Physical quantities. Units of physical quantities Units of the international system of units of quantities
To eliminate the arbitrary choice of units of physical quantities, to ensure a uniform expression and adequate understanding of the quality of parameters, characteristics and properties of various objects, processes, states, i.e. in order to ensure the conditions for uniformity of measurements, units of physical quantities must be generally accepted and generally accepted. These requirements are fully met by the International System of Units of Physical Measurements (SI), which is the modern form of presentation and development of the metric system of measures.
The advantages of the SI system are:
- ? universality, which implies its coverage of all areas of science, technology, and production; all derived units are formed according to a single rule. This makes it possible to create new derivative units as science and technology develop;
- ? coherence, which allows you to simplify calculation formulas to a minimum by eliminating conversion factors (when the numerical factor is equal to 1). For example, the speed of movement of bodies can be expressed by the relation V = = L/t, Where L- path length in meters; t- movement time in seconds. Substituting the dimensions of the indicated quantities into the formula gives V== 1m/s;
- ? unification of units of all areas of measurement, which is understood as bringing units to uniformity on the basis of a rational reduction in the number of their varieties.
Based on their conditional dependence on other quantities, units are divided into basic (independent physical quantities located in the basic system of units) and derivatives (conditionally dependent on the basic quantities).
There are seven primary and two supplementary units in the SI system. Complementary units are used to form derived units depending on certain conditions associated with plane and solid angles.
The main and additional units of the International System are given in Table. 1.1.
Table 1.1
International System (SI) units
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Name physical quantities |
Designation physical quantities | |||
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Unit name |
Designation |
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international |
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Basic units |
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kilogram |
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Electric current strength |
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Thermodynamic temperature |
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Ending
The decisions of the General Conference on Weights and Measures established the following definitions basic units:
U meter - the length of the path traveled by light in a vacuum in 1/299792458 of a second;
- ? kilogram - a unit of mass equal to the mass of the international prototype of the kilogram;
- ? a second is equal to 9,192,631,770 periods of radiation corresponding to the transition between two hyperfine levels of the ground state of the cesium-133 atom;
- ? An ampere is equal to the strength of a constant current, which, passing through two normal parallel conductors of infinite length and negligibly small circular cross-sectional area, located in a vacuum at a distance of 1 m from each other, causes an interaction force between the conductors equal to 2 10 7 N for each meter of length ;
- ? kelvin - a unit of thermodynamic temperature equal to 1/273.16 of the thermodynamic temperature of the triple point of water;
- ? candela is equal to the luminous intensity in a given direction of a source emitting monochromatic radiation with a frequency of 540 10 12 Hz, the luminous energy intensity of which in this direction is 1/683 W/sr;
- ? mole - the amount of substance in a system containing as many structural elements as there are atoms contained in carbon-12 weighing 0.012 kg.
Additional units- These are units of plane and solid angles (radians and steradians). They are not included in the main ones due to difficulties in interpreting the dimensions of quantities associated with rotation.
They cannot be classified as derivatives, since they do not depend on the basic quantities. These units are independent of the size of the unit of length.
Radian- a unit of plane angle equal to the angle between two radii of a circle, the length of the arc between which is equal to the radius. In degrees, 1 rad = 57° 17"45".
Steradian - a unit equal to the solid angle with its vertex at the center of the sphere, cutting out on the surface of the sphere an area equal to the area of a square with a side equal to the radius of the sphere.
Derived units SI units are formed from basic and additional units based on equations between physical quantities. Derived SI units with special names are given in table. 1.2.
Table 1.2
Derived SI units with special names
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Name of quantity | |||
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Name |
Designation |
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international |
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Strength, weight |
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Mechanical stress pressure, elastic modulus |
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Energy, work, amount of heat |
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Power, energy flow |
W |
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Electric voltage, electric potential, electromotive force, electric potential difference |
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Electrical capacity |
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Electrical resistance |
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Electrical conductivity |
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Magnetic induction flux, magnetic flux |
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Magnetic flux density, magnetic induction |
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Inductance, mutual inductance |
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Light flow |
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Ending
In order to avoid obtaining too large or small values of physical quantities, the SI establishes the use of decimal multiples and submultiples of SI units, which are formed using multipliers and contain prefixes corresponding to the multipliers (Table 1.3).
Table 1.3
Unit multipliers and prefixes
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Factor |
Console |
Prefix designation |
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international |
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The names of multiple and submultiple units of physical quantities formed in this way are written together with the name of the main or derived SI unit, for example, kilometer - km, megawatt - MW, micrometer - micrometer, millivolt - mV, etc. Two or more prefixes cannot be used.
In principle, one can imagine any large number of different systems of units, but only a few are widely used. All over the world, the metric system is used for scientific and technical measurements and in most countries in industry and everyday life.
Basic units.
In the system of units, for each measured physical quantity there must be a corresponding unit of measurement. Thus, a separate unit of measurement is needed for length, area, volume, speed, etc., and each such unit can be determined by choosing one or another standard. But the system of units turns out to be much more convenient if in it only a few units are selected as basic ones, and the rest are determined through the basic ones. So, if the unit of length is a meter, the standard of which is stored in the State Metrological Service, then the unit of area can be considered a square meter, the unit of volume is a cubic meter, the unit of speed is a meter per second, etc.
The convenience of such a system of units (especially for scientists and engineers, who deal with measurements much more often than other people) is that the mathematical relationships between the basic and derived units of the system turn out to be simpler. In this case, a unit of speed is a unit of distance (length) per unit of time, a unit of acceleration is a unit of change in speed per unit of time, a unit of force is a unit of acceleration per unit of mass, etc. In mathematical notation it looks like this: v = l/t, a = v/t, F = ma = ml/t 2. The presented formulas show the “dimension” of the quantities under consideration, establishing relationships between units. (Similar formulas allow you to determine units for quantities such as pressure or electric current.) Such relationships are of a general nature and are valid regardless of what units (meter, foot or arshin) the length is measured in and what units are chosen for other quantities.
In technology, the basic unit of measurement of mechanical quantities is usually taken not as a unit of mass, but as a unit of force. Thus, if in the system most commonly used in physical research, a metal cylinder is taken as a standard of mass, then in a technical system it is considered as a standard of force that balances the force of gravity acting on it. But since the force of gravity is not the same at different points on the Earth's surface, location specification is necessary to accurately implement the standard. Historically, the location was sea level at a latitude of 45°. Currently, such a standard is defined as the force necessary to give the specified cylinder a certain acceleration. True, in technology, measurements are usually not carried out with such high accuracy that it is necessary to take care of variations in gravity (if we are not talking about the calibration of measuring instruments).
