Kilogram

The kilogram (symbol: kg), is the base unit of mass in the International System of Units (SI). It is a measurement widely used in science, engineering, and commerce around the world, and is often simply called a kilo in everyday speech.

It is the only basic unit that uses a prefix and the last SI unit that continued to be defined by a standard object and not by a fundamental physical characteristic. On May 20, 2019, its definition became linked to the constant of Planck, a natural constant that describes the packets of energy emitted in the form of radiation. This allows a properly equipped metrology laboratory to calibrate a mass measuring instrument such as a power balance.

Kilogram definition

The official definition of the kilogram, according to the General Conference on Weights and Measures, is:

"The kilogram, symbol kg, is the SI unit of mass. It is defined by setting the numerical value of the Planck constant, h{displaystyle h}Like, 6.626 070 15 × 10⁻³⁴ expressed J·s (julios per second), unit equal to kg·m2·s⁻¹where the metro and the second are defined according to c (light in the void) and Δ._Cs (during the second atomic). »

Of the exact relationship h{displaystyle h}=6.626 070 15·10⁻³⁴ kg·m2·s^-1 you get the unit kg·m2·s^-1 (the unity of physical quantities action and angular moment) and of this the expression for the kilogram according to the value of the Planck constant, h{displaystyle h}:

1kg=(h6.62607015× × 10− − 34)m− − 2s{displaystyle 1{text{kg}}=left({frac {h}{6.62607015times 10^{-34}}}{right){text{m}}}{-2}{text{s}}}}}

Hence, along with the definitions of the second and the subway, the definition of the mass unit is obtained according to the three constants h{displaystyle h}, Δ._Cs and c{displaystyle c}:

1kg=(299792458)2(6.62607015× × 10− − 34)(9192631770)hΔ Δ .. Csc2≈ ≈ 1.4755214× × 1040hΔ Δ .. Csc2{displaystyle 1{text{kg}}={frac {left(299792458right){2}{2}{left(6.62607015times 10^{-34}{right)left(9192631770right)}{frac {hcHFFFFFF}{cHFFFF}{cHFFFFFFFFFFFFFFFFFFFF}{c}{c}{cHFF}{cHFFFFFFFFFF}{cHFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF}{c}{c}{c}{c}{cHFFFFFFFFFFFFFFFFFFFFFFFFFF}{cHFF}{cHFFFF}{c}{c}{c}{cHFF}{cHFFFFFFFFFFFFFFFFFFFFFFFFFFFFFF}{cHFFFFFF}{c}{

History of previous definitions

The first definition, decided upon in 1795 during the French Revolution, specified that the gram was the mass of one cubic centimeter of pure water at the melting point of ice (approximately 4 °C). This definition was difficult to make exactly, because the density of water is slightly dependent on pressure, so the melting point of ice did not have an exact value.

In 1875, the Meter Convention is signed, leading to the production of the International Prototype of the Kilogram in 1879 and its adoption in 1889. This prototype was made of an alloy of platinum and iridium —in a ratio of 90-10 %, respectively, measured by weight—in the form of a right circular cylinder, with a height equal to the diameter of 39 millimeters. It had a mass equal to the mass of 1 dm³ of water at atmospheric pressure and at the temperature of its maximum density, which is about 4 °C. This prototype is kept at the International Bureau of Weights and Measures, located in Sèvres, near Paris, France. This international prototype is one of three cylinders originally made in 1879. In 1883 the prototype proved to be indistinguishable from the mass. of the kilogram standardized at the time, and was formally ratified as the kilogram at the first General Conference on Weights and Measures in 1889.

By definition, the error in the measurement of the mass of the International Prototype of the Kilogram was exactly zero, since the International Prototype of the Kilogram was the kilogram. However, over time small changes have been detected by comparing the standard against its official copies. By comparing the relative masses between the standards over time the stability of the standard is estimated. The international prototype for the kilogram appeared to have lost about 50 micrograms in the last 100 years, and the reason for the loss remains unknown.

Pattern redefinition

The balance of Watt NIST-4, which began to operate in early 2015 at the National Institute of American Standards and Technology in Gaithersburg (Maryland), which measured Planck's constant with a precision of 13 parts per billion in 2017, which was accurate enough to help with the redefinition of the kilogram.

