The kilogram or kilogramme (symbol: kg) is the base unit of mass in the International System of Units (SI). Until 20 May 2019, it remains defined by a platinum alloy cylinder, the International Prototype Kilogram (informally Le Grand K or IPK), manufactured in 1889, and carefully stored in Saint-Cloud, a suburb of Paris. After 20 May, it will be defined in terms of fundamental physical constants.
The kilogram was originally defined as the mass of a litre (cubic decimetre) of water. That was an inconvenient quantity to precisely replicate, so in 1799 a platinum artefact was fashioned to define the kilogram. That artefact, and the later IPK, have been the standard of the unit of mass for the metric system ever since.
In spite of best efforts to maintain it, the IPK has diverged from its replicas by approximately 50 micrograms since their manufacture late in the 19th century. This led to efforts to develop measurement technology precise enough to allow replacing the kilogram artifact with a definition based directly on physical phenomena, which is now scheduled to take place in 2019.
The new definition is based on invariant constants of nature, in particular the Planck constant, which will change to being defined rather than measured, thereby fixing the value of the kilogram in terms of the second and the metre, and eliminating the need for the IPK. The new definition was approved by the General Conference on Weights and Measures (CGPM) on 16 November 2018. The Planck constant relates a light particle's energy, and hence mass, to its frequency. The new definition only became possible when instruments were devised to measure the Planck constant with sufficient accuracy based on the IPK definition of the kilogram.
|Unit system||SI base unit|
|1 kg in ...||... is equal to ...|
|Avoirdupois||≈ 2.205 pounds[Note 1]|
|British Gravitational||≈ 0.0685 slugs|
The gram, 1/1000 of a kilogram, was provisionally defined in 1795 as the mass of one cubic centimetre of water at the melting point of ice. The final kilogram, manufactured as a prototype in 1799 and from which the International Prototype Kilogram (IPK) was derived in 1875, had a mass equal to the mass of 1 dm3 of water under atmospheric pressure and at the temperature of its maximum density, which is approximately 4 °C.
The kilogram is the only named SI unit with an SI prefix (kilo) as part of its name. Until the 2019 redefinition of SI base units, it was also the last SI unit that was still directly defined by an artefact rather than a fundamental physical property that could be independently reproduced in different laboratories. Three other base units (cd, A, mol) and 17 derived units (N, Pa, J, W, C, V, F, Ω, S, Wb, T, H, kat, Gy, Sv, lm, lx) in the SI system are defined in relation to the kilogram, and thus its stability is important. The definitions of only eight other named SI units do not depend on the kilogram: those of temperature (K, °C), time and frequency (s, Hz, Bq), length (m), and angle (rad, sr).
The IPK is rarely used or handled. Copies of the IPK kept by national metrology laboratories around the world were compared with the IPK in 1889, 1948, and 1989 to provide traceability of measurements of mass anywhere in the world back to the IPK.
The International Prototype Kilogram was commissioned by the General Conference on Weights and Measures (CGPM) under the authority of the Metre Convention (1875), and in the custody of the International Bureau of Weights and Measures (BIPM) who hold it on behalf of the CGPM. After the International Prototype Kilogram had been found to vary in mass over time relative to its reproductions, the International Committee for Weights and Measures (CIPM) recommended in 2005 that the kilogram be redefined in terms of a fundamental constant of nature. At its 2011 meeting, the CGPM agreed in principle that the kilogram should be redefined in terms of the Planck constant, h. The decision was originally deferred until 2014; in 2014 it was deferred again until the next meeting. CIPM has proposed revised definitions of the SI base units, for consideration at the 26th CGPM. The formal vote, which took place on 16 November 2018, approved the change, with the new definitions coming into force on 20 May 2019. The accepted redefinition defines the Planck constant as exactly 6.62607015×10−34 kg⋅m2⋅s−1, thereby defining the kilogram in terms of the second and the metre. Since the second and metre are defined completely in terms of physical constants, the kilogram is defined in terms of physical constants only.
The avoirdupois (or international) pound, used in both the imperial and US customary systems, is now defined in terms of the kilogram. Other traditional units of weight and mass around the world are now also defined in terms of the kilogram, making the kilogram the primary standard for virtually all units of mass on Earth.
The word kilogramme or kilogram is derived from the French kilogramme, which itself was a learned coinage, prefixing the Greek stem of χίλιοι khilioi "a thousand" to gramma, a Late Latin term for "a small weight", itself from Greek γράμμα. The word kilogramme was written into French law in 1795, in the Decree of 18 Germinal, which revised the older system of units introduced by the French National Convention in 1793, where the gravet had been defined as weight (poids) of a cubic centimetre of water, equal to 1/1000 of a grave. In the decree of 1795, the term gramme thus replaced gravet, and kilogramme replaced grave.
The French spelling was adopted in Great Britain when the word was used for the first time in English in 1795,  with the spelling kilogram being adopted in the United States. In the United Kingdom both spellings are used, with "kilogram" having become by far the more common.[Note 2] UK law regulating the units to be used when trading by weight or measure does not prevent the use of either spelling.
In the 19th century the French word kilo, a shortening of kilogramme, was imported into the English language where it has been used to mean both kilogram and kilometre. While kilo is acceptable in many generalist texts, for example The Economist, its use is typically considered inappropriate in certain applications including scientific, technical and legal writing, where authors should adhere strictly to SI nomenclature. When the United States Congress gave the metric system legal status in 1866, it permitted the use of the word kilo as an alternative to the word kilogram, but in 1990 revoked the status of the word kilo.
During the 19th century, the standard system of metric units was the centimetre–gram–second system of units, treating the gram as the fundamental unit of mass and the kilogram simply as a derived unit. In 1901, however, following the discoveries by James Clerk Maxwell to the effect that electric measurements could not be explained in terms of the three fundamental units of length, mass and time, Giovanni Giorgi proposed a new standard system that would include a fourth fundamental unit to measure quantities in electromagnetism. In 1935 this was adopted by the IEC as the Giorgi system, now also known as MKS system, and in 1946 the CIPM approved a proposal to adopt the ampere as the electromagnetic unit of the "MKSA system".:109,110 In 1948 the CGPM commissioned the CIPM "to make recommendations for a single practical system of units of measurement, suitable for adoption by all countries adhering to the Metre Convention". This led to the launch of SI in 1960 and the subsequent publication of the "SI Brochure", which stated that "It is not permissible to use abbreviations for unit symbols or unit names ...".[Note 3] The CGS and MKS systems co-existed during much of the early-to-mid 20th century, but as a result of the decision to adopt the "Giorgi system" as the international system of units in 1960, the kilogram is now the SI base unit for mass, while the definition of the gram is derived from that of the kilogram.
The kilogram is a unit of mass, a property corresponding to the common perception of how "heavy" an object is. Mass is an inertial property; that is, it is related to the tendency of an object at rest to remain at rest, or if in motion to remain in motion at a constant velocity, unless acted upon by a force.
While the weight of an object is dependent on the strength of the local gravitational field, the mass of an object is independent of gravity, as mass is a measure of the quantity of matter. 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 and inertia, an astronaut must exert ten times as much force to accelerate a 10‑kilogram object at the same rate as a 1‑kilogram object.