There is a lot of confusion surrounding the concepts of mass, force and weight. The fact is that there are units of all these three quantities that have the same names. Mass is an inertial characteristic of a body, showing how difficult it is to remove it from a state of rest or uniform and linear motion by an external force. A unit of force is a force that, acting on a unit of mass, changes its speed by one unit of speed per unit of time.
All bodies attract each other. Thus, any body near the Earth is attracted to it. In other words, the Earth creates the force of gravity acting on the body. This force is called its weight. The force of weight, as stated above, is not the same at different points on the surface of the Earth and at different altitudes above sea level due to differences in gravitational attraction and in the manifestation of the Earth's rotation. However, the total mass of a given amount of substance is unchanged; it is the same both in interstellar space and at any point on Earth.
Precise experiments have shown that the force of gravity acting on different bodies (i.e. their weight) is proportional to their mass. Consequently, masses can be compared on scales, and masses that turn out to be the same in one place will be the same in any other place (if the comparison is carried out in a vacuum to exclude the influence of displaced air). If a certain body is weighed on a spring scale, balancing the force of gravity with the force of an extended spring, then the results of measuring the weight will depend on the place where the measurements are taken. Therefore, spring scales must be adjusted at each new location so that they correctly indicate the mass. The simplicity of the weighing procedure itself was the reason that the force of gravity acting on the standard mass was adopted as an independent unit of measurement in technology. HEAT.
Metric system of units.
The metric system is the general name for the international decimal system of units, the basic units of which are the meter and the kilogram. Although there are some differences in details, the elements of the system are the same throughout the world.
Story.
The metric system grew out of regulations adopted by the French National Assembly in 1791 and 1795 defining the meter as one ten-millionth of the portion of the earth's meridian from the North Pole to the equator.
By decree issued on July 4, 1837, the metric system was declared mandatory for use in all commercial transactions in France. It gradually replaced local and national systems in other European countries and was legally accepted as acceptable in the UK and USA. An agreement signed on May 20, 1875 by seventeen countries created an international organization designed to preserve and improve the metric system.
It is clear that by defining the meter as a ten-millionth part of a quarter of the earth's meridian, the creators of the metric system sought to achieve invariance and accurate reproducibility of the system. They took the gram as a unit of mass, defining it as the mass of one millionth of a cubic meter of water at its maximum density. Since it would not be very convenient to carry out geodetic measurements of a quarter of the earth's meridian with each sale of a meter of cloth or to balance a basket of potatoes at the market with the appropriate amount of water, metal standards were created that reproduced these ideal definitions with extreme accuracy.
It soon became clear that metal length standards could be compared with each other, introducing much less error than when comparing any such standard with a quarter of the earth's meridian. In addition, it became clear that the accuracy of comparing metal mass standards with each other is much higher than the accuracy of comparing any such standard with the mass of the corresponding volume of water.
In this regard, the International Commission on the Meter in 1872 decided to accept the “archival” meter stored in Paris “as it is” as the standard of length. Similarly, the members of the Commission accepted the archival platinum-iridium kilogram as the standard of mass, “considering that the simple relationship established by the creators of the metric system between the unit of weight and the unit of volume is represented by the existing kilogram with an accuracy sufficient for ordinary applications in industry and commerce, and the exact Sciences do not need a simple numerical relationship of this kind, but an extremely perfect definition of this relationship.” In 1875, many countries around the world signed a meter agreement, and this agreement established a procedure for coordinating metrological standards for the world scientific community through the International Bureau of Weights and Measures and the General Conference on Weights and Measures.
The new international organization immediately began developing international standards for length and mass and transmitting copies of them to all participating countries.
Standards of length and mass, international prototypes.
The international prototypes of the standards of length and mass - the meter and the kilogram - were deposited with the International Bureau of Weights and Measures, located in Sèvres, a suburb of Paris. The meter standard was a ruler made of a platinum alloy with 10% iridium, the cross-section of which was given a special X-shape to increase bending rigidity with a minimum volume of metal. In the groove of such a ruler there was a longitudinal flat surface, and the meter was defined as the distance between the centers of two strokes applied across the ruler at its ends, at a standard temperature of 0 ° C. The mass of a cylinder made of the same platinum was taken as the international prototype of the kilogram. iridium alloy, the same as the standard meter, with a height and diameter of about 3.9 cm. The weight of this standard mass, equal to 1 kg at sea level at latitude 45°, is sometimes called kilogram-force. Thus, it can be used either as a standard of mass for an absolute system of units, or as a standard of force for a technical system of units in which one of the basic units is the unit of force.
The international prototypes were selected from a large batch of identical standards produced simultaneously. Other standards of this batch were transferred to all participating countries as national prototypes (state primary standards), which are periodically returned to the International Bureau for comparison with international standards. Comparisons made at various times since then show that they do not show deviations (from international standards) beyond the limits of measurement accuracy.
International SI system.
The metric system was very favorably received by scientists of the 19th century. partly because it was proposed as an international system of units, partly because its units were theoretically assumed to be independently reproducible, and also because of its simplicity. Scientists began to develop new units for the various physical quantities they dealt with, based on the elementary laws of physics and linking these units to the metric units of length and mass. The latter increasingly conquered various European countries, in which previously many unrelated units for different quantities were in use.
Although all countries that adopted the metric system of units had nearly the same standards for metric units, various discrepancies in derived units arose between different countries and different disciplines. In the field of electricity and magnetism, two separate systems of derived units emerged: electrostatic, based on the force with which two electric charges act on each other, and electromagnetic, based on the force of interaction between two hypothetical magnetic poles.
The situation became even more complicated with the advent of the so-called system. practical electrical units introduced in the mid-19th century. by the British Association for the Advancement of Science to meet the demands of rapidly developing wire telegraph technology. Such practical units do not coincide with the units of both systems mentioned above, but differ from the units of the electromagnetic system only by factors equal to whole powers of ten.
Thus, for such common electrical quantities as voltage, current and resistance, there were several options for accepted units of measurement, and each scientist, engineer, and teacher had to decide for himself which of these options was best for him to use. In connection with the development of electrical engineering in the second half of the 19th and first half of the 20th centuries. Practical units were increasingly used and eventually came to dominate the field.
