Encyclopaedia of the seven Basic SI Units

Definitions and information about all metric base units.

 

The seven basic SI units are the base units for all measurement units worldwide. Every single weight and measure, historic or current, can be converted back into the seven units listed below.

The definitions of the seven basic measurement units are very precise to meet the highest possible scientific standards. For common usage, the definitions have little practical meaning. Measurement units are visualised as a reference in relation to familiar sizes, weights, time spans, etc. Usually, remembering just two to four points of reference is fully sufficient for being familiar with a unit. For example, it tends to be more useful to know that a meter is a pace and that the width of a hand is ten centimeters than to know the scientific definition of a meter.

 

Go to: Ampere, candela, kelvin, kilogram, meter, mole, second.

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This definition makes it possible for scientists to calibrate measuring equipment. However, in order to understand what an ampere actually measures, it is helpful to look at the current that is producing the force mentioned in the above definition:

 

Current is a flow of electrical-charge carriers, usually the elementary particle electron. The electric charge or amount of electricity is measured in coulomb. One coloumb represents the elctricla charge carried by 6.241 506 × 10¹⁸ electrons (6.2 quintillion or 6 241 506 000 000 000 000).

Ampere is used to measure the electric flow or electric current – how much electricity passes through over time. The flow of electrons (or other electrical-charge carriers like electron-deficient atoms) is an electric current.

The electric current is the quotient of the electric charge flowing through a conductor (for example a power cable) and the time needed for this charge to pass through. Consequently, one ampere is equivalent to one coulomb (unit for electric charge) per second (1 A = 1 C / s).

One coulomb represents the electrical charge that is carried by 6.241 506 × 10¹⁸ electrons (6.2 quintillion or 6 241 506 000 000 000 000). One ampere means that this particular charge of one coulomb is moving past a specific point (for example in a power cable) in a second.

When a power cable in a household carries an electric current of 16 A, 99.86 quintillion electrons are moving through the cable each second.

 

Analogy between water and electricity

The above can be illustrated using a simple comparison: Coulombs are used to measure an electric charge or quantity of electricity, similar to measuring the amount or volume of water in litres. Litres help measure the quantity of water, for example in a bucket.

When moving water is measured, for example in a water pipe, river or streaming out of a water tap, the flow rate tells us how much water passes through over time. A water flow rate of 0.5 litres per second means that a 5 litre bucket can be filled in ten seconds.

The flow rate of water is measured in litres per second, which is comparable to amperes. Amperes are used to measure coulombs per second.

A flow rate or electric current of one ampere means that one coloumb (or 6.2 quintillion electrons) are passing through in one second.

 

 

All other electrical units in the metric system (and there are many) are defined in terms of the ampere.

Some examples: One ampere of current results from a power production of 1 watt per 1 volt of electric potential difference (1 A = 1 W / V). One ampere of current also results from a potential distribution of 1 volt per 1 ohm of resistance (1 A = V / Ω).

 

 

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The candela measures the intensity of light. The strength or power of a light or a light source could simply be measured in watts, but the candela also takes the human factor into account.

The definition of the candela sets the frequency of the emitted light to 540 terahertz. The definition uses a frequency, not a wavelength, to describe light of a certain colour. This was done because the wavelength of light can vary, depending on the medium the light travels through.

540 terahertz is equal to a wavelength of 555.016 nanometers in standard air. Light of this wavelength has a yellow-green colour. This light colour was chosen because the human eye is more sensitive to this wavelength than to any other. Other wavelengths appear less bright, even if the power of the light (in watts) is the same.

In order to determine the luminous intensity of light sources which emit other wavelengths, the relative sensitivity of the eye has to be taken into account. Depending on the relative sensitivity of the emitted wavelengths, the luminous intensity varies. Tables with values for the relative sensitivity at different wavelengths provide the basis for converting the luminous intensity back to the standard of 540 terahertz or 555.016 nanometers. These values, so-called “spectral luminous efficiency functions”, are maintained by the International Commission on Illumination (CIE). Naturally, infrared or ultraviolet light, which can not be seen by humans, is thus eliminated from any measurement.

Candelas therefore give a true picture of how bright the human eyes see light.