Because at any given point on Earth the weight of an object is proportional to its mass, the mass of an object in kilograms is usually measured by comparing its weight to the weight of a standard mass, whose mass is known in kilograms, using a device called a weighing scale. The ratio of the force of gravity on the two objects, measured by the scale, is equal to the ratio of their masses.
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 as massive as the gram—the kilogram.
At the same time, work was commissioned to precisely determine the mass of a cubic decimetre (one litre) of water.[Note 4] Although the decreed definition of the kilogram specified water at 0 °C—its highly stable temperature point—the French chemist Louis Lefèvre-Gineau and the Italian naturalist Giovanni Fabbroni after several years of research chose to redefine the standard in 1799 to water's most stable density point: the temperature at which water reaches maximum density, which was measured at the time as 4 °C.[Note 5] They concluded that one cubic decimetre of water at its maximum density was equal to 99.9265% of the target mass of the provisional kilogram standard made four years earlier.[Note 6] 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 one cubic decimetre of water at 4 °C. The prototype was presented to the Archives of the Republic in June and on December 10, 1799, the prototype was formally ratified as the kilogramme des Archives (Kilogram of the Archives) and the kilogram was defined as being equal to its mass. This standard stood for the next 90 years.
Since 1889 the magnitude of the kilogram has been defined as the mass of an object called the International Prototype of the Kilogram, often referred to in the professional metrology world as the "IPK". The IPK is made of a platinum alloy known as "Pt‑10Ir", which is 90% platinum and 10% iridium (by mass) and is machined into a right-circular cylinder (height = diameter) of about 39 millimetres 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 (almost twice as dense as lead and more than 21 times as dense as water), satisfactory electrical and thermal conductivities, and low magnetic susceptibility. The IPK and its six sister copies are stored at the International Bureau of Weights and Measures (known by its French-language initials BIPM) in an environmentally monitored safe in the lower vault located in the basement of the BIPM's Pavillon de Breteuil in Saint-Cloud[Note 7] on the outskirts of Paris (see External images, below, for photographs). 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, thereby providing traceability of local measurements back to the IPK.
The Metre Convention was signed on May 20, 1875 and further formalized the metric system (a predecessor to the SI), quickly leading to the production of the IPK. The IPK is one of three cylinders made in 1879 by Johnson Matthey, which continues to manufacture nearly all of the national prototypes today. In 1883, the mass of the IPK was found to be indistinguishable from that of the Kilogramme des Archives made eighty-four years prior, and was formally ratified as the kilogram by the 1st CGPM in 1889.
Modern measurements of Vienna Standard Mean Ocean Water, which is pure distilled water with an isotopic composition representative of the average of the world's oceans, show that it has a density of 0.999975 ±0.000001 kg/L at its point of maximum density (3.984 °C) under one standard atmosphere (101 325 Pa or 760 torr) of pressure. Thus, a cubic decimetre of water at its point of maximum density is only 25 parts per million less massive than the IPK; that is to say, the 25 milligram difference shows that the scientists over 220 years ago managed to make the mass of the Kilogram of the Archives equal that of a cubic decimetre of water at 4 °C, with a margin of error at most within the mass of a single excess grain of rice.
The various copies of the international prototype kilogram are given the following designations in the literature:
By definition, the error in the measured value of the IPK's mass is exactly zero; the mass of the IPK is the kilogram. However, any changes in the IPK's mass over time can be deduced by comparing its mass to that of its official copies stored throughout the world, a rarely undertaken process called "periodic verification". The only three verifications occurred in 1889, 1948, and 1989. For instance, the US owns four 90% platinum / 10% iridium (Pt‑10Ir) kilogram standards, two of which, K4 and K20, are from the original batch of 40 replicas delivered in 1884.[Note 10] The K20 prototype was designated as the primary national standard of mass for the US. Both of these, as well as those from other nations, are periodically returned to the BIPM for verification. Great care is exercised when transporting prototypes. In 1984, the K4 and K20 prototypes were hand-carried in the passenger section of separate commercial airliners.
Note that none of the replicas has a mass precisely equal to that of the IPK; their masses are calibrated and documented as offset values. For instance, K20, the US's primary standard, originally had an official mass of 1 kg − 39 μg (micrograms) in 1889; that is to say, K20 was 39 μg less than the IPK. A verification performed in 1948 showed a mass of 1 kg − 19 μg. The latest verification performed in 1989 shows a mass precisely identical to its original 1889 value. Quite unlike transient variations such as this, the US's check standard, K4, has persistently declined in mass relative to the IPK—and for an identifiable reason: check standards are used much more often than primary standards and are prone to scratches and other wear. K4 was originally delivered with an official mass of 1 kg − 75 μg in 1889, but as of 1989 was officially calibrated at 1 kg − 106 μg and ten years later was 1 kg − 116 μg. Over a period of 110 years, K4 lost 41 μg relative to the IPK.
Beyond the simple wear that check standards can experience, the mass of even the carefully stored national prototypes can drift relative to the IPK for a variety of reasons, some known and some unknown. Since the IPK and its replicas are stored in air (albeit under two or more nested bell jars), they gain mass through adsorption of atmospheric contamination onto their surfaces. Accordingly, they are cleaned in a process the BIPM developed between 1939 and 1946 known as "the BIPM cleaning method" that comprises firmly rubbing with a chamois soaked in equal parts ether and ethanol, followed by steam cleaning with bi-distilled water, and allowing the prototypes to settle for 7–10 days before verification. Before the BIPM's published report in 1994 detailing the relative change in mass of the prototypes, different standard bodies used different techniques to clean their prototypes. The NIST's practice before then was to soak and rinse its two prototypes first in benzene, then in ethanol, and to then clean them with a jet of bi-distilled water steam. Cleaning the prototypes removes between 5 and 60 μg of contamination depending largely on the time elapsed since the last cleaning. Further, a second cleaning can remove up to 10 μg more. After cleaning—even when they are stored under their bell jars—the IPK and its replicas immediately begin gaining mass again. The BIPM even developed a model of this gain and concluded that it averaged 1.11 μg per month for the first 3 months after cleaning and then decreased to an average of about 1 μg per year thereafter. Since check standards like K4 are not cleaned for routine calibrations of other mass standards—a precaution to minimize the potential for wear and handling damage—the BIPM's model of time-dependent mass gain has been used as an "after cleaning" correction factor.
Because the first forty official copies are made of 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. What has become clear after the third periodic verification performed between 1988 and 1992 is that masses of the entire worldwide ensemble of prototypes have been slowly but inexorably diverging from each other. It is also clear that the mass of the IPK lost perhaps 50 μg over the last century, and possibly significantly more, in comparison to its official copies. The reason for this drift has eluded physicists who have dedicated their careers to the SI unit of mass. No plausible mechanism has been proposed to explain either a steady decrease in the mass of the IPK, or an increase in that of its replicas dispersed throughout the world.[Note 11] Moreover, there are no technical means available to determine whether or not the entire worldwide ensemble of prototypes suffers from even greater long-term trends upwards or downwards because their mass "relative to an invariant of nature is unknown at a level below 1000 μg over a period of 100 or even 50 years". Given the lack of data identifying which of the world's kilogram prototypes has been most stable in absolute terms, it is equally valid to state that the first batch of replicas has, as a group, gained an average of about 25 μg over one hundred years in comparison to the IPK.[Note 12]
What is known specifically about the IPK is that it exhibits a short-term instability of about 30 μg over a period of about a month in its after-cleaned mass. The precise reason for this short-term instability is not understood but is thought to entail surface effects: microscopic differences between the prototypes' polished surfaces, possibly aggravated by hydrogen absorption due to catalysis of the volatile organic compounds that slowly deposit onto the prototypes as well as the hydrocarbon-based solvents used to clean them.