To eliminate such confusion at the beginning of the 20th century. a proposal was put forward to combine practical electrical units with corresponding mechanical ones based on metric units of length and mass, and build some kind of coherent system. In 1960, the XI General Conference on Weights and Measures adopted a unified International System of Units (SI), defined the basic units of this system and prescribed the use of certain derived units, “without prejudice to others that may be added in the future.” Thus, for the first time in history, an international coherent system of units was adopted by international agreement. It is now accepted as a legal system of units of measurement by most countries in the world.
The International System of Units (SI) is a harmonized system that provides one and only one unit of measurement for any physical quantity, such as length, time, or force. Some of the units are given special names, an example is the unit of pressure pascal, while the names of others are derived from the names of the units from which they are derived, for example the unit of speed - meter per second. The basic units, together with two additional geometric ones, are presented in Table. 1. Derived units for which special names are adopted are given in table. 2. Of all the derived mechanical units, the most important are the unit of force newton, the unit of energy the joule and the unit of power the watt. Newton is defined as the force that imparts an acceleration of one meter per second squared to a mass of one kilogram. A joule is equal to the work done when the point of application of a force equal to one Newton moves a distance of one meter in the direction of the force. A watt is the power at which one joule of work is done in one second. Electrical and other derived units will be discussed below. The official definitions of major and minor units are as follows.
A meter is the length of the path traveled by light in a vacuum in 1/299,792,458 of a second. This definition was adopted in October 1983.
A kilogram is equal to the mass of the international prototype of the kilogram.
A second is the duration of 9,192,631,770 periods of radiation oscillations corresponding to transitions between two levels of the hyperfine structure of the ground state of the cesium-133 atom.
Kelvin is equal to 1/273.16 of the thermodynamic temperature of the triple point of water.
A mole is equal to the amount of a substance that contains the same number of structural elements as atoms in the carbon-12 isotope weighing 0.012 kg.
A radian is a plane angle between two radii of a circle, the length of the arc between which is equal to the radius.
The steradian is equal to the solid angle with its vertex at the center of the sphere, cutting out on its surface an area equal to the area of a square with a side equal to the radius of the sphere.
To form decimal multiples and submultiples, a number of prefixes and factors are prescribed, indicated in the table. 3.
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Table 3. Prefixes and multipliers of the international system of units |
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| exa | deci | ||||
| peta | centi | ||||
| tera | Milli | ||||
| giga | micro |
mk |
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| mega | nano | ||||
| kilo | pico | ||||
| hecto | femto | ||||
| soundboard |
Yes |
atto | |||
Thus, a kilometer (km) is 1000 m, and a millimeter is 0.001 m. (These prefixes apply to all units, such as kilowatts, milliamps, etc.)
It was originally intended that one of the base units should be the gram, and this was reflected in the names of the units of mass, but nowadays the base unit is the kilogram. Instead of the name megagram, the word “ton” is used. In physics disciplines, such as measuring the wavelength of visible or infrared light, a millionth of a meter (micrometer) is often used. In spectroscopy, wavelengths are often expressed in angstroms (Å); An angstrom is equal to one tenth of a nanometer, i.e. 10 - 10 m. For radiation with a shorter wavelength, such as X-rays, in scientific publications it is allowed to use a picometer and an x-unit (1 x-unit = 10 –13 m). A volume equal to 1000 cubic centimeters (one cubic decimeter) is called a liter (L).
Mass, length and time.
All basic SI units, except the kilogram, are currently defined in terms of physical constants or phenomena that are considered immutable and reproducible with high accuracy. As for the kilogram, a way to implement it with the degree of reproducibility that is achieved in procedures for comparing various mass standards with the international prototype of the kilogram has not yet been found. Such a comparison can be carried out by weighing on a spring balance, the error of which does not exceed 1H 10 –8. Standards of multiple and submultiple units for a kilogram are established by combined weighing on scales.
Since the meter is defined in terms of the speed of light, it can be reproduced independently in any well-equipped laboratory. Thus, using the interference method, line and end length measures, which are used in workshops and laboratories, can be checked by comparing directly with the wavelength of light. The error with such methods under optimal conditions does not exceed one billionth (1H 10 –9). With the development of laser technology, such measurements have become very simplified, and their range has expanded significantly.
Likewise, the second, according to its modern definition, can be independently realized in a competent laboratory in an atomic beam facility. The beam's atoms are excited by a high-frequency oscillator tuned to the atomic frequency, and an electronic circuit measures time by counting the periods of oscillation in the oscillator circuit. Such measurements can be carried out with an accuracy of the order of 1H 10 -12 - much higher than was possible with previous definitions of the second, based on the rotation of the Earth and its revolution around the Sun. Time and its reciprocal, frequency, are unique in that their standards can be transmitted by radio. Thanks to this, anyone who has the appropriate radio receiving equipment can receive signals of exact time and reference frequency, almost no different in accuracy from those transmitted over the air.
Mechanics.
Temperature and warmth.
Mechanical units do not allow solving all scientific and technical problems without involving any other relationships. Although the work done when moving a mass against the action of a force, and the kinetic energy of a certain mass are equivalent in nature to the thermal energy of a substance, it is more convenient to consider temperature and heat as separate quantities that do not depend on mechanical ones.
Thermodynamic temperature scale.
The unit of thermodynamic temperature Kelvin (K), called kelvin, is determined by the triple point of water, i.e. the temperature at which water is in equilibrium with ice and steam. This temperature is taken to be 273.16 K, which determines the thermodynamic temperature scale. This scale, proposed by Kelvin, is based on the second law of thermodynamics. If there are two thermal reservoirs with a constant temperature and a reversible heat engine transferring heat from one of them to the other in accordance with the Carnot cycle, then the ratio of the thermodynamic temperatures of the two reservoirs is given by T 2 /T 1 = –Q 2 Q 1 where Q 2 and Q 1 – the amount of heat transferred to each of the reservoirs (the minus sign indicates that heat is taken from one of the reservoirs). Thus, if the temperature of the warmer reservoir is 273.16 K, and the heat taken from it is twice as much as the heat transferred to the other reservoir, then the temperature of the second reservoir is 136.58 K. If the temperature of the second reservoir is 0 K, then it no heat will be transferred at all, since all the gas energy has been converted into mechanical energy in the adiabatic expansion section of the cycle. This temperature is called absolute zero. The thermodynamic temperature commonly used in scientific research coincides with the temperature included in the equation of state of an ideal gas PV = RT, Where P- pressure, V– volume and R– gas constant. The equation shows that for an ideal gas, the product of volume and pressure is proportional to temperature. This law is not exactly satisfied for any of the real gases. But if corrections are made for virial forces, then the expansion of gases allows us to reproduce the thermodynamic temperature scale.