 

Candela measures the intensity of a beam of light

Measures for light are not always easy to understand, since the three-dimensional character of emitted light adds an additional layer of complexity. A light source usually radiates light in many directions; some light sources, like the sun, in all directions. The light emitted by the sun could be imagined like a growing sphere or ball with the sun at its centre.

Candelas do not measure the total light given out by a light source; only the light radiated in a certain direction. A candela measures only the luminous intensity in a part of that growing sphere of light coming from the light source.

The definition of the candela includes the angle which contains the measured light. This angle is three-dimensional (not two-dimensional such as measured by the familiar degree of arc) and its measurement unit is steradian. One steradian is about 8% of a sphere or ball. About 12.6 steradians (the exact number is 4 × π steradians) cover a complete sphere, just like 360° cover a full circle.

 

One candela therefore measures the amount of light given out through this angle of one steradian (about 8 % of a sphere). A light source has one candela if it emits 1/683 watt (about 1.46 milliwatts) of the defined light per steradian.

If the light source was emitting the same light uniformly in all directions, the total emission would be about 18.4 milliwatts (1.46 milliwatts times the number of steradians in a full ball).

To measure the total light emission of a light source, the unit lumen [lm] is used. If a light source is a very tiny point and emits light evenly in all directions, the formula 1 cd = 4 × π lm (≈ 12.6 lm) can be used to convert candela into lumen and vice versa.

The candela was chosen as the base unit of light instead of the lumen, because it can be measured with more accuracy.

History of the candela

The candela replaced the old unit “candle”, which attempted to quantify the light intensity of an actual candle. The magnitude of the candela was chosen to reflect the old “candle”.

 

When the candela was in the process of being added to the metric system, the name “new candle” was used. In 1948, when the new unit was officially added, the name “candela” was chosen to avoid any confusion with older units and to have the same unit name for all languages.

Candelas are also used to measure luminance

Luminance is measured in candelas per square meter (cd/m²). Luminance is the luminous intensity per area. This area could be clearly defined, like the size of a computer or TV screen, the display of a pocket calculator, a watch face or the transparent surface of a photo flash. It could also be the apparent or visible area of a distant object like the sun or moon. It does not matter whether the measured area is actually emitting light or just reflecting light. Luminance or candela per square meter actually measures how bright an object appears to the eye.

Luminance (candela per square meter) is different from the illuminance (measured in lumen per square meter or lux). It measures the apparent brightness of an object or area. Lux measures how much light an object or area receives. The main difference is the amount of light reflected by the object.

A black sheet of paper can receive the same amount of light as a white sheet (both give the same value in lux when illuminance is measured), but the white sheet will appear much brighter. When measuring the luminance, the white sheet will therefore give a much higher candela per square meter reading. Candela per square meter thus takes into account how much light an object reflects or absorbs.

 

 

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The kelvin is the basic unit of temperature in the metric system. In addition to kelvin, the metric system specifies another unit of temperature, the degree Celsius. More about the history of these two units can be found under the entry for degree Celsius. Kelvin is the basic unit and the definition of degree Celsius is derived from it, meaning that degree Celsius is defined in terms of the kelvin.

 

The temperature of a substance does not measure its heat content, but rather the average kinetic energy of its molecules, resulting from their motion. The hotter a substance gets, the faster the molecules it contains move around. As a substance cools, the molecule movements slow down. The point at which the molecule movements stop completely, is called absolute zero. This is the lowest possible temperature - the thermodynamic temperature is zero. By definition, nothing can be colder than absolute zero. Temperature scales, whose zero point is defined to correspond to this zero average kinetic energy, are called absolute temperature scales.

Kelvin is such a measurement of temperature that is based on the concept of the absolute zero temperature. By using absolute zero as the starting point of the kelvin temperature scale, negative temperatures can be avoided altogether (negative temperatures cause difficulties in certain calculations and comparisons). 0 kelvin is the lowest possible temperature in the universe.

 

Kelvin, like all temperature scales, measures the kinetic energy of molecules. The heat content or quantity of heat in a substance or an object is measured in joule. A one kilogram block of iron and a two kilogram block of iron at the same temperature do not have the same heat content. Because they are at the same temperature the average kinetic energy of the molecules is the same; however, the two kilogram block has more molecules than the one kilogram block and thus has greater heat energy.