It has been possible to rule out many explanations of the observed divergences in the masses of the world's prototypes proposed by scientists and the general public. The BIPM's FAQ explains, for example, that the divergence is dependent on the amount of time elapsed between measurements and not dependent on the number of times the prototype or its copies have been cleaned or possible changes in gravity or environment. Reports published in 2013 by Peter Cumpson of Newcastle University based on the X-ray photoelectron spectroscopy of samples that were stored alongside various prototype kilograms suggested that one source of the divergence between the various prototypes could be traced to mercury that had been absorbed by the prototypes being in the proximity of mercury-based instruments. The IPK has been stored within centimetres of a mercury thermometer since at least as far back as the late 1980s. In this Newcastle University work six platinum weights made in the nineteenth century were all found to have mercury at the surface, the most contaminated of which had the equivalent of 250 μg of mercury when scaled to the surface area of a kilogram prototype.
Scientists are seeing far greater variability in the prototypes than previously believed. The increasing divergence in the masses of the world's prototypes and the short-term instability in the IPK has prompted research into improved methods to obtain a smooth surface finish using diamond turning on newly manufactured replicas and was one of the reasons that led to the redefinition of the Kilogram. See § Redefinition agreed on 16 November 2018, below.
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 one kilogram at one metre per second squared. If the mass of the IPK were to change slightly then the newton would also change proportionally. 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 metre. 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.
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 140-year-old, golf-ball-sized piece of metal, the quality of the IPK must be diligently protected to preserve the integrity of the SI system. Yet, despite the best stewardship, the average mass of the worldwide ensemble of prototypes and the mass of the IPK have likely diverged another 7 μg since the third periodic verification 30 years ago.[Note 13] Further, the world's national metrology laboratories 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 metre is defined as the distance light travels in a vacuum during a time interval of 1⁄299,792,458 of a second. However, the metre's practical realization typically takes the form of a helium–neon laser, and the metre's length is delineated—not defined—as 1579800.298728 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 extremely stable with a reproducibility of a few parts in 1015). There would be no automatic effect on the metre because the second—and thus the metre's length—is abstracted via the laser comprising the metre's practical realization. Scientists performing metre 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 parts per billion" (equivalent to 42 μg).
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.
The International Committee for Weights and Measures (CIPM) approved a proposed redefinition of SI base units in November 2018 that defines the kilogram by defining the Planck constant to be exactly 6.62607015×10−34 kg⋅m2⋅s−1. This approach effectively defines the kilogram in terms of the second and the metre, and will take effect on 20 May 2019.
Prior to the redefinition the kilogram, and several other SI units based on the kilogram, were defined by a man-made metal artefact: the Kilogram des Archives from 1799 to 1889, and the International Prototype Kilogram from 1889 onward.
In 1960, the metre, previously similarly having been defined with reference to a single platinum-iridium bar with two marks on it, was redefined in terms of an invariant physical constant (the wavelength of a particular emission of light emitted by krypton, and later the speed of light) so that the standard can be independently reproduced in different laboratories by following a written specification.
In October 2010, the CIPM voted to submit a resolution for consideration at the General Conference on Weights and Measures (CGPM), to "take note of an intention" that the kilogram be defined in terms of the Planck constant, h (which has dimensions of energy times time) together with other physical constants. This resolution was accepted by the 24th conference of the CGPM in October 2011 and further discussed at the 25th conference in 2014. Although the Committee recognised that significant progress had been made, they concluded that the data did not yet appear sufficiently robust to adopt the revised definition, and that work should continue to enable the adoption at the 26th meeting, scheduled for 2018. Such a definition would theoretically permit any apparatus that was capable of delineating the kilogram in terms of the Planck constant to be used as long as it possessed sufficient precision, accuracy and stability. The Kibble balance (discussed below) is one way do this.
As part of this project, a variety of very different technologies and approaches were considered and explored over many years. They too are covered below. Some of these now-abandoned approaches were based on equipment and procedures that would have enabled 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, physical constants. Others were based on devices that measured either the acceleration or weight of hand-tuned kilogram test masses and which expressed their magnitudes in electrical terms via special components that permit traceability to physical constants. All approaches depend on converting a weight measurement to a mass, and therefore require the precise measurement of the strength of gravity in laboratories. All approaches would have precisely fixed one or more constants of nature at a defined value.
The Kibble balance (known as a "watt balance" before 2016) is essentially a single-pan weighing scale that measures the electric power necessary to oppose the weight of a kilogram test mass as it is pulled by Earth's gravity. It is a variation of an ampere balance, with an extra calibration step that eliminates the effect of geometry. The electric potential in the Kibble balance is delineated by a Josephson voltage standard, which allows voltage to be linked to an invariant constant of nature with extremely high precision and stability. Its circuit resistance is calibrated against a quantum Hall effect resistance standard.
The Kibble balance requires extremely precise measurement of the local gravitational acceleration g in the laboratory, using a gravimeter. For instance when the elevation of the centre of the gravimeter differs from that of the nearby test mass in the Kibble balance, the NIST compensates for Earth's gravity gradient of 309 μGal per metre, which affects the weight of a one-kilogram test mass by about 316 μg/m.
In April 2007, the NIST's implementation of the Kibble balance demonstrated a combined relative standard uncertainty (CRSU) of 36 μg.[Note 14] The UK's National Physical Laboratory's Kibble balance demonstrated a CRSU of 70.3 μg in 2007. That Kibble balance was disassembled and shipped in 2009 to Canada's Institute for National Measurement Standards (part of the National Research Council), where research and development with the device could continue.
Gravity and the nature of the Kibble balance, which oscillates test masses up and down against the local gravitational acceleration g, are exploited so that mechanical power is compared against electrical power, which is the square of voltage divided by electrical resistance. However, g varies significantly—by nearly 1%—depending on where on the Earth's surface the measurement is made (see Earth's gravity). There are also slight seasonal variations in g at a location due to changes in underground water tables, and larger semimonthly and diurnal changes due to tidal distortions in the Earth's shape caused by the Moon and the Sun. Although g would not be a term in the definition of the kilogram, it would be crucial in the process of measurement of the kilogram when relating energy to power. Accordingly, g must be measured with at least as much precision and accuracy as are the other terms, so measurements of g must also be traceable to fundamental constants of nature. For the most precise work in mass metrology, g is measured using dropping-mass absolute gravimeters that contain an iodine-stabilized helium–neon laser interferometer. The fringe-signal, frequency-sweep output from the interferometer is measured with a rubidium atomic clock. Since this type of dropping-mass gravimeter derives its accuracy and stability from the constancy of the speed of light as well as the innate properties of helium, neon, and rubidium atoms, the 'gravity' term in the delineation of an all-electronic kilogram is also measured in terms of invariants of nature—and with very high precision. For instance, in the basement of the NIST's Gaithersburg facility in 2009, when measuring the gravity acting upon Pt‑10Ir test masses (which are denser, smaller, and have a slightly lower center of gravity inside the Kibble balance than stainless steel masses), the measured value was typically within 8 ppb of 9.80101644 m/s2.