International temperature scale.
In accordance with the definition outlined above, temperature can be measured with very high accuracy (up to approximately 0.003 K near the triple point) by gas thermometry. A platinum resistance thermometer and a gas reservoir are placed in a thermally insulated chamber. When the chamber is heated, the electrical resistance of the thermometer increases and the gas pressure in the reservoir increases (in accordance with the equation of state), and when cooled, the opposite picture is observed. By measuring resistance and pressure simultaneously, you can calibrate the thermometer by gas pressure, which is proportional to temperature. The thermometer is then placed in a thermostat in which the liquid water can be kept in equilibrium with its solid and vapor phases. By measuring its electrical resistance at this temperature, a thermodynamic scale is obtained, since the temperature of the triple point is assigned a value equal to 273.16 K.
There are two international temperature scales - Kelvin (K) and Celsius (C). Temperature on the Celsius scale is obtained from temperature on the Kelvin scale by subtracting 273.15 K from the latter.
Accurate temperature measurements using gas thermometry require a lot of labor and time. Therefore, the International Practical Temperature Scale (IPTS) was introduced in 1968. Using this scale, thermometers of different types can be calibrated in the laboratory. This scale was established using a platinum resistance thermometer, a thermocouple and a radiation pyrometer, used in the temperature intervals between certain pairs of constant reference points (temperature benchmarks). The MPTS was supposed to correspond to the thermodynamic scale with the greatest possible accuracy, but, as it turned out later, its deviations were very significant.
Fahrenheit temperature scale.
The Fahrenheit temperature scale, which is widely used in combination with the British technical system of units, as well as in non-scientific measurements in many countries, is usually determined by two constant reference points - the melting point of ice (32 ° F) and the boiling point of water (212 ° F) at normal (atmospheric) pressure. Therefore, to get the Celsius temperature from the Fahrenheit temperature, you need to subtract 32 from the latter and multiply the result by 5/9.
Units of heat.
Since heat is a form of energy, it can be measured in joules, and this metric unit has been adopted by international agreement. But since the amount of heat was once determined by the change in temperature of a certain amount of water, a unit called a calorie became widespread and is equal to the amount of heat required to increase the temperature of one gram of water by 1 ° C. Due to the fact that the heat capacity of water depends on temperature , I had to clarify the calorie value. At least two different calories appeared - “thermochemical” (4.1840 J) and “steam” (4.1868 J). The “calorie” used in dietetics is actually a kilocalorie (1000 calories). The calorie is not an SI unit and has fallen into disuse in most fields of science and technology.
Electricity and magnetism.
All commonly accepted electrical and magnetic units of measurement are based on the metric system. In accordance with modern definitions of electrical and magnetic units, they are all derived units, derived by certain physical formulas from the metric units of length, mass and time. Since most electrical and magnetic quantities are not so easy to measure using the standards mentioned, it was found that it is more convenient to establish, through appropriate experiments, derivative standards for some of the indicated quantities, and to measure others using such standards.
SI units.
Below is a list of SI electrical and magnetic units.
The ampere, a unit of electric current, is one of the six SI base units. Ampere is the strength of a constant current, which, when passing through two parallel straight conductors of infinite length with a negligibly small circular cross-sectional area, located in a vacuum at a distance of 1 m from each other, would cause on each section of the conductor 1 m long an interaction force equal to 2H 10 - 7 N.
Volt, a unit of potential difference and electromotive force. Volt is the electrical voltage in a section of an electrical circuit with a direct current of 1 A with a power consumption of 1 W.
Coulomb, a unit of quantity of electricity (electric charge). Coulomb is the amount of electricity passing through the cross-section of a conductor at a constant current of 1 A in 1 s.
Farad, a unit of electrical capacitance. Farad is the capacitance of a capacitor on the plates of which, when charged at 1 C, an electric voltage of 1 V appears.
Henry, unit of inductance. Henry is equal to the inductance of the circuit in which a self-inductive emf of 1 V occurs when the current in this circuit changes uniformly by 1 A in 1 s.
Weber unit of magnetic flux. Weber is a magnetic flux, when it decreases to zero, an electric charge equal to 1 C flows in the circuit connected to it, which has a resistance of 1 Ohm.
Tesla, a unit of magnetic induction. Tesla is the magnetic induction of a uniform magnetic field, in which the magnetic flux through a flat area of 1 m2, perpendicular to the induction lines, is equal to 1 Wb.
Practical standards.
Light and illumination.
Luminous intensity and illuminance units cannot be determined based on mechanical units alone. We can express the energy flux in a light wave in W/m2, and the intensity of the light wave in V/m, as in the case of radio waves. But the perception of illumination is a psychophysical phenomenon in which not only the intensity of the light source is significant, but also the sensitivity of the human eye to the spectral distribution of this intensity.
By international agreement, the unit of luminous intensity is the candela (previously called a candle), equal to the luminous intensity in a given direction of a source emitting monochromatic radiation of frequency 540H 10 12 Hz ( l= 555 nm), the energy force of light radiation of which in this direction is 1/683 W/sr. This roughly corresponds to the luminous intensity of a spermaceti candle, which once served as a standard.
If the luminous intensity of the source is one candela in all directions, then the total luminous flux is 4 p lumens. Thus, if this source is located at the center of a sphere with a radius of 1 m, then the illumination of the inner surface of the sphere is equal to one lumen per square meter, i.e. one suite.
X-ray and gamma radiation, radioactivity.
X-ray (R) is an obsolete unit of exposure dose of x-ray, gamma and photon radiation, equal to the amount of radiation that, taking into account secondary electron radiation, forms ions in 0.001 293 g of air that carry a charge equal to one unit of the CGS charge of each sign. The SI unit of absorbed radiation dose is the gray, equal to 1 J/kg. The standard for absorbed radiation dose is a setup with ionization chambers that measure the ionization produced by radiation.