 

Any temperature scale needs two reference points to be defined properly. In addition to absolute zero as the obvious starting point for the kelvin scale, the second reference point chosen is the so called triple point of water.

The triple point of any substance is that temperature and pressure at which the material can coexist in all three phases (solid, liquid and gas) in equilibrium. There is only one temperature that allows water to exist in all three of its forms as ice, steam and liquid at the same time. This temperature is set by the above definition to 273.16 K.

The pressure needed to achieve this thermal equilibrium or the triple point of water is about 611 pascals. Even a tiny change in temperature or pressure will cause the equilibrium to disappear. This makes it easy to tell when the triple point is reached, and the definition of the kelvin therefore provides an excellent calibration point for thermometers and a good reference point for a temperature scale. Another advantage of this definition is that pressure need not be specified.

By the above definition, 1 kelvin is the fraction 1/273.16 of the triple point of water. This odd fraction has been chosen to make conversions between the much older degrees Celsius temperature scale and kelvin as easy as possible. The degrees Celsius scale and the kelvin scale are simply shifted against each other, the magnitude of the increment of one degree Celsius and one kelvin are identical. Conversions between the two scales involve only the subtraction or addition of 273.15, to arrive at the other scale. If the division of the degrees of the degrees Celsius had not been maintained, the conversion would have had to be more complicated.

To convert kelvins into degrees Celsius: subtract 273.15.

To convert degrees Celsius into kelvins: add 273.15.

The conversion factor is 273.15, not 273.16 as might be read from the definition of the kelvin scale because the original definition of the degree Celsius was based on the ice point or freezing point of water (the point at which liquid water and ice can coexist indefinitely) at standard atmospheric pressure, which is 0.01 °C lower than the triple point of water. The ice point of water is 0 °C, the triple point is 0.01 °C. In the kelvin scale, the ice point is at 273.15 K and the triple point is at 273.16 K.

To this day, both the kelvin and degree Celsius scale remain units of the official metric system. They can both be used for measuring temperature. Kelvin tends to be used only by scientists working with temperatures below 0 °C. For nearly all other purposes degrees Celsius is used.

 

Before the definition was updated in 1967, this unit was named degree Kelvin.

 

                                                                                             

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The kilogram was originally defined as the mass of one liter of water at the freezing point. One liter was defined as a cubic decimeter (a cube that measures 10 cm by 10 cm by 10 cm). Because it proved to be difficult to measure the mass of a defined volume of water under standard conditions, a prototype of the kilogram was constructed and its mass taken to be the definition of the kilogram. This platinum prototype was deposited into the Archives of the French Republic on 22 June 1799. The prototype then became the definitive standard for the kilogram.

Today’s international prototype is a platinum-iridium cylinder kept at the BIPM (International Office for Weights and Measures) at Sevres in France. The kilogram is now the only basic unit still defined in terms of a material object, and the only one with a prefix [kilo] already in place. Other prefixes are used with the word gram, not added to the name kilogram.

After the prototype of the kilogram was made in the late 18^th century, it turned out to be about 0.002 8 % heavier than the mass of one liter of water (either the kilogram was too heavy or the liter was too small). One liter of water (at 4 °C, under standard atmospheric pressure) actually weighs 0.999 972 kg; one kilogram of water occupies a volume of 1.000 028 liter. However, the mass of the kilogram was never changed from the original prototype, as it is one of the basic rules of the metric system that a unit must never change its magnitude.

A possible new definition of the kilogram?

The current definition of the kilogram as an actual piece of metal is a problem since tiny mass changes of this object do seem to occur over time. These changes in weight can not be satisfactorily explained. It appears that the kilogram prototype lost about 50 micrograms over the 20^th century.

Scientists are looking into possible newer definitions of the kilogram, which could ensure greater precision, stability over long periods of time and reproducibility in laboratories.

However, a satisfactory definition that could replace the prototype and meet all requirements still has not been found. Possible solutions for a better definition could be defining a piece of a monocrystaline structure, such as silicon, by dimension or to use an exact number of molecules or atoms. If one of these concepts were to be used in the future, the definitions of the base units kilogram and mole might become linked to each other.