The virtue of electronic realizations like the Kibble balance is that the definition and dissemination of the kilogram would no longer be dependent upon the stability of kilogram prototypes, which must be very carefully handled and stored. It would free physicists from the need to rely on assumptions about the stability of those prototypes. Instead, hand-tuned, close-approximation mass standards would simply be weighed and documented as being equal to one kilogram plus an offset value. With the Kibble balance, while the kilogram would be delineated in electrical and gravity terms, all of which are traceable to invariants of nature; it would be defined in a manner that is directly traceable to three fundamental constants of nature. The Planck constant defines the kilogram in terms of the second and the metre. By fixing the Planck constant, the definition of the kilogram would in addition depend only on the definitions of the second and the metre. The definition of the second depends on a single defined physical constant: the ground state hyperfine splitting frequency of the caesium 133 atom Δν(133Cs)hfs. The metre depends on the second and on an additional defined physical constant: the speed of light c. Once the kilogram is redefined in this manner, physical objects such as the IPK will no longer be part of the definition, but will instead become transfer standards.
Scales like the Kibble balance also permit more flexibility in choosing materials with especially desirable properties for mass standards. For instance, Pt‑10Ir could continue to be used so that the specific gravity of newly produced mass standards would be the same as existing national primary and check standards (≈21.55 g/ml). This would reduce the relative uncertainty when making mass comparisons in air. Alternatively, entirely different materials and constructions could be explored with the objective of producing mass standards with greater stability. For instance, osmium-iridium alloys could be investigated if platinum's propensity to absorb hydrogen (due to catalysis of VOCs and hydrocarbon-based cleaning solvents) and atmospheric mercury proved to be sources of instability. Also, vapor-deposited, protective ceramic coatings like nitrides could be investigated for their suitability for chemically isolating these new alloys.
The challenge with Kibble balances is not only in reducing their uncertainty, but also in making them truly practical realizations of the kilogram. Nearly every aspect of Kibble balances and their support equipment requires such extraordinarily precise and accurate, state-of-the-art technology that—unlike a device like an atomic clock—few countries would currently choose to fund their operation. For instance, the NIST's Kibble balance used four resistance standards in 2007, each of which was rotated through the Kibble balance every two to six weeks after being calibrated in a different part of NIST headquarters facility in Gaithersburg, Maryland. It was found that simply moving the resistance standards down the hall to the Kibble balance after calibration altered their values 10 ppb (equivalent to 10 μg) or more. Present-day technology is insufficient to permit stable operation of Kibble balances between even biannual calibrations. When the new definition takes effect, it is likely there will only be a few—at most—Kibble balances initially operating in the world.
Several alternative approaches to redefining the kilogram that were fundamentally different from the Kibble balance were explored to varying degrees, with some abandoned. The Avogadro project, in particular, was important for the 2018 redefinition decision because it provided an accurate measurement of the Planck constant that was consistent with and independent of the Kibble balance method. The alternative approaches included:
Another Avogadro constant-based approach, known as the International Avogadro Coordination's Avogadro project, would define and delineate the kilogram as a 93.6 mm diameter sphere of silicon atoms. Silicon was chosen because a commercial infrastructure with mature processes for creating defect-free, ultra-pure monocrystalline silicon already exists to service the semiconductor industry. To make a practical realization of the kilogram, a silicon boule (a rod-like, single-crystal ingot) would be produced. Its isotopic composition would be measured with a mass spectrometer to determine its average relative atomic mass. The boule would be cut, ground, and polished into spheres. The size of a select sphere would be measured using optical interferometry to an uncertainty of about 0.3 nm on the radius—roughly a single atomic layer. The precise lattice spacing between the atoms in its crystal structure (≈ 192 pm) would be measured using a scanning X-ray interferometer. This permits its atomic spacing to be determined with an uncertainty of only three parts per billion. With the size of the sphere, its average atomic mass, and its atomic spacing known, the required sphere diameter can be calculated with sufficient precision and low uncertainty to enable it to be finish-polished to a target mass of one kilogram.
Experiments are being performed on the Avogadro Project's silicon spheres to determine whether their masses are most stable when stored in a vacuum, a partial vacuum, or ambient pressure. However, no technical means currently exist to prove a long-term stability any better than that of the IPK's, because the most sensitive and accurate measurements of mass are made with dual-pan balances like the BIPM's FB‑2 flexure-strip balance (see § External links, below). Balances can only compare the mass of a silicon sphere to that of a reference mass. Given the latest understanding of the lack of long-term mass stability with the IPK and its replicas, there is no known, perfectly stable mass artefact to compare against. Single-pan scales, which measure weight relative to an invariant of nature, are not precise to the necessary long-term uncertainty of 10–20 parts per billion. Another issue to be overcome is that silicon oxidizes and forms a thin layer (equivalent to 5–20 silicon atoms deep) of silicon dioxide (quartz) and silicon monoxide. This layer slightly increases the mass of the sphere, an effect that must be accounted for when polishing the sphere to its finished size. Oxidation is not an issue with platinum and iridium, both of which are noble metals that are roughly as cathodic as oxygen and therefore don't oxidize unless coaxed to do so in the laboratory. The presence of the thin oxide layer on a silicon-sphere mass prototype places additional restrictions on the procedures that might be suitable to clean it to avoid changing the layer's thickness or oxide stoichiometry.
All silicon-based approaches would fix the Avogadro constant but vary in the details of the definition of the kilogram. One approach would use silicon with all three of its natural isotopes present. About 7.78% of silicon comprises the two heavier isotopes: 29Si and 30Si. As described in § Carbon-12 below, this method would define the magnitude of the kilogram in terms of a certain number of 12C atoms by fixing the Avogadro constant; the silicon sphere would be the practical realization. This approach could accurately delineate the magnitude of the kilogram because the masses of the three silicon nuclides relative to 12C are known with great precision (relative uncertainties of 1 ppb or better). An alternative method for creating a silicon sphere-based kilogram proposes to use isotopic separation techniques to enrich the silicon until it is nearly pure 28Si, which has a relative atomic mass of 27.9769265325(19). With this approach, the Avogadro constant would not only be fixed, but so too would the atomic mass of 28Si. As such, the definition of the kilogram would be decoupled from 12C and the kilogram would instead be defined as 1000⁄27.9769265325 ⋅ 6.02214179×1023 atoms of 28Si (≈ 35.74374043 fixed moles of 28Si atoms). Physicists could elect to define the kilogram in terms of 28Si even when kilogram prototypes are made of natural silicon (all three isotopes present). Even with a kilogram definition based on theoretically pure 28Si, a silicon-sphere prototype made of only nearly pure 28Si would necessarily deviate slightly from the defined number of moles of silicon to compensate for various chemical and isotopic impurities as well as the effect of surface oxides.