130 years after its implantation, efforts began to define the kilogram pattern through physical properties that did not vary over time. Two main avenues of investigation were established. The first was to base the definition on the atomic mass of silicon. For this, it was necessary to set the value of Avogadro's number and count the exact number of atoms present in a silicon sphere, almost perfect in its geometry and isotopic composition, whose dimensional characteristics can be known with great accuracy. Specifically, the volume occupied by the sphere and each of its atoms would be determined, and finally, with Avogadro's number, the mass would be determined.

The other alternative was to fix the value of the electron load or the constant of Planck, which relates the energy and frequency of an electromagnetic wave by means of expression E=h.. {displaystyle E=hnu } and can be described as the energy unit emitted in electromagnetic interactions. The relationship between energy and mass is given by the equation determined by Einstein E=mc2{displaystyle E=mc^{2}}. To obtain a precise definition of the kilogram, the value of h{displaystyle h} It was to be determined by several measurements with different equipment; the values obtained should have a standard deviation that did not exceed five parts by one hundred million and match between them with a confidence value of 95%. To this end, several national metrology institutes worked on the set-up of a device developed by Bryan Kibble of the British National Physical Laboratory, called Kibble scale, also called Watt or Watt scale, because the watt (watt In English) is the unity of the magnitude with which a mechanical power is compared with an electric power. Kibble's balance establishes the relationship between a mass, the acceleration of gravity, a speed, two frequencies, and Planck's constant.

At the beginning of 2011, shortly before the celebration of the 24th General Conference on Weights and Measures, a consensus was found that the method to be used would be that of Planck's constant. In 2017 several laboratories obtained measurements of the constant that satisfied the requirements of the International Bureau of Weights and Measures. On November 16, 2018, the 26th General Conference on Weights and Measures announced that the definition of the kilogram would become tied to Planck's constant. In this way, the different kilogram standards spread throughout the world can be calibrated using a Kibble scale and the new value of the constant. The new definition entered into force on May 20, 2019, leaving the "Grand Kilo » —the Parisian standard— as a secondary mass standard. Planck's constant came to be defined as 6.62607015×10−34 kg⋅m²⋅s−1, leaving the kilogram defined from this and, consequently, from of two other basic units of the YES, the second and the meter.

The previous definition set the value of the mass of the international prototype of the kilogram as exactly equal to one kilogram, and the value of the Planck constant h{displaystyle h} was piloted, with associated uncertainty. The current definition sets the exact numerical value h{displaystyle h} and it is the mass of the prototype that inherits its uncertainty (1 x 10⁻⁸), to be determined from now on experimentally. This same occurs for the rest of the units.

Name and terminology

The kilogram is the only base SI unit with an SI (kilo) prefix as part of its name. The word kilogramme or kilogram derives from the French kilogramme, which in turn was a learned coinage, by prefixing the Greek root khilioi from χίλιοι khilioi 'thousand' to gramma, a Late Latin term for 'a small weight', itself from Greek γράμμα gramma. The word kilogram was introduced into French law in 1795, in the Decree of Germinal 18, which revised the provisional system of units introduced by the French National Convention two years earlier, in which the gravet had been defined as the weight of a cubic centimeter of water, equivalent to 1/1000 of a grave.

The French spelling was adopted in Great Britain when the word was first used in English in 1795, and the kilogram spelling was adopted in the United States. Both spellings are used in the UK, with "kilogram" the most common by far. British legislation governing the units to be used in trade by weight or measure does not prevent the use of either spelling.

In the 19th century, the French word kilo, an abbreviation of kilogramme, became imported into the English language, where it has been used to mean both kilogram and kilometer. While kilo as an alternative is acceptable, for The Economist, for example, the Canadian government's Termium Plus system states that "the use of the SI (International System of Units), followed in scientific and technical writing" disallows its use and is described as "a common informal name" in Russ Rowlett's Dictionary of Units of Measurement. When the The United States Congress granted the metric system legal status in 1866, allowed the use of the word kilo as an alternative to the word kilogram, but in 1990 revoked the status of the word kilo.

The SI system was introduced in 1960, and in 1970 the International Bureau of Weights and Measures (BIPM) began publishing the SI Pamphlet, which contains all relevant decisions and recommendations of the General Conference on Weights and Measures (CGPM).) relative to units. The SI pamphlet states that "it is not permitted to use abbreviations for unit symbols or unit names...", so it is not correct to use the abbreviation "kilo" to refer to the kilogram.