Three options for a new kilogram-definition

§         An exact number of silicon atoms (21.507 626 4 ∙ 10²⁴ silicon atoms could be the definition) or a perfectly round silicon ball of a defined size.

§         An exact number of gold atoms.

§         Definition by electromagnetic force.

With current technology, none of these different approaches has achieved the accuracy and precision of the present definition that links the kilogram to a prototype. The number of silicon atoms could be higher a lower by a few trillion; the so-called watt balance that compares the mass of the kilogram against an electromagnetic force is affected by even the tiniest changes in gravity.

That’s why the definition of the kilogram has not yet changed. The decrease in mass over time is currently seen as less of a problem than the difficulties associated with the proposed new definitions.

 

 

Another unit for mass is the tonne, which equals 1 000 kg. Usually, the tonne is used for measures larger than about 1 000 kg, instead of megagrams, gigagrams, etc.

 

 

 

 

 

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Measurements of length are probably the most common in life and therefore the most important. The meter was the original measure of the metric system and gave the system its name.

 

Early History of an universal measure

The desire for a universal measure “for all people, for all time” was voiced by many scientists and philosophers throughout history. One of the ideas was to replace arbitrary human measures (such as the foot of one particular king, the shoe sizes of randomly chosen people) with a measure derived from nature, from creation itself. However, the strongest reason for creating a new, universal measure was the fact that it was impossible for rulers and people at the time to agree on a standard existing measure. If three countries have a measure called “foot” and each of the three feet was different in length, how could a consensus be achieved? It has never been human nature for two of the three countries to change their laws to converge with the standard of a third country and bear the cost of the change, even if all three countries would have benefited. Creating a new, international measure was the only way forward, the only option for replacing local measures.

This universal measure would cut confusion and help trade, communication, science and understanding between people and nations. For example, the Royal Society of Britain proposed in 1660 such a measure to be based on the length of a pendulum that completes one oscillation in one second. This was also suggested by Thomas Jefferson (1743–1826), later president of the USA, in 1790 and Christopher Wren (1632–1723).

Another concept on defining the universal measure was suggested as early as 1670 by the French mathematician Gabriel Mouton (1618–1694). He wanted to base the meter on the dimensions of the earth, namely its circumference. Estimates and calculations of the earth’s circumference were available, so that a convenient and easy relationship between the meter and the earth could be found. Obviously, the basic measure needed to be of a size convenient for human requirements.

The name meter had been in discussion since 1675, when the Italian-Polish scientist Tito Livio Burattini (1617–1681) published a book suggesting that this unit (from the Greek word “metron”, meaning measure) should be used by “all civilized people on earth despite differences in languages and custom”.

Original definition of the meter

After the French revolution in 1789, the new democracy decided to introduce such a new, universal measure. French scientists, like their colleagues in other European countries had been considering a new, universal measuring system for years. At the same time, measurements and science became ever more precise. Science, especially the geographers, needed a trusted basis of measurement. Trade and commerce were also greatly impeded by the bewildering array of measures, often with the same name, but describing different quantities. It has been estimated that in France alone, about 250 000 different measurement units were in use at the time. This situation was probably matched by an equal chaos in Germany and other countries. Even in countries where government was more centralized and less power was given to local authorities, the situation was confusing. Some quotations from British parliamentary reports from the 1800s illustrate the situation: “a chaldron of coals, at Newcastle, is fifty-two and a half hundred-weights; in London, about half as much…”; “a truss of old hay in London and Westminster is 56 pounds… A truss of straw, in Bristol, is seven pounds; in London, 36”. The situation in Britain was further complicated by three different sets of weights and measures, usually with identical names, but describing different quantities, being used at the same time (avoirdupois, troy and apothecary measures).

 On 26 March 1791, the French Academy of Sciences chose the standard of the meter to be the 10 000 000^th part of the distance from the equator to the North Pole (consequently, the total circumference of the earth across the poles should have been about 40 000 km). This standard won over the pendulum definition, since the slight variations in the force of gravity over the surface of the earth would have affected the length of the pendulum and thus the reproducibility of the meter in different countries. Other difficulties were the definition of a latitude where the pendulum standard should be measured and the varying durations of the second, as the second was by definition a part of the fluctuating solar day.