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 (12C) 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 1000⁄12 moles (83 1⁄3 mol) of 12C has a mass of precisely one kilogram. The number of atoms in a mole, a quantity known as the Avogadro constant, is experimentally determined, and the current best estimate of its value is 6.022140857(74)×1023 entities per mole. This new definition of the kilogram proposed to fix the Avogadro constant at precisely 6.02214X×1023 mol−1 with the kilogram being defined as "the mass equal to that of 1000⁄12 ⋅ 6.02214X×1023 atoms of 12C".
The accuracy of the measured value of the Avogadro constant is currently limited by the uncertainty in the value of the Planck constant. That relative standard uncertainty has been 50 parts per billion (ppb) since 2006. By fixing the Avogadro constant, the practical effect of this proposal would be that the uncertainty in the mass of a 12C atom—and the magnitude of the kilogram—could be no better than the current 50 ppb uncertainty in the Planck constant. Under this proposal, the magnitude of the kilogram would be subject to future refinement as improved measurements of the value of the Planck constant become available; electronic realizations of the kilogram would be recalibrated as required. Conversely, an electronic definition of the kilogram (see § Electronic approaches, below), which would precisely fix the Planck constant, would continue to allow 83 1⁄3 moles of 12C to have a mass of precisely one kilogram but the number of atoms comprising a mole (the Avogadro constant) would continue to be subject to future refinement.
A variation on a 12C-based definition proposes to define the Avogadro constant as being precisely 844468893 (≈ 6.02214162×1023) atoms. An imaginary realization of a 12-gram mass prototype would be a cube of 12C atoms measuring precisely 84446889 atoms across on a side. With this proposal, the kilogram would be defined as "the mass equal to 844468893 × 83 1⁄3 atoms of 12C."[Note 16]
Another Avogadro-based approach, ion accumulation, since abandoned, would have defined and delineated the kilogram by precisely creating new metal prototypes on demand. It would have done so by accumulating gold or bismuth ions (atoms stripped of an electron) and counting them by measuring the electric current required to neutralize the ions. Gold (197Au) and bismuth (209Bi) were chosen because they can be safely handled and have the two highest atomic masses among the mononuclidic elements that are stable (gold) or effectively so (bismuth).[Note 17] See also Table of nuclides.
With a gold-based definition of the kilogram for instance, the relative atomic mass of gold could have been fixed as precisely 196.9665687, from the current value of 196.9665687(6). As with a definition based upon carbon‑12, the Avogadro constant would also have been fixed. The kilogram would then have been defined as "the mass equal to that of precisely 1000⁄196.9665687 ⋅ 6.02214179×1023 atoms of gold" (precisely 3,057,443,620,887,933,963,384,315 atoms of gold or about 5.07700371 fixed moles).
In 2003, German experiments with gold at a current of only 10 μA demonstrated a relative uncertainty of 1.5%. Follow-on experiments using bismuth ions and a current of 30 mA were expected to accumulate a mass of 30 g in six days and to have a relative uncertainty of better than 1 ppm. Ultimately, ion‑accumulation approaches proved to be unsuitable. Measurements required months and the data proved too erratic for the technique to be considered a viable future replacement to the IPK.
Among the many technical challenges of the ion-deposition apparatus was obtaining a sufficiently high ion current (mass deposition rate) while simultaneously decelerating the ions so they could all deposit onto a target electrode embedded in a balance pan. Experiments with gold showed the ions had to be decelerated to very low energies to avoid sputtering effects—a phenomenon whereby ions that had already been counted ricochet off the target electrode or even dislodged atoms that had already been deposited. The deposited mass fraction in the 2003 German experiments only approached very close to 100% at ion energies of less than around 1 eV (< 1 km/s for gold).
If the kilogram had been defined as a precise quantity of gold or bismuth atoms deposited with an electric current, not only would the Avogadro constant and the atomic mass of gold or bismuth have to have been precisely fixed, but also the value of the elementary charge (e), likely to 1.60217X×10−19 C (from the currently recommended value of 1.6021766208(98)×10−19 C). Doing so would have effectively defined the ampere as a flow of 1⁄1.60217X×10−19 electrons per second past a fixed point in an electric circuit. The SI unit of mass would have been fully defined by having precisely fixed the values of the Avogadro constant and elementary charge, and by exploiting the fact that the atomic masses of bismuth and gold atoms are invariant, universal constants of nature.
Beyond the slowness of making a new mass standard and the poor reproducibility, there were other intrinsic shortcomings to the ion‑accumulation approach that proved to be formidable obstacles to ion-accumulation-based techniques becoming a practical realization. The apparatus necessarily required that the deposition chamber have an integral balance system to enable the convenient calibration of a reasonable quantity of transfer standards relative to any single internal ion-deposited prototype. Furthermore, the mass prototypes produced by ion deposition techniques would have been nothing like the freestanding platinum-iridium prototypes currently in use; they would have been deposited onto—and become part of—an electrode imbedded into one pan of a special balance integrated into the device. Moreover, the ion-deposited mass wouldn't have had a hard, highly polished surface that can be vigorously cleaned like those of current prototypes. Gold, while dense and a noble metal (resistant to oxidation and the formation of other compounds), is extremely soft so an internal gold prototype would have to be kept well isolated and scrupulously clean to avoid contamination and the potential of wear from having to remove the contamination. Bismuth, which is an inexpensive metal used in low-temperature solders, slowly oxidizes when exposed to room-temperature air and forms other chemical compounds and so would not have produced stable reference masses unless it was continually maintained in a vacuum or inert atmosphere.
This approach would define the kilogram as "the mass which would be accelerated at precisely 2×10−7 m/s2 when subjected to the per-metre force between two straight parallel conductors of infinite length, of negligible circular cross section, placed one metre apart in vacuum, through which flow a constant current of 1⁄1.60217X×10−19 elementary charges per second".
Effectively, this would define the kilogram as a derivative of the ampere rather than the present relationship, which defines the ampere as a derivative of the kilogram. This redefinition of the kilogram would specify elementary charge (e) as precisely 1.60217X×10−19 coulomb rather than the current recommended value of 1.6021766208(98)×10−19 C. It would necessarily follow that the ampere (one coulomb per second) would also become an electric current of this precise quantity of elementary charges per second passing a given point in an electric circuit. The virtue of a practical realization based upon this definition is that unlike the Kibble 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 g 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 performed similar research that used different techniques to levitate the mass.
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 unit gram, not 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).
|Value||SI symbol||Name||Value||SI symbol||Name|
|10−1 g||dg||decigram||101 g||dag||decagram|
|10−2 g||cg||centigram||102 g||hg||hectogram|
|10−3 g||mg||milligram||103 g||kg||kilogram|
|10−6 g||µg||microgram||106 g||Mg||megagram (tonne)|
|10−9 g||ng||nanogram||109 g||Gg||gigagram|
|10−12 g||pg||picogram||1012 g||Tg||teragram|
|10−15 g||fg||femtogram||1015 g||Pg||petagram|
|10−18 g||ag||attogram||1018 g||Eg||exagram|
|10−21 g||zg||zeptogram||1021 g||Zg||zettagram|
|10−24 g||yg||yoctogram||1024 g||Yg||yottagram|
|Common prefixed units are in bold face.[Note 18]|
[BIPM director Martin] Milton responded to a question about what would happen if ... the CIPM or the CGPM voted not to move forward with the redefinition of the SI. He responded that he felt that by that time the decision to move forward should be seen as a foregone conclusion.
