufacture of Platinum-Iridium Mass Standards, T. J. Quinn, Platinum Metals Rev., 1986, 30, (2), Pg. 74 – 79
7. ^ Water Structure and Science, Water Properties, Density maximum (and molar volume) at temperature of maximum density, a (by London South Bank University). Link to Web site.
8. ^ Citations: Recalibration of the U.S. National Prototype Kilogram, R. S. Davis, Journal of Research of the National Bureau of Standards, 90, No. 4, July–August 1985 (5.5 MB PDF here); and Frequently asked questions - mass and density by National Physical Laboratory — the U.K.’s national measurement laboratory; and The Kilogram and Measurements of Mass and Force, Z. J. Jabbour et al., J. Res. Natl. Inst. Stand. Technol. 106, 2001, 25–46 (3.5 MB PDF, here)
9. ^ Reuters. "Scientists grinding 'perfect' spheres", Cable News Network, June 15, 2007. Retrieved on 2007-06-15.
10. ^ Proceedings of the 94th meeting (October 2005) of the International Committee for Weights and Measures, (1.1 MB zip file, here)
11. ^ On Earth, masses with densities less than that of air float and have negative weight; that is, they are buoyant. Such masses have weight in a vacuum.
12. ^ For instance, buoyancy’s diminishing effect upon one’s body weight (a relatively low-density object) is 1/860th that of gravity. Variations in barometric pressure rarely affect one’s weight more than ±1 part in 30,000. Assumptions: An air density of 1160 g/m³, an average density of a human body (with collapsed lungs) equal to that of water, and variations in barometric pressure rarely exceeding ±22 torr. Assumptions primary variables: An altitude of 194 meters above mean sea level (the worldwide median altitude of human habitation), an indoor temperature of 23 °C, a dewpoint of 9 °C, and 760 mm–Hg sea level–corrected barometric pressure.
13. ^ International Recommendation OIML R33. See International Organization of Legal Metrology Web site.
14. ^ Assuming standard gravity and an air density of 1160 g/m³.

[edit] External links

* National Physical Laboratory FAQ on kilogram definition, the need for a new definition, and some alternatives
* More on the NIST Watt Balance
* Redefinition of the kilogram: a decision whose time has come
* More on the Avogadro project
* 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 Online
* Robert Matthews: What a kilogram really weighs. Article about the current problem of defining the kilogram.

Retrieved from "http://en.wikipedia.org/wiki/Kilogram"

Categories: SI base units | Units of mass
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