Another, more philosophical, reason for using the earth as a standard was that a measurement taken from earth itself would link the meter to creation, to God and humans themselves. Peasants measuring their land in meters should be able feel this connection to our earth. A measurement derived from nature itself would be less arbitrary than the old measures it was intended to replace. Thus it was part of the decision in 1790 to create a better measurement system that the basic measure, the length, should be taken from nature.

However, most scientists in countries such as Germany, Britain and the USA would have preferred the pendulum standard. This scientific disagreement initially impeded the acceptance of the meter outside of France.

The new metric system was codified in French law on 1 August 1793. This law defined a provisional meter, calculated by the three physicists Jean-Charles de Borda (1733–1799), Joseph Louis Lagrange (1736–1813) and Pierre-Simon Laplace (1749–1827). Their calculation was based on César-François Cassini de Thury’s (1714–1784) survey in 1740 and set the metre to be 443.44 lignes in the old Paris units (one ligne is an old French linear measure, equal to 1/12 of one pouce, which was the French version of the inch). In units of the later definitive meter, the provisional meter was about 1.000 324 839 meters long – a tiny bit longer (0,03 %) than today’s definitive meter.

Setting the length of the new meter in old units was not done for a love of the old units, but because the meridian standard was impractical as a legal standard and to have an interim measure before a final standard for the meter could be created. Based on this 443.44 ligne standard, an official provisional metre stick was constructed of copper by Etienne Lenoir (1744–1822) in 1793. For everyday measuring and to familiarize people with the new standard, metre sticks were mass-produced and supplied to citizens.

To determine the exact distance from the equator to the North Pole, the French Academy of Sciences commissioned a survey of the distance from Dunkirk in France to Barcelona in Spain. Motives for this costly exercise were the desire to have a footing for the new meter as sound as possible and the need to demonstrate to the international scientific community that the latest technology and highest possible precision was employed in arriving at the new meter standard. This was important, as the French scientists saw the meter as the beginning of a universal measure for all people and wanted to avoid it being defined by old French measures or standards.

The distance chosen for the survey, spanning nearly 10° (or 2.7 %) of the earth’s surface, was to give an indication of the earth’s circumference as exact as possible. It took two astronomers, Jean-Baptiste Delambre (1749–1822) and Pierre Méchain (1744–1804), six years, until 1798, to complete this task.

Their findings were reviewed by an international commission in 1799. This international commission – the first international scientific conference in history – was made up of those invited scientists from western European nations that had not been prevented by war to attend. Based on their findings, the final prototype of the meter was constructed by Lenoir in platinum and, on 22 June 1799, deposited into the Archives of the French Republic. In old units, the new definitive meter standard was 443.296 Paris lignes, replacing the provisional meter bar of 443.44 lignes. The new, definitive meter was thus 0,032 % shorter than the provisional meter.

For the first time in history, the world had a definitive and universal standard of length.

Measuring earth to find the first meter

Measuring the earth is very complex, since the earth is not a perfect sphere or ball. Earth bulges around the Equator and is flattened at the poles. The actual shape is uneven due to mountains and valleys. Measurements of circumference therefore need to be adjusted to a standard elevation, such as sea level. In the 1790s, it became clear that the distance between the North Pole and the Equator would depend on the meridian used to measure this distance. In other words, the distance from the North Pole to the Equator as measured through Greenwich is slightly different from the distance measured through Paris and even more different from other meridians further away. The French Academy of Science was aware of these issues. It was clearly not possible to arrive at a precise figure for the meter, but the objective was to find the best approximation possible at the time. Obviously, the definition of the meter as 1/10 000 000 of the distance North Pole-Equator also meant that the meter would not be exactly 1/40 000 000 of the earth’s circumference as the other three quarters of this circumference might have different lengths. Even the distance North Pole-Equator could not be physically measured in the 1790s - that is why the distance Dunkirk to Barcelona was chosen to give an indication of the full distance. Dunkirk–Barcelona is only about 11 % of the actual distance North Pole–Equator; the remainder had to be approximated.