1. The General Conference on Weights and Measures (GCPM) in 1954 defined six basic units of physical quantities for use in international relations: meter, kilogram, second, ampere, Kelvin and candle. The XI General Conference on Weights and Measures in 1960 approved the International System of Units, designated SI (from the initial letters of the French name Systeme International d" Unites), in Russian - SI. In subsequent years, the General Conference adopted a number of additions and changes, in As a result, the system became seven basic units, additional and derivative units of physical greatness, and also developed the following definitions of basic units:
unit of length-- meter - the length of the path that light travels in a vacuum in 1/299792458 of a second;
unit of mass-- kilogram -- mass equal to the mass of the international prototype of the kilogram;
unit of time-- second -- duration of 9192631770 periods of radiation, which corresponds to the transition between two hyperfine levels of the ground state of the cesium-133 atom in the absence of disturbance from external fields;
unit of electric current- ampere - the strength of a constant current, which, when passing through two parallel conductors of infinite length and negligible circular cross-section, located at a distance of 1 m from each other in a vacuum, would create a force between these conductors equal to 2 10 -7 Z per meter length;
thermodynamic temperature unit-- kelvin -- 1/273.16 part of the thermodynamic temperature of the triple point of iodine. The use of the Celsius scale is also permitted;
unit of amount of substance-- mole -- the amount of substance in a system containing the same number of structural elements as there are atoms contained in a carbon-12 nuclide weighing 0.012 kg;
unit of luminous intensity-- candela - the intensity of light in a given direction of a source emitting monochromatic radiation with a frequency of 540 · 10 12 Hz, the energy force of which in this direction is 1/683 W/sr.
The given definitions are quite complex and require a sufficient level of knowledge, primarily in physics. But they give an idea of the natural, natural origin of the accepted units, and their interpretation became more complicated as science developed and thanks to new high achievements in theoretical and practical physics, mechanics, mathematics and other fundamental fields of knowledge. This made it possible, on the one hand, to present the basic units as reliable and accurate, and on the other hand, as explainable and, as it were, understandable for all countries of the world, which is the main condition for the system of units to become international.
The International SI System is considered the most advanced and universal compared to its predecessors. In addition to the basic units, the SI system has additional units for measuring plane and solid angles - radians and steradians, respectively, as well as a large number of derived units of space and time, mechanical quantities, electrical and magnetic quantities, thermal, light and acoustic quantities, as well as ionizing radiation.
2. SI (System International) is the international system of units, a modern version of the metric system. SI is the most widely used system of units in the world, both in everyday life and in science and technology.
SI is now accepted as the primary system of units by most countries in the world and is almost always used in engineering, even in countries where traditional units are used in everyday life. In these few countries (for example, the USA), the definitions of traditional units were changed - they began to be defined in terms of SI units.
In Russia, GOST 8.417--2002 is in force, which prescribes the mandatory use of SI units. It lists the units of physical quantities permitted for use, gives their international and Russian designations and establishes the rules for their use.
GOST 8.417 is a state standard that establishes units of measurement used in the Russian Federation and some other countries that were formerly part of the USSR. The standard defines the names, designations, definitions and rules for using these units. In Russia, since September 1, 2003, “GOST 8.417-2002 GSI” has been in force. Units of quantities", which replaced "GOST 8.417--81 GSI. Units of physical quantities".
Derived units can be expressed in terms of base units using mathematical operations: multiplication and division. Some of the derived units are given their own names for convenience; such units can also be used in mathematical expressions to form other derived units.
Decimal multiples and submultiples are formed using standard factors and SI prefixes attached to the name or symbol of the unit.
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Multiplicity |
Console |
Designation |
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international |
international |
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dal - deciliter |
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hPa - hectopascal |
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kN - kilonewton |
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MPa - megapascal |
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GHz - gigahertz |
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TV - teravolt |
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|
Pflop - petaflop |
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|
EB - exabyte |
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|
ZeV - zettaelectronvolt |
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|
Yb - yottabyte |
Most prefixes are derived from Greek words.
3. Unit designations are printed in straight font; a dot is not placed after the designation as an abbreviation sign.
Designations are placed after the numerical values of quantities separated by a space; transfer to another line is not allowed. Exceptions are notations in the form of a sign above a line; they are not preceded by a space. Examples: 10 m/s, 15°.
If a numeric value is a fraction with a slash, it is enclosed in parentheses, for example: (1/60) s -1 .
When indicating the values of quantities with maximum deviations, they are enclosed in brackets or a unit designation is placed behind the numerical value of the quantity and its maximum deviation: (100.0 ± 0.1) kg, 50 g ± 1 g.
The designations of units included in the product are separated by dots on the center line (N m, Pa s); it is not allowed to use the symbol “H” for this purpose. In typewritten texts, it is allowed not to raise the period or to separate symbols with spaces if this does not cause misunderstandings.
You can use a horizontal bar or a slash (only one) as a division sign in notation. When using a slash, if the denominator contains a product of units, it is enclosed in parentheses. Correct: W/(m·K), incorrect: W/m/K, W/m·K.
It is allowed to use unit designations in the form of a product of unit designations raised to powers (positive and negative): W m-2 K-1, A mI. When using negative powers, you must not use a horizontal bar or a slash (divide sign).
It is allowed to use combinations of special characters with letter designations, for example: °/s (degrees per second).
It is not allowed to combine designations and full names of units. Incorrect: km/h, correct: km/h.
Unit designations derived from surnames are written with capital letters, including those with SI prefixes, for example: ampere - A, megapascal - MPa, kilonewton - kN, gigahertz - GHz.
Questions and assignments.
73. In what year did the CGPM define six basic units of physical quantities for their use in international relations?
74. Name the seven basic SI units.
75. What is determined by GOST 8.417--2002 GSI. Units of quantities?
76. What are the basic rules for writing the designation of units?
Kolchkov V.I. METROLOGY, STANDARDIZATION AND CERTIFICATION. M.: Textbook
3. Metrology and technical measurements
3.3. International system of units of physical quantities
The Harmonized International System of Units of Physical Quantities was adopted in 1960 by the XI General Conference on Weights and Measures. International system - SI (SI), SI- initial letters of the French name Systeme International. The system provides a list of seven basic units: meter, kilogram, second, ampere, kelvin, candela, mole and two additional ones: radian, steradian, as well as prefixes for the formation of multiples and submultiples.