The kilogram becomes a basic unit: role of units for electromagnetism

The kilogram, rather than the gram, was eventually adopted as the basic SI unit of mass, mainly because of the units for electromagnetism. The series of relevant debates and decisions began in about the 1850s and effectively concluded in 1946. In short, at the end of the 19th century, the "practical units" for electrical and magnetic quantities, such as the ampere and the volt, were well established in practice (for example, for telegraphy). Unfortunately, they were not consistent with the basic units of length and mass then in force, the centimeter and the gram. However, "practical units" also included some purely mechanical units; in particular, the product of the ampere and the volt gives a purely mechanical unit of power, the watt. It was observed that purely mechanical practical units, such as the watt, would be consistent in a system in which the base unit of length was the meter and the base unit of mass was the kilogram. In fact, since no one wanted to replace the second as the base time unit, the meter and kilogram are the only pair of base units of length and mass that allow:

1. that the watt is a coherent power unit,
2. that the base units of length and time are full power relations of ten with the meter and the gram (so that the system remains "metric"), and
3. that the sizes of the base units of length and mass are suitable for practical use.

This would leave out purely electrical and magnetic units: while purely mechanical practical units, like the watt, are consistent in the meter-kilogram-second system, explicitly electrical and magnetic units, like the volt, ampere, etc., they are not. The only way to make those units also consistent with the meter-kilogram-second system is to modify that system in another way: You have to increase the number of fundamental dimensions from three (length, mass, and time) to four (the three above)., plus a purely electric one).

The state of electromagnetism units at the end of the 19th century

During the second half of the XIX century, the centimeter-gram-second system of units was imposed for work scientific, treating the gram as the base unit of mass and the kilogram as a decimal multiple of the base unit formed by the use of a metric prefix. However, as the century drew to a close, there was widespread discontent with the status of the units for electricity and magnetism in the CGS system. To begin with, there were two obvious choices for the absolute units of electromagnetism: the "electrostatic" system (CGS-ESU) and the "electromagnetic" system (CGS-EMU). But the main problem was that the sizes of the coherent electric and magnetic units were not suitable in any of these systems; for example, the ESU unit of electrical resistance, later called the statohm, corresponds to about 9×10¹¹ ohms, while the EMU unit, later called the abohm, corresponds to 10⁻⁹ ohms. For quite some time, the ESU and EMU units did not have special names; one would only say, for example, the resistance unit ESU. Apparently, it was only in 1903 that AE Kennelly suggested that the names of the EMU units be derived by preceding the name of the 'practical unit' with the name of the 'practical unit'. corresponding by 'ab-' (abbreviation of 'absolute', giving the 'abohm', 'abvolt', the 'abampere', etc.), and that the names of ESU units are obtained analogously using the prefix 'abstat-', later shortened to 'stat-' (giving the 'statohm', 'statvolt' 'statampere', etc.). This naming system was widely used in the United States, but, apparently, not in Europe.

To get around this difficulty, a third set of units was introduced: the so-called practical units. Practical units were derived as decimal multiples of CGS-EMU consistent units, chosen so that the resulting quantities are convenient for practical use and so that the practical units are as consistent as possible with each other. Practical units included such units as the volt, ampere, ohm, etc. In fact, the main reason the meter and kilogram were later chosen as the base units of length and mass was that they are the only combination of multiples or submultiples Reasonably sized decimals of the meter and gram that can be consistent with the volt, ampere, etc.

The reason is that electrical quantities cannot be isolated from mechanical and thermal ones: they are connected by relationships such as "current × electric potential difference = power". For this reason, the practical system also includes consistent units for certain mechanical quantities. For example, the above equation implies that the "ampere × volt" is a coherent practical unit derived from power; this unit was called a watt. The coherent unit of energy is then the watt per second, which is called the joule. The joule and watt also have convenient magnitudes and are decimal multiples of the CGS coherent units for energy, erg, and power (erg per second). The watt is not consistent in the centimeter-gram-second system, but it is consistent in the meter-kilogram-second system and in no other system whose base units of length and mass are reasonably sized decimal multiples or submultiples of the meter and of the meter. gram.

However, unlike the watt and the joule, the explicitly electrical and magnetic units (the volt, the ampere…) are not coherent even in the (absolute three-dimensional) meter-kilogram-second system. Indeed, one can calculate what the basic units of length and mass must be so that all practical units are coherent (the watt and the joule, as well as the volt, the ampere, etc.). The values are: 10⁷ meters (half an Earth meridian, called a quadrant) and 10⁻¹¹ grams (called an eleventh gram).