Geodetic length measurements are based on calculations using the angles of triangles. For the survey of the distance between Dunkirk and Barcelona, a new instrument that could minimise measurement errors (the Borda circle for measuring angles) was used. Again, the scientists measuring the earth to determine the length of the meter were aware of the margin of error that is part of every measure. It was their task to minimise this error. In hindsight, they did a magnificent job.

According to the most current geodetic data (World Geodetic System of 1984; WGS 84), the actual polar circumference of earth is 40 007.863 km. The equatorial circumference is 40 075.017 km. These measurements were arrived at with a formula that defines the shape of the earth and the most accurate satellite data available. As in the 1790s, this data is only an approximation of the actual measures. However, the information according to WGS 84 is considered the best representation of earth today.

Comparing the data from 1798 and today, it is remarkable that today’s best data shows the polar circumference of earth to be 40 007.863 km – a difference of only 7.863 km or 0.019% to the theoretical measure of 40 000 km. If the meter was tied to earth’s circumference, it should be 1.000 196 575 m long or about 197 µm longer than our meter. This small difference shows the remarkable accuracy of triangulation in the 1790s.

Sometimes the meter is criticised for having been measured incorrectly. In my opinion, it is hard to see how scientists of the 18th century could have achieved a higher degree of accuracy. However, the accuracy in determining the circumference of earth actually does not matter at all. It was used to calculate the length of the first meter standard. Once the definitive meter prototype was produced, it became the standard and the definition of the meter.

Setting the standard for the meter

The length of the original meter prototype was never revised. In several new definitions through history, only the precision of the definition was improved and the uncertainty reduced; the length was always kept the same. Stability and consistency is one of the fundamentals of the metric system: the magnitude of a unit never changes.

Another requirement for a good system of weights and measures is reproducibility of standards. National standards laboratories have to work with exactly the same standards and have to be able to compare their standards to the original. This is another reason why the meter bar had to be the definition of the meter; not the circumference of earth. Measuring the earth is too complex, too expensive and has too high a margin of error to be practical. Comparing several metal bars with each other was relatively easy and exact.

With the internationalisation of the metric system and the signing of the Treaty of the Meter on 20 May 1875 by seventeen nations, the BIPM (International Bureau of Weights and Measures) was established. The BIPM took offices in the historic Pavilion de Breteuil at Sèvres, just outside Paris on the banks of the river Seine. The site of the Pavilion de Breteuil is, by law, international territory.

On 28 September 1889, a new, international meter prototype was deposited at the BIPM in Sevres, where it remains today. However, newer definitions have made the platinum prototype of the meter obsolete. In 1960, the meter was officially defined in terms of a wavelength. This definition ensured greater reproducibility in laboratories around the world, precision and stability over time.

The newest definition, as shown at the beginning of this chapter, defines the meter by the distance light travels in a fraction of a second. Speed of light is a constant of nature; it does not change. The definition of the meter sets the speed of light to be exactly 299 792 458 meters per second (299 792.458 km/s or about 1 079 252 849 km/h ≈ one billion kilometers per hour). The speed of light is so well researched and its measurement so precise that more exact definitions in the future are difficult to imagine. However, some scientists have suggested that even constants of nature can change over very long periods of time. If this is the case, the definition of the meter might still have to be improved.

 

Since its conception in the 1790s, the meter has had remarkable success. It is now the only official base unit for length in all countries. All other units for length, archaic or still in use, are defined in terms of the meter and benefit from its stability and the very small uncertainty of its definition. The meter is also the basis for measures of area (square meters), measures of volume (cubic meter) and forms part of many other combined measures (such as speed which is measured in metres per second or kilometres per hour).

 

 

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Moles are used to measure the actual number of atoms, molecules or other elementary particles in a substance. One mole contains as many units as there are atoms in 12 gram of carbon 12 (carbon 12 is the most common form of carbon, consisting of 6 protons and 6 neutrons). Measurements have determined that 12 gram of carbon 12 contain about 602.214 199 × 10²¹ (or 602 sextillion) atoms.

One mole of a substance therefore contains about 602 sextillion elementary units. This number is called Avogadro’s number or Avogadro’s constant after the Italian chemist and physicist Amedeo Avogadro (1776–1856).

Example: One mole of H₂O (chemical symbol for pure water) describes an amount of water that contains 602 214 199 000 000 000 000 000 water molecules.