3.3.1 SI base units
- Meter equal to the length of the path traveled by light in a vacuum in 1/299.792.458 of a second.
- Kilogram equal to the mass of the international prototype kilogram.
- Second equal to 9.192.631.770 periods of radiation corresponding to the transition between two hyperfine levels of the ground state of the cesium-133 atom.
- Ampere is equal to the force of an electric current that does not change in time, which, when passing through two parallel straight conductors of infinite length and a negligibly small circular cross-sectional area, located at a distance of 1 m from each other in a vacuum, causes an interaction force equal to 2 on each section of the conductor 1 m long 10 to the minus 7th power N.
- Kelvin equal to 1/273.16 of the thermodynamic temperature of the triple point of water.
- Mole equal to the amount of substance in a system containing the same number of structural elements as there are atoms in carbon-12 weighing 0.012 kg.
- Candela equal to the luminous intensity in a given direction of a source emitting monochromatic radiation with a frequency of 540 10 to the 12th power of Hz, the energetic luminous intensity of which in this direction is 1/683 W/sr.
Table 3.1. SI Major and Supplementary Units
Basic SI units |
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Magnitude |
Designation |
||
Name |
Name |
international |
|
kilogram |
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Electric current strength I |
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Thermodynamic |
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The power of light |
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Quantity of substance |
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Derived SI units |
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Magnitude |
Designation |
||
Name |
Name |
international |
|
Flat angle |
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Solid angle |
steradian |
||
3.3.2. Derived SI units
Derived units of the International System of Units are formed using the simplest equations between physical quantities in which the numerical coefficients are equal to unity. For example, to determine the dimension of linear speed, we will use the expression for the speed of uniform rectilinear motion. If the length of the distance traveled is v = l/t(m), and the time during which this path is covered is t(s), then the speed is obtained in meters per second (m/s). Consequently, the SI unit of speed - meter per second - is the speed of a rectilinearly and uniformly moving point, at which it moves a distance of 1 m in 1 s. Other units are formed in a similar way, incl. with a coefficient not equal to one.
Table 3.2. Derived SI units (see also Table 3.1)
Derived SI units with their own names |
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Name |
Expressing a derived unit in terms of SI units |
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Magnitude |
Name |
Designation |
other units |
basic and additional units |
s–1 |
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m kg s–2 |
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Pressure |
N/m2 |
m–1 kg s–2 |
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Energy, work, |
m2 kg s–2 |
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Power |
m2 kg s–3 |
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Electr. charge |
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Electric potential |
m2 kg s–3 A–1 |
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Electr. capacity |
m–2 kg–1 s4 A2 |
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El..resistance |
m2 kg s–3 A–2 |
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Electrical conductivity |
m–2 kg–1 s3 A2 |
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Magnetic induction flux |
m2 kg s–2 A–1 | |||
Since 1963, in the USSR (GOST 9867-61 “International System of Units”), in order to unify units of measurement in all fields of science and technology, the international (international) system of units (SI, SI) has been recommended for practical use - this is a system of units of measurement of physical quantities , adopted by the XI General Conference on Weights and Measures in 1960. It is based on 6 basic units (length, mass, time, electric current, thermodynamic temperature and luminous intensity), as well as 2 additional units (plane angle, solid angle) ; all other units given in the table are their derivatives. The adoption of a unified international system of units for all countries is intended to eliminate the difficulties associated with the transfer of numerical values of physical quantities, as well as various constants from any one currently operating system (GHS, MKGSS, ISS A, etc.) into another.
| Name of quantity | Units; SI values | Designations | |
|---|---|---|---|
| Russian | international | ||
| I. Length, mass, volume, pressure, temperature | |||
| Meter is a measure of length, numerically equal to the length of the international standard meter; 1 m=100 cm (1·10 2 cm)=1000 mm (1·10 3 mm) |
m | m | |
| Centimeter = 0.01 m (1·10 -2 m) = 10 mm | cm | cm | |
| Millimeter = 0.001 m (1 10 -3 m) = 0.1 cm = 1000 μm (1 10 3 μm) | mm | mm | |
| Micron (micrometer) = 0.001 mm (1·10 -3 mm) = 0.0001 cm (1·10 -4 cm) = 10,000 |
mk | μ | |
| Angstrom = one ten-billionth of a meter (1·10 -10 m) or one hundred-millionth of a centimeter (1·10 -8 cm) | Å | Å | |
| Weight | The kilogram is the basic unit of mass in the metric system of measures and the SI system, numerically equal to the mass of the international standard kilogram; 1 kg=1000 g |
kg | kg |
| Gram=0.001 kg (1·10 -3 kg) |
G | g | |
| Ton= 1000 kg (1 10 3 kg) | T | t | |
| Centner = 100 kg (1 10 2 kg) |
ts | ||
| Carat - a non-systemic unit of mass, numerically equal to 0.2 g | ct | ||
| Gamma = one millionth of a gram (1 10 -6 g) | γ | ||
| Volume | Liter = 1.000028 dm 3 = 1.000028 10 -3 m 3 | l | l |
| Pressure | Physical, or normal, atmosphere - pressure balanced by a mercury column 760 mm high at a temperature of 0° = 1.033 atm = = 1.01 10 -5 n/m 2 = 1.01325 bar = 760 torr = 1.033 kgf/cm 2 |
atm | atm |
| Technical atmosphere - pressure equal to 1 kgf/cmg = 9.81 10 4 n/m 2 = 0.980655 bar = 0.980655 10 6 dynes/cm 2 = 0.968 atm = 735 torr | at | at | |
| Millimeter of mercury = 133.32 n/m 2 | mmHg Art. | mm Hg | |
| Tor is the name of a non-systemic unit of pressure measurement equal to 1 mm Hg. Art.; given in honor of the Italian scientist E. Torricelli | torus | ||
| Bar - unit of atmospheric pressure = 1 10 5 n/m 2 = 1 10 6 dynes/cm 2 | bar | bar | |
| Pressure (sound) | Bar is a unit of sound pressure (in acoustics): bar - 1 dyne/cm2; Currently, a unit with a value of 1 n/m 2 = 10 dynes/cm 2 is recommended as a unit of sound pressure |
bar | bar |
| Decibel is a logarithmic unit of measurement of excess sound pressure level, equal to 1/10 of the unit of measurement of excess sound pressure - bela | dB | db | |
| Temperature | Degree Celsius; temperature in °K (Kelvin scale), equal to temperature in °C (Celsius scale) + 273.15 °C | °C | °C |
| II. Force, power, energy, work, amount of heat, viscosity | |||