Obsolete Units As stated in the 1990 Federal Register notice, ...
Gramme, le poids absolu d'un volume d'eau pure égal au cube de la centième partie du mètre, et à la température de la glace fondante.
Из 40 изготовленных копий прототипа две (№12 и №26) были переданы России. Эталон №12 принят в СССР в качестве государственного первичного эталона единицы массы, а №26 — в качестве эталона-копии.
Avogadro’s constant and the Planck constant are intertwined in the laws of physics. Having measured Avogadro’s constant, Dr. Bettin could derive the Planck constant. And with a precise measure of the Planck constant, he could validate the results of Dr. Kibble’s work, and vice versa.
2014 CODATA recommended values
2014 CODATA recommended values
|BIPM: The IPK in three nested bell jars|
|NIST: K20, the US National Prototype Kilogram resting on an egg crate fluorescent light panel|
|BIPM: Steam cleaning a 1 kg prototype before a mass comparison|
|BIPM: The IPK and its six sister copies in their vault|
|The Age: Silicon sphere for the Avogadro Project|
|NPL: The NPL's Watt Balance project|
|NIST: This particular Rueprecht Balance, an Austrian-made precision balance, was used by the NIST from 1945 until 1960|
|BIPM: The FB‑2 flexure-strip balance, the BIPM's modern precision balance featuring a standard deviation of one ten-billionth of a kilogram (0.1 μg)|
|BIPM: Mettler HK1000 balance, featuring 1 μg resolution and a 4 kg maximum mass. Also used by NIST and Sandia National Laboratories' Primary Standards Laboratory|
|Micro-g LaCoste: FG‑5 absolute gravimeter, (diagram), used in national laboratories to measure gravity to 2 μGal accuracy|
A redefinition of SI base units is scheduled to come into force on 20 May 2019. The kilogram, ampere, kelvin, and mole will then be defined by setting exact numerical values for the Planck constant (h), the elementary electric charge (e), the Boltzmann constant (k), and the Avogadro constant (NA), respectively. The metre, second and candela are already defined by physical constants, subject to correction to their present definitions. The new definitions aim to improve the SI without changing the size of any units, thus ensuring continuity with existing measurements. In November 2018, the 26th General Conference on Weights and Measures (CGPM) unanimously approved these changes, which the International Committee for Weights and Measures (CIPM) had proposed earlier that year.:23The previous major change of the metric system was in 1960 when the International System of Units (SI) was formally published. At this time the metre was redefined, from being defined in terms of the prototype metre, to being defined in terms of the wavelength of a spectral line of a krypton-86 radiation, making it derivable from universal natural phenomena. The kilogram remained defined in terms of a physical prototype, leaving it the only artefact upon which the SI unit definitions depend. At this time the SI, as a coherent system, was constructed around seven base units, powers of which were used to construct all other units. With the 2019 redefinition, the SI is instead constructed around seven defining constants, allowing all units to be constructed directly from these constants, with the designation of base units being retained although no longer essential.
The metric system was originally conceived as a system of measurement that was derivable from unchanging phenomena, but practical limitations necessitated the use of artefacts (the prototype metre and prototype kilogram) when the metric system was first introduced in France in 1799. Although designed for long-term stability, the masses of the kilogram prototype and its secondary copies have shown small variations over time relative to each other, and they are not thought to be adequate for the increasing accuracy demanded by science, prompting a search for a suitable replacement. Also, some units were defined based on measurements that are difficult to precisely realise in a laboratory, such as the definition of the kelvin in terms of the triple point of water. With the 2019 redefinition, the SI is for the first time wholly derivable from natural phenomena, with most units based on fundamental physical constants.
A number of authors have published criticisms of the revised definitions – including that the proposal had failed to address the impact of breaking the link between the definition of the dalton and the definitions of the kilogram, the mole, and the Avogadro constant.Calorie
The calorie is a unit of energy. The Calorie (note the capital C) is 1,000 calories.
That capital C, distinguishing Calorie from calorie, is a long-established scientific convention but is not always understood more widely. Where the context is clearly about food, nutrition and exercise, the term often appears without the capital C. The Calorie is also termed the large calorie or kilocalorie — symbols: Cal, kcal — or food calorie, defined as the heat energy involved in warming one kilogram of water by one degree Celsius.The small calorie (symbol: cal) was later defined as the heat energy to raise the temperature of one gram of water — rather than a kilogram — by the same amount. (See below for details of the definitions.)
Although both units relate to the metric system, they have been considered obsolete, or deprecated, in scientific usage, since the adoption of the SI system. (The SI unit of energy is the joule.) But the small calorie is still often used in laboratory measurements and calculations, with the values thus established typically being reported in kilocalories.Curb weight
Curb weight (American English) or kerb weight (British English) is the total mass of a vehicle with standard equipment and all necessary operating consumables such as motor oil, transmission oil, coolant, air conditioning refrigerant, and sometimes a full tank of fuel, while not loaded with either passengers or cargo.
This definition may differ from definitions used by governmental regulatory agencies or other organizations. For example, many European Union manufacturers include the weight of a 75-kilogram (165 lb) driver to follow European Directive 95/48/EC. Organizations may also define curb weight with fixed levels of fuel and other variables to equalize the value for the comparison of different vehicles.
The United States Environmental Protection Agency regulations define curb weight as follows: Curb weight means the actual or the manufacturer’s estimated weight of the vehicle in operational status with all standard equipment, and weight of fuel at nominal tank capacity, and the weight of optional equipment computed in accordance with §86.1832–01; incomplete light-duty trucks shall have the curb weight specified by the manufacturer.
Unladen mass depends on the manufacturer and can be the same as curb weight, however, it is often the total mass of the car without a driver, fluid or any additional equipment.Giovanni Giorgi
Giovanni Giorgi (27 November 1871 – 19 August 1950) was an Italian physicist and electrical engineer who proposed the Giorgi system of measurement, the precursor to the International System of Units (SI).Gram
The gram (alternative spelling: gramme; SI unit symbol: g) (Latin gramma, from Greek γράμμα, grámma) is a metric system unit of mass.
Originally defined as "the absolute weight of a volume of pure water equal to the cube of the hundredth part of a metre [1 cm3], and at the temperature of melting ice" (later at 4 °C, the temperature of maximum density of water). However, in a reversal of reference and defined units, a gram is now defined as one thousandth of the SI base unit, the kilogram, or 1×10−3 kg, which itself is now defined by the International Bureau of Weights and Measures, not in terms of grams, but by "the amount of electricity needed to counteract its force"International System of Units
The International System of Units (SI, abbreviated from the French Système international (d'unités)) is the modern form of the metric system, and is the most widely used system of measurement. It comprises a coherent system of units of measurement built on seven base units, which are the ampere, kelvin, second, metre, kilogram, candela, mole, and a set of twenty prefixes to the unit names and unit symbols that may be used when specifying multiples and fractions of the units. The system also specifies names for 22 derived units, such as lumen and watt, for other common physical quantities.