Therefore, the complete absolute system of units in which practical electrical units are consistent is the quadrant-eleventh-gram-second (QES) system. However, the extremely inconvenient magnitudes of the base units for length and mass meant that no one seriously considered adopting the QES system. Thus, people working on practical applications of electricity had to use units for electrical quantities and for energy and power that were not consistent with the units they used for, for example, length, mass, and force..

Meanwhile, scientists developed another fully coherent absolute system, which came to be called the Gaussian system, in which the units for purely electrical quantities are taken from the CGE-ESU, while the units for magnetic quantities are taken from of the CGS-EMU. This system proved very convenient for scientific work and is still widely used. However, their unit sizes were still too large or too small—by many orders of magnitude—for practical applications.

Lastly, in addition to all this, in both CGS-ESU and CGS-EMU, as well as in the Gauss system, Maxwell's equations are "unrationalized", which means they contain several factors of 4π that many workers found it uncomfortable. So another system was developed to rectify this: the "rationalized" Gaussian system, usually called the Lorentz-Heaviside system. This system is still used in some subfields of physics. However, the units of that system are related to the Gaussian units by factors of √4π ≈ 3.5, which means that their magnitudes were still, like those of the Gaussian units, too large or too small for practical applications.

Giorgi's proposal

In 1901, Giovanni Giorgi proposed a new system of units that would remedy this state of affairs. He observed that practical mechanical units like the joule and the watt are consistent not only in the QES system, but also in the meter-kilogram-second (MKS) system. Of course, it was known that simply adopting the meter and the kilogram as base units - obtaining the three-dimensional system MKS - would not solve the problem: while the watt and the joule would be coherent, the volt, the ampere, the joule would not. ohm and the rest of the practical units for electrical and magnetic quantities (the only three-dimensional absolute system in which all practical units are consistent is the QES system).

But Giorgi pointed out that the volt and the rest could be coherent if we abandoned the idea that all physical quantities must be expressible in terms of the dimensions of length, mass, and time, and admitted a fourth base dimension for the electrical magnitudes. Any practical electrical unit could be chosen as the new fundamental unit, independent of the meter, the kilogram, and the second. The most likely candidates for the fourth independent unit were the coulomb, the ampere, the volt, and the ohm, but ultimately the ampere turned out to be the most suitable for metrology. Furthermore, the freedom gained by separating an electrical unit from mechanical units could be used to rationalize Maxwell's equations.

The idea that one had to give up having a purely “absolute” system, that is, one in which only length, mass, and time are the basic dimensions, was far from the point of view that seemed to underlie early advances by Gauss and Weber (especially their famous "absolute measurements" of the Earth's magnetic field), and it took some time for the scientific community to accept it, mainly because many scientists clung to the idea that the dimensions of a quantity in terms of length, mass, and time they somehow specify its "fundamental physical nature."

Gram

The gram is the term to which the SI prefixes apply. The reason why the basic unit of mass has a prefix is historical. Originally, the formation of a decimal system of units was commissioned by Louis XVI of France and, in the original plans, the kilogram equivalent was called "grave". Along with grave, a smaller unit called gravet, which was equivalent to 0.001 kg (1 gram), as well as a larger unit called bar, which was equivalent to 1000 kg (1 ton) With these measurements the following scale was created: milligravet, centigravet, decigravet, gravet (gr), centigrave, decigrave, grave (kg), centibar, decibar, bar (t). However, the metric system did not enter into force until after the French Revolution.

In 1795 a new law replaced the three names (gravet, grave and bar) by a single generic unit name: the gram. The new gram was equal to the old gravet. Four new prefixes were added to cover the same range of units as in 1793 (milligram, centigram, decigram, gram, decagram, hectogram, kilogram, and myriagram). The gram was also the base unit of the older system of measurement: the CGS system, which is not very widely used.

Others

It is also common for the word to be used as a unit of force in the Technical System of Units, although it must be done under the name of kilogram-force or kilopond. The kilogram force or kilopond is, by definition, the weight of a mass of 1 kilogram in standard gravity on the earth's surface; that is, 9.80665 m/s². That is why a mass of 1 kilogram (International System of Units) weighs 1 kilogram of force (Technical System) only if gravity has that value.

Multiples and submultiples

Equivalences

1 kilogram is equivalent to:

• 1 000 000 mg
• 100 000 cg
• 10 000 dg
• 1000 g
• 100 dag
• 10 hg
• 0.1 mag
• 0.01 q
• 0.001 t