| Force | Dyna is a unit of force in the CGS system (cm-g-sec.), in which an acceleration of 1 cm/sec 2 is imparted to a body with a mass of 1 g; 1 din - 1·10 -5 n | ding | dyn |
| Kilogram-force is a force that imparts an acceleration to a body with a mass of 1 kg equal to 9.81 m/sec 2 ; 1kg=9.81 n=9.81 10 5 din | kg, kgf | ||
| Power | Horsepower =735.5 W | l. With. | HP |
| Energy | Electron-volt is the energy that an electron acquires when moving in an electric field in a vacuum between points with a potential difference of 1 V; 1 eV = 1.6·10 -19 J. It is allowed to use multiple units: kiloelectron-volt (Kv) = 10 3 eV and megaelectron-volt (MeV) = 10 6 eV. In modern times, particle energy is measured in Bev - billions (billions) eV; 1 Bzv=10 9 eV |
ev | eV |
| Erg=1·10 -7 j; The erg is also used as a unit of work, numerically equal to the work done by a force of 1 dyne along a path of 1 cm | erg | erg | |
| Job | Kilogram-force-meter (kilogrammometer) is a unit of work numerically equal to the work done by a constant force of 1 kg when moving the point of application of this force a distance of 1 m in its direction; 1 kGm = 9.81 J (at the same time kGm is a measure of energy) | kGm, kgf m | kGm |
| Quantity of heat | Calorie is an off-system unit of measurement of the amount of heat equal to the amount of heat required to heat 1 g of water from 19.5 ° C to 20.5 ° C. 1 cal = 4.187 J; common multiple unit kilocalorie (kcal, kcal), equal to 1000 cal | feces | cal |
| Viscosity (dynamic) | Poise is a unit of viscosity in the GHS system of units; viscosity at which in a layered flow with a velocity gradient equal to 1 sec -1 per 1 cm 2 of the layer surface, a viscous force of 1 dyne acts; 1 pz = 0.1 n sec/m 2 | pz | P |
| Viscosity (kinematic) | Stokes is a unit of kinematic viscosity in the CGS system; equal to the viscosity of a liquid having a density of 1 g/cm 3 that resists a force of 1 dyne to the mutual movement of two layers of liquid with an area of 1 cm 2 located at a distance of 1 cm from each other and moving relative to each other at a speed of 1 cm per second | st | St |
| III. Magnetic flux, magnetic induction, magnetic field strength, inductance, electrical capacitance | |||
| Magnetic flux | Maxwell is a unit of measurement of magnetic flux in the CGS system; 1 μs is equal to the magnetic flux passing through an area of 1 cm 2 located perpendicular to the magnetic field induction lines, with an induction equal to 1 gf; 1 μs = 10 -8 wb (Weber) - units of magnetic current in the SI system | mks | Mx |
| Magnetic induction | Gauss is a unit of measurement in the GHS system; 1 gf is the induction of such a field in which a straight conductor 1 cm long, located perpendicular to the field vector, experiences a force of 1 dyne if a current of 3 10 10 CGS units flows through this conductor; 1 gs=1·10 -4 tl (tesla) | gs | Gs |
| Magnetic field strength | Oersted is a unit of magnetic field strength in the CGS system; one oersted (1 oe) is taken to be the intensity at a point in the field at which a force of 1 dyne (dyn) acts on 1 electromagnetic unit of the amount of magnetism; 1 e=1/4π 10 3 a/m |
uh | Oe |
| Inductance | Centimeter is a unit of inductance in the CGS system; 1 cm = 1·10 -9 g (Henry) | cm | cm |
| Electrical capacity | Centimeter - unit of capacity in the CGS system = 1·10 -12 f (farads) | cm | cm |
| IV. Luminous intensity, luminous flux, brightness, illumination | |||
| The power of light | A candle is a unit of luminous intensity, the value of which is taken such that the brightness of the full emitter at the solidification temperature of platinum is equal to 60 sv per 1 cm2 | St. | CD |
| Light flow | Lumen is a unit of luminous flux; 1 lumen (lm) is emitted within a solid angle of 1 ster from a point source of light having a luminous intensity of 1 light in all directions | lm | lm |
| Lumen-second - corresponds to the light energy generated by a luminous flux of 1 lm emitted or perceived in 1 second | lm sec | lm·sec | |
| A lumen hour is equal to 3600 lumen seconds | lm h | lm h | |
| Brightness | Stilb is a unit of brightness in the CGS system; corresponds to the brightness of a flat surface, 1 cm 2 of which gives in a direction perpendicular to this surface a luminous intensity equal to 1 ce; 1 sb=1·10 4 nits (nit) (SI unit of brightness) | Sat | sb |
| Lambert is a non-systemic unit of brightness, derived from stilbe; 1 lambert = 1/π st = 3193 nt | |||
| Apostilbe = 1/π s/m 2 | |||
| Illumination | Phot - unit of illumination in the SGSL system (cm-g-sec-lm); 1 photo corresponds to the illumination of a surface of 1 cm2 with a uniformly distributed luminous flux of 1 lm; 1 f=1·10 4 lux (lux) | f | ph |
| V. Radiation intensity and dose | |||
| Intensity | Curie is the basic unit of measurement of the intensity of radioactive radiation, the curie corresponding to 3.7·10 10 decays per 1 second. any radioactive isotope |
curie | C or Cu |
| millicurie = 10 -3 curies, or 3.7 10 7 acts of radioactive decay in 1 second. | mcurie | mc or mCu | |
| microcurie= 10 -6 curie | mccurie | μC or μCu | |
| Dose | X-ray - the number (dose) of X-rays or γ-rays, which in 0.001293 g of air (i.e. in 1 cm 3 of dry air at t° 0° and 760 mm Hg) causes the formation of ions carrying one electrostatic unit of quantity of electricity of each sign; 1 p causes the formation of 2.08 10 9 pairs of ions in 1 cm 3 of air | R | r |
| milliroentgen = 10 -3 p | mr | mr | |
| microroentgen = 10 -6 p | microdistrict | μr | |
| Rad - the unit of absorbed dose of any ionizing radiation is equal to rad 100 erg per 1 g of irradiated medium; when air is ionized by X-rays or γ-rays, 1 r is equal to 0.88 rad, and when tissue is ionized, almost 1 r is equal to 1 rad | glad | rad | |
| Rem (biological equivalent of an x-ray) is the amount (dose) of any type of ionizing radiation that causes the same biological effect as 1 r (or 1 rad) of hard x-rays. The unequal biological effect with equal ionization by different types of radiation led to the need to introduce another concept: the relative biological effectiveness of radiation - RBE; the relationship between doses (D) and the dimensionless coefficient (RBE) is expressed as D rem = D rad RBE, where RBE = 1 for x-rays, γ-rays and β-rays and RBE = 10 for protons up to 10 MeV, fast neutrons and α - natural particles (according to the recommendation of the International Congress of Radiologists in Copenhagen, 1953) | reb, reb | rem | |
Note. Multiple and submultiple units of measurement, with the exception of units of time and angle, are formed by multiplying them by the appropriate power of 10, and their names are added to the names of the units of measurement. It is not allowed to use two prefixes to the name of the unit. For example, you cannot write millimicrowatt (mmkW) or micromicrofarad (mmf), but you must write nanowatt (nw) or picofarad (pf). Prefixes should not be applied to the names of such units that indicate a multiple or submultiple unit of measurement (for example, micron). To express the duration of processes and designate calendar dates of events, the use of multiple units of time is allowed.