The base units are derived from invariant constants of nature, such as the speed of light in vacuum and the triple point of water, which can be observed and measured with great accuracy, and one physical artefact. The artefact is the international prototype kilogram, certified in 1889, and consisting of a cylinder of platinum-iridium, which nominally has the same mass as one litre of water at the freezing point. Its stability has been a matter of significant concern, culminating in a revision of the definition of the base units entirely in terms of constants of nature, scheduled to be put into effect on 20 May 2019.Derived units may be defined in terms of base units or other derived units. They are adopted to facilitate measurement of diverse quantities. The SI is intended to be an evolving system; units and prefixes are created and unit definitions are modified through international agreement as the technology of measurement progresses and the precision of measurements improves. The most recent derived unit, the katal, was defined in 1999.
The reliability of the SI depends not only on the precise measurement of standards for the base units in terms of various physical constants of nature, but also on precise definition of those constants. The set of underlying constants is modified as more stable constants are found, or may be more precisely measured. For example, in 1983 the metre was redefined as the distance that light propagates in vacuum in a given fraction of a second, thus making the value of the speed of light in terms of the defined units exact.
The motivation for the development of the SI was the diversity of units that had sprung up within the centimetre–gram–second (CGS) systems (specifically the inconsistency between the systems of electrostatic units and electromagnetic units) and the lack of coordination between the various disciplines that used them. The General Conference on Weights and Measures (French: Conférence générale des poids et mesures – CGPM), which was established by the Metre Convention of 1875, brought together many international organisations to establish the definitions and standards of a new system and standardise the rules for writing and presenting measurements. The system was published in 1960 as a result of an initiative that began in 1948. It is based on the metre–kilogram–second system of units (MKS) rather than any variant of the CGS. Since then, the SI has been adopted by all countries except the United States, Liberia and Myanmar.Kilogram-force
The kilogram-force (kgf or kgF), or kilopond (kp, from Latin pondus meaning weight), is a gravitational metric unit of force. It is equal to the magnitude of the force exerted on one kilogram of mass in a 9.80665 m/s2 gravitational field (standard gravity, a conventional value approximating the average magnitude of gravity on Earth). Therefore, one kilogram-force is by definition equal to 9.80665 N. Similarly, a gram-force is 9.80665 mN, and a milligram-force is 9.80665 μN. One kilogram-force is approximately 2.204622 pound-force.
Kilogram-force is a non-standard unit and is classified in SI Metric System as a unit that is unacceptable for use with SI.Litre
The litre (international spelling) or liter (American spelling) (symbols L, l or ℓ) is an SI accepted metric system unit of volume equal to 1 cubic decimetre (dm3), 1,000 cubic centimetres (cm3) or 1/1,000 cubic metre. A cubic decimetre (or litre) occupies a volume of 10 cm×10 cm×10 cm (see figure) and is thus equal to one-thousandth of a cubic metre.
The original French metric system used the litre as a base unit. The word litre is derived from an older French unit, the litron, whose name came from Greek — where it was a unit of weight, not volume — via Latin, and which equalled approximately 0.831 litres. The litre was also used in several subsequent versions of the metric system and is accepted for use with the SI, although not an SI unit — the SI unit of volume is the cubic metre (m3). The spelling used by the International Bureau of Weights and Measures is "litre", a spelling which is shared by almost all English-speaking countries. The spelling "liter" is predominantly used in American English.One litre of liquid water has a mass of almost exactly one kilogram, because the kilogram was originally defined in 1795 as the mass of one cubic decimetre of water at the temperature of melting ice. Subsequent redefinitions of the metre and kilogram mean that this relationship is no longer exact.MKS system of units
The MKS system of units is a physical system of measurement that uses the metre, kilogram, and second (MKS) as base units.
Adopted in 1889, use of the MKS system of units succeeded the centimetre–gram–second system of units (CGS) in commerce and engineering. The metre and kilogram system served as the basis for the development of the International System of Units (abbreviated SI), which now serves as the international standard. Because of this, the standards of the CGS system were gradually replaced with metric standards incorporated from the MKS system.An advantage of MKS units is that since the derived units (like joules) are based on MKS units, using MKS units naturally gives answers in the appropriate SI unit. For example, the kinetic energy of an object is defined by 1/2 × mass × velocity2. If the calculation is done in MKS units of kilogram and meters per second then the result is in joules, the SI unit for energy. If the same calculation is done using CGS units the answer is in ergs (1 erg = 10−7 joules).
The exact list of units used in the MKS system changed over time. It incorporated base units other than the metre, kilogram, and second in addition to derived units. An incomplete list of the base and derived units appears below. Since the MKS system of units never had a governing body to rule on a standard definition, the list of units depended on different conventions at different times.
Cycle (This dimensionless quantity became synonymous with the term "cycle per second" as an abbreviation. This circumstance confused the exact definition of the term cycle. Therefore, the phrase "cycle per metre" became ill-defined. The cycle did not become an SI unit.)
Cycle per second
Cycle per metre (This measure of wavenumber became ill-defined due to the abbreviation of "cycle per second" as "cycle".)In 1901, Giovanni Giorgi proposed to the Associazione elettrotecnica italiana (AEI) that this system, extended with a fourth unit to be taken from the units of electromagnetism, be used as an international system.
This system was strongly promoted by electrical engineer George A. Campbell.Metre per second squared
The metre per second squared is the unit of acceleration in the International System of Units (SI). As a derived unit, it is composed from the SI base units of length, the metre, and time, the second. Its symbol is written in several forms as m/s2, m·s−2 or m s−2, or less commonly, as m/s/s.As acceleration, the unit is interpreted physically as change in velocity or speed per time interval, i.e. metre per second per second and is treated as a vector quantity.Metric system
The metric system is an internationally recognised decimalised system of measurement. It is in widespread use, and where it is adopted, it is the only or most common system of weights and measures (see metrication). It is now known as the International System of Units (SI). It is used to measure everyday things such as the mass of a sack of flour, the height of a person, the speed of a car, and the volume of fuel in its tank. It is also used in science, industry and trade.
In its modern form, it consists of a set of base units including metre for length, kilogram for mass, second for time and ampere for electrical current, and a few others, which together with their derived units, can measure any physical quantity. Metric system may also refer to other systems of related base and derived units defined before the middle of the 20th century, some of which are still in limited use today.
The metric system was designed to have properties that make it easy to use and widely applicable, including units based on the natural world, decimal ratios, prefixes for multiples and sub-multiples, and a structure of base and derived units. It is also a coherent system, which means that its units do not introduce conversion factors not already present in equations relating quantities. It has a property called rationalisation that eliminates certain constants of proportionality in equations of physics.
The units of the metric system, originally taken from observable features of nature, are now defined by phenomena such as the microwave frequency of a caesium atomic clock which accurately measures seconds. One unit, the kilogram, remains defined in terms of a man-made artefact, but scientists recently voted to change the definition to one based on Planck's constant via a Kibble balance. The new definition is expected to be formally propagated on 20 May 2019.
While there are numerous named derived units of the metric system, such as watt and lumen, other common quantities such as velocity and acceleration do not have their own unit, but are defined in terms of existing base and derived units such as metres per second for velocity.
Though other currently or formerly widespread systems of weights and measures continue to exist, such as the British imperial system and the US customary system of weights and measures, in those systems most or all of the units are now defined in terms of the metric system, such as the US foot which is now a defined decimal fraction of a metre.