 

The mole is especially useful for chemists. One mole of carbon 12 weighs exactly 12 grams, as per the definition of the mole. From weighing a substance and checking with a table that lists the molar mass for this substance, it can be determined how many moles (and therefore how many elementary particles) are in a particular amount of the substance.

Example: Cane sugar (chemical formula C₁₂H₂₂O₁₁) has a molar mass of 342.3 grams (meaning that one mole of cane sugar weighs 342.3 grams). One kilogram of sugar contains therefore 2.92 moles (= 1 000 g / 342.3 g) of its molecules. By multiplying the number of moles with Avogadro’s number, the number of molecules can now be calculated.

Moles are also a powerful tool for calculating required quantities for chemical reactions. Water consists of two hydrogen atoms, one oxygen atom and has the chemical formula H₂O. Hydrogen has the molar mass of 1.008 g and oxygen has the molar mass of 16.000 g. Consequently, water has the molar mass of 18.016 g (2 × 1.008 g + 16.000 g).          

If we want to produce 1 kg of water from hydrogen and oxygen, we can calculate:
   1 kg of water = 55.506 moles of water molecules =
   111.012 moles (2 × 55.506) of hydrogen atoms and 55.506 moles of oxygen atoms =
   111.901 g of hydrogen and 888.099 g of oxygen
are needed for a reaction that does not leave any remains of either hydrogen or oxygen.

 

 

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The oldest unit of time is the day. When timekeeping needed to become more precise, the day was subdivided first into hours, then further into minutes and seconds. The subdivisions were (and still are) 24 hours per day, 60 minutes per hour and 60 seconds per minute. One hour has therefore 3 600 seconds, one day has 86 400 seconds.

The convention of dividing the day into 24 hours and the hours and minutes into 60 smaller segments has its roots in the cultures of the ancient Babylonians (around 2000 BC) and Sumerians (around 3000 BC). They used a very complex numbering system based on the numbers 60 (sexagesimal system) and 10 (decimal system). The ancient Greek astronomer Claudius Ptolemaeus (who lived from about 87 to 150 AD) paid tribute to the old system when he divided the 360 degrees of a circle further into 60 minutes each and the minutes into 60 seconds each. Medieval astronomers followed this ancient custom when they invented the minute and the second as measurements of time.

 

The original metric definition of the second was the 86 400^th part of a solar day on earth (1 day = 24 hours × 60 minutes × 60 seconds = 86 400 seconds). When this definition was found to be not accurate enough (because of the variations of the duration of a solar day), other, more precise definitions were employed. In 1960, the second was defined as a fraction of the length of the year 1900.

The newest definition, different again, as shown at the beginning of this chapter, defines the second as the length of time that passes between a certain number of fluctuations in a certain atom. However, the length of the second did not change. This, most current definition still fixes the second as an average second of earth rotation time in 1900.

This length of time is taken to be consistent; it does not change. Each second has therefore exactly the same duration, which is necessary for high precision time measurements and for calculations involving long time spans.

Other units of time (minute, hour and day) are defined by the metric system as multiples of the second, making them as consistent and reliable as the second itself. Measurement units for longer periods of time (week, month, year and others) are not defined within the metric system and their duration and definition can vary.

Changing the definition of the unit of time away from the solar day (the time it takes for the sun to appear at the same spot in the sky each day) has meant that time units became much more precise and reliable. Another effect of this more precise definition is that fluctuations of the solar day sometimes make it necessary to change the length of a particular calendar day by inserting or deducting a leap second. This practice ensures that our calendar stays aligned with the movements of the earth and the sun.

The BIPM (International Bureau of Weights and Measures) is responsible for keeping the Coordinated Universal Time (UTC), which is the basis for legal time worldwide. Its unit interval is the second. The current UTC can be checked on the website of the BIPM.

Mainly due to tidal friction, the rotation of the earth is slowing down by 0.5 ms to 3.5 ms per century. In the distant future, the day will be longer than 86 400 seconds.

 

 

Other units of time defined by the SI

minute [min]

hour [h]

day [d]

week

month

year      The symbol for the year is ‘a’, taken from the Latin word for year ‘annus’.

 

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