The most important units of the International System of Units (SI)
Basic units
(length, mass, temperature, time, electric current, light intensity)
| Name of quantity | Designations | ||
|---|---|---|---|
| Russian | international | ||
| Length | Meter - length equal to 1650763.73 wavelengths of radiation in vacuum, corresponding to the transition between levels 2p 10 and 5d 5 of krypton 86 * |
m | m |
| Weight | Kilogram - mass corresponding to the mass of the international standard kilogram | kg | kg |
| Time | Second - 1/31556925.9747 part of a tropical year (1900)** | sec | S, s |
| Electric current strength | Ampere is the strength of a constant current, which, passing through two parallel straight conductors of infinite length and negligible circular cross-section, located at a distance of 1 m from each other in a vacuum, would cause between these conductors a force equal to 2 10 -7 N per meter length | A | A |
| The power of light | A candle is a unit of luminous intensity, the value of which is taken such that the brightness of a complete (absolutely black) emitter at the solidification temperature of platinum is equal to 60 sec per 1 cm 2 *** | St. | CD |
| Temperature (thermodynamic) | Degree Kelvin (Kelvin scale) is a unit of measurement of temperature on the thermodynamic temperature scale, in which the temperature of the triple point of water**** is set to 273.16° K | °K | °K |
** That is, a second is equal to the specified part of the time interval between two successive passages by the Earth in its orbit around the Sun of the point corresponding to the vernal equinox. This gives greater accuracy in determining the second than defining it as a part of the day, since the length of the day varies.
*** That is, the luminous intensity of a certain reference source emitting light at the melting temperature of platinum is taken as a unit. The old international candle standard is 1.005 of the new candle standard. Thus, within the limits of normal practical accuracy, their values can be considered identical.
**** Triple point - the temperature at which ice melts in the presence of saturated water vapor above it.
Additional and derived units
| Name of quantity | Units; their definition | Designations | |
|---|---|---|---|
| Russian | international | ||
| I. Plane angle, solid angle, force, work, energy, amount of heat, power | |||
| Flat angle | Radian - the angle between two radii of a circle, cutting out an arc on the circle, the length of which is equal to the radius | glad | rad |
| Solid angle | Steradian is a solid angle whose vertex is located at the center of the sphere and which cuts out an area on the surface of the sphere equal to the area of a square with a side equal to the radius of the sphere | erased | sr |
| Force | Newton is a force under the influence of which a body with a mass of 1 kg acquires an acceleration equal to 1 m/sec 2 | n | N |
| Work, energy, amount of heat | Joule is the work done by a constant force of 1 N acting on a body along a path of 1 m traveled by the body in the direction of the force. | j | J |
| Power | Watt - power at which in 1 second. 1 J of work done | W | W |
| II. Amount of electricity, electrical voltage, electrical resistance, electrical capacitance | |||
| Amount of electricity, electric charge | Coulomb - the amount of electricity flowing through the cross-section of a conductor for 1 second. at a DC current of 1 A | To | C |
| Electrical voltage, electrical potential difference, electromotive force (EMF) | Volt is the voltage in a section of an electrical circuit through which 1 k of electricity passes through which 1 j of work is done. | V | V |
| Electrical resistance | Ohm - the resistance of a conductor through which, at a constant voltage at the ends of 1 V, a constant current of 1 A passes | ohm | Ω |
| Electrical capacity | Farad is the capacitance of a capacitor, the voltage between the plates of which changes by 1 V when charging it with an amount of electricity of 1 k. | f | F |
| III. Magnetic induction, magnetic flux, inductance, frequency | |||
| Magnetic induction | Tesla is the induction of a uniform magnetic field, which acts on a section of a straight conductor 1 m long, placed perpendicular to the direction of the field, with a force of 1 N when a direct current of 1 A passes through the conductor | tl | T |
| Magnetic induction flux | Weber - magnetic flux created by a uniform field with a magnetic induction of 1 T through an area of 1 m 2 perpendicular to the direction of the magnetic induction vector | wb | Wb |
| Inductance | Henry is the inductance of a conductor (coil) in which an emf of 1 V is induced when the current in it changes by 1 A in 1 second. | gn | H |
| Frequency | Hertz is the frequency of a periodic process in which in 1 sec. one oscillation occurs (cycle, period) | Hz | Hz |
| IV. Luminous flux, luminous energy, brightness, illumination | |||
| Light flow | Lumen is a luminous flux that gives within a solid angle of 1 ster a point source of light of 1 sv, emitting equally in all directions | lm | lm |
| Light energy | Lumen-second | lm sec | lm·s |
| Brightness | Nit - the brightness of a luminous plane, each square meter of which gives in the direction perpendicular to the plane a luminous intensity of 1 light | nt | nt |
| Illumination | Lux - illumination created by a luminous flux of 1 lm with its uniform distribution over an area of 1 m2 | OK | lx |
| Lighting quantity | Lux second | lx sec | lx·s |