The metric system is also extensible, and new base and derived units are defined as needed in fields such as radiology and chemistry. The most recent derived unit, the katal, for catalytic activity, was added in 1999. Recent changes are directed toward defining base units in terms of invariant constants of physics to provide more precise realisations of units for advances in science and industry.Mole (unit)
The mole is the base unit of amount of substance in the International System of Units (SI). Effective 20 May 2019, the mole is defined as the amount of a chemical substance that contains exactly 6.02214076×1023 (Avogadro constant) constitutive particles, e.g., atoms, molecules, ions or electrons.This definition was adopted in November 2018, revising its old definition based on the number of atoms in 12 grams of carbon-12 (12C) (the isotope of carbon with relative atomic mass 12 Da by definition). The mole is an SI base unit, with the unit symbol mol.
The mole is widely used in chemistry as a convenient way to express amounts of reactants and products of chemical reactions. For example, the chemical equation 2H2 + O2 → 2H2O can be interpreted to mean that 2 mol dihydrogen (H2) and 1 mol dioxygen (O2) react to form 2 mol water (H2O). The mole may also be used to represent the number of atoms, ions, or other entities in a given sample of a substance. The concentration of a solution is commonly expressed by its molarity, defined as the amount of dissolved substance per unit volume of solution, for which the unit typically used is moles per litre (mol/l), commonly abbreviated M.
The term gram-molecule was formerly used for essentially the same concept. The term gram-atom has been used for a related but distinct concept, namely a quantity of a substance that contains an Avogadro's number of atoms, whether isolated or combined in molecules. Thus, for example, 1 mole of MgBr2 is 1 gram-molecule of MgBr2 but 3 gram-atoms of MgBr2.Newton (unit)
The newton (symbol: N) is the International System of Units (SI) derived unit of force. It is named after Isaac Newton in recognition of his work on classical mechanics, specifically Newton's second law of motion.
See below for the conversion factors.Newton second
The newton second (also newton-second, symbol N s or N·s) is the derived SI unit of impulse. It is dimensionally equivalent to the momentum unit kilogram metre per second (kg·m/s). One newton second corresponds to a one-newton force applied for one second.
It can be used to identify the resultant velocity of a mass if a force accelerates the mass for a specific time interval.Planck constant
The Planck constant (denoted h, also called Planck's constant) is a physical constant that is the quantum of electromagnetic action, which relates the energy carried by a photon to its frequency. A photon's energy is equal to its frequency multiplied by the Planck constant. The Planck constant is of fundamental importance in quantum mechanics, and in metrology it is the basis for the definition of the kilogram.
At the end of the 19th century, physicists were unable to explain why the observed spectrum of black body radiation, which by then had been accurately measured, diverged significantly at higher frequencies from that predicted by existing theories. In 1900, Max Planck empirically derived a formula for the observed spectrum. He assumed that a hypothetical electrically charged oscillator in a cavity that contained black body radiation could only change its energy in a minimal increment, E, that was proportional to the frequency of its associated electromagnetic wave. He was able to calculate the proportionality constant, h, from the experimental measurements, and that constant is named in his honor. In 1905, the value E was associated by Albert Einstein with a "quantum" or minimal element of the energy of the electromagnetic wave itself. The light quantum behaved in some respects as an electrically neutral particle, as opposed to an electromagnetic wave. It was eventually called a photon. Max Planck received the 1918 Nobel Prize in Physics "in recognition of the services he rendered to the advancement of Physics by his discovery of energy quanta".
Since energy and mass are equivalent, the Planck constant also relates mass to frequency. By 2017, the Planck constant had been measured with sufficient accuracy in terms of the SI base units, that it was central to replacing the metal cylinder, called the International Prototype of the Kilogram (IPK), that had defined the kilogram since 1889. The new definition was unanimously approved at the General Conference on Weights and Measures (CGPM) on 16 November 2018 as part of the 2019 redefinition of SI base units. For this new definition of the kilogram, the Planck constant, as defined by the ISO standard, was set to 6.62607015×10−34 J⋅s exactly. The kilogram was the last SI base unit to be re-defined by a fundamental physical property to replace a physical artefact.SI base unit
The International System of Units (SI = Systeme Internationale) defines seven units of measure as a basic set from which all other SI units can be derived. The SI base units and their physical quantities are the metre for measurement of length, the kilogram for mass, the second for time, the ampere for electric current, the kelvin for temperature, the candela for luminous intensity, and the mole for amount of substance.
The SI base units form a set of mutually independent dimensions as required by dimensional analysis commonly employed in science and technology.
The names and symbols of SI base units are written in lowercase, except the symbols of those named after a person, which are written with an initial capital letter. For example, the metre (US English: meter) has the symbol m, but the kelvin has symbol K, because it is named after Lord Kelvin and the ampere with symbol A is named after André-Marie Ampère.
Several other units, such as the litre (US English: liter), are formally not part of the SI, but are accepted for use with SI.SI derived unit
SI derived units are units of measurement derived from the seven base units specified by the International System of Units (SI). They are either dimensionless or can be expressed as a product of one or more of the base units, possibly scaled by an appropriate power of exponentiation.
The SI has special names for 22 of these derived units (for example, hertz, the SI unit of measurement of frequency), but the rest merely reflect their derivation: for example, the square metre (m2), the SI derived unit of area; and the kilogram per cubic metre (kg/m3 or kg m−3), the SI derived unit of density.
The names of SI derived units, when written in full, are in lowercase. However, the symbols for units named after persons are written with an uppercase initial letter. For example, the symbol for hertz is "Hz"; but the symbol for metre is "m".Specific energy
Energy density has tables of specific energies of devices and materials.Specific energy is energy per unit mass. (It is also sometimes called "energy density," though "energy density" more precisely means energy per unit volume.) It is used to quantify, for example, stored heat and other thermodynamic properties of substances such as specific internal energy, specific enthalpy, specific Gibbs free energy, and specific Helmholtz free energy. It may also be used for the kinetic energy or potential energy of a body. Specific energy is an intensive property, whereas energy and mass are extensive properties.
The SI unit for specific energy is the joule per kilogram (J/kg). Other units still in use in some contexts are the kilocalorie per gram (Cal/g or kcal/g), mostly in food-related topics, watt hours per kilogram in the field of batteries, and the Imperial unit BTU per pound (BTU/lb), in some engineering and applied technical fields.The concept of specific energy is related to but distinct from the chemical notion of molar energy, that is energy per mole of a substance, which uses units of energy per mole, such as J/mol, kJ/mol, or the older (but still widely used) kcal/mol.Torque
Torque, moment, or moment of force is the rotational equivalent of linear force. The concept originated with the studies of Archimedes on the usage of levers. Just as a linear force is a push or a pull, a torque can be thought of as a twist to an object. The symbol for torque is typically , the lowercase Greek letter tau. When being referred to as moment of force, it is commonly denoted by M.
In three dimensions, the torque is a pseudovector; for point particles, it is given by the cross product of the position vector (distance vector) and the force vector. The magnitude of torque of a rigid body depends on three quantities: the force applied, the lever arm vector connecting the origin to the point of force application, and the angle between the force and lever arm vectors. In symbols:
The SI unit for torque is N⋅m. For more on the units of torque, see Units.
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with special names
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