Physical values \u200b\u200band units of their measurement. Physical quantities
In its purpose and the requirements, the following types of standards are distinguished.
Primary standard - Provides reproduction and storage of a unity of physical quantity with the highest in the country (compared to other standards of the same value) accuracy. Primary standards are unique measuring complexes created taking into account the latest achievements of science and technology and ensuring the unity of measurements in the country.
Special standard - Provides reproduction of a physical unit under special conditions, in which the direct transmission of the size of the unit from the primary standard with the required accuracy is not realized, and serves for these conditions the primary benchmark.
Primary or special standard, officially approved as the original for the country, is called state. State standards are approved by the State Standard, and they are approved for each of them state standard. State standards are created, stored and applied by the Central Scientific Metrological Institutions of the country.
Secondary standard - Stores the size of a unit of physical quantity obtained by comparison with the primary benchmark of the corresponding physical value. Secondary standards relate to subordinate tools for storing units and transmitting their size during testing work and ensure the safety and lowest wear of state primary standards.
According to its metrological purpose, secondary standards are divided into copy standards, reference standards, and witness standards and working standards.
Standard-copy - Designed to transmit the size of a unit of physical quantity by a working benchmark with a large amount of calibration. It is a copy of the state primary reference only on metrological purpose, but is not always a physical copy.
Reference reference - It is used for comparison of standards, which for one or another can not be directly complicated with each other.
Etalon-witness - Designed to verify the safety and invariance of the state standard and replace it in case of damage or loss. Since most of the state standards are created on the basis of using the most sustainable physical phenomena and are on this non-destructive, currently only a kilogram standard has a witness standard.
Work standard - It is used to transmit the size of the unity of the physical size by the working means of measurement. This is the most common type of standards that are used for testing work by territorial and departmental metrological services. Work standards are divided into discharges that determine the order of their coeximation in accordance with the testing scheme.
Standards of major units si.
Standard units . A time unit - a second - for a long time was determined as 1/86400 part of the average sunny day. Later, it was revealed that the rotation of the Earth around the axis occurs unevenly. Then the definition of the unit of time was based on the period of rotation of the Earth around the Sun - the tropical year, i.e. The time interval between the two spring equinons, next one after the other. The second size was defined as 1 / 31556925,9747 part of the tropical year. This allowed almost 1000 times to improve the accuracy of determining the unit of time. However, in 1967, the 13th General Conference on measures and weighs adopted a new definition of a second as a time interval, during which 919,26,31,1770 oscillations corresponding to the resonant frequency of the energy transition between the levels of the hyperfine structure of the basic state of the cesium atom-133 in the absence of perturbation by external fields are performed. This definition is implemented using cesium frequency reper.
In 1972, a transition to the system of global coordinated time was carried out. Since 1997, the state primary control and the state calibration scheme for measuring time and frequency are determined by the rules of interstate standardization of PMG18-96 "Interstate Turning Scheme for Measuring Time and Frequency Measurement."
The state primary standard unit of time consisting of a set of measuring funds provides reproduction of time units with an average quadratic deviation of the measurement result not exceeding 1 * 10 -14 in three months.
Standard units of length. In 1889, the meter was adopted equal to the distance between two strokes deposited on the metal rod x-shaped cross-section. Although the international and national meter standards were made of platinum and iridium alloy, characterized by significant hardness and greater resistance to oxidation, but there was no complete confidence that the length of the standard over time does not change. In addition, the accuracy of comparison between the platinum-iridium stroke meters is + 1.1 * 10 -7 m (+0.11 μm), and since the strokes have a significant width, it is impossible to significantly improve the accuracy of this compaction.
After studying the spectral lines of a number of elements it was found that the greatest accuracy of the reproduction unit of length provides an orange line of cryptone-86 isotope. In 1960, the 11th General Conference on measures and weights adopted the expression of the size of the meter in the lengths of these waves as the most accurate value.
The crypton meter made it possible to improve the accuracy of the reproduction of the length of the length. However, further research made it possible to obtain a more accurate standard of meter based on the wavelength in the vacuum of monochromatic radiation generated by a stabilized laser. The development of new reference sets of meter reproduction led to a meter definition as a distance that lights light in Vacuum for 1/299792458 share of a second. This definition of the meter is enshrined in 1985.
The new reference meter reproduction complex besides increasing the measurement accuracy in the necessary cases, it also makes it possible to monitor the constancy of a platinum-iridium standard that has now become a secondary standard used to transmit the size of the unit to the working standard.
Etalon units of mass. When setting a metric system of measures, a mass of one cubic decimeter took clean water At the temperature of its greatest density (4 0 s).
During this period were held accurate definitions The masses of the known volume of water by consistent weighing in the air and water of an empty bronze cylinder, the dimensions of which were carefully defined.
The first prototype kilogram, made on the basis of these weighing, was a platinum cylindrical weight with a height of 39 mm equal to its diameter. Like a prototype of a meter, he was transferred to storage in the National Archive of France. In the 19th century, several thorough measurements of the mass of one cubic decimeter of pure water at a temperature of 4 0 s were re-carried out at a temperature of 4 0 S. It was found that this mass is a bit (approximately 0, 028g) less than the prototype of the archive kilogram. In order for further, more accurate, weighing to change the value of the initial unit of mass, the International Commission on the prototypes of the metric system in 1872. It was decided for a unit of mass to take a mass of the prototype kilogram of the archive.
In the manufacture of platinum-iridium standards, a kilogram for an international prototype was adopted by one, the mass of which was less different from the mass of the prototype kilogram of the archive.
In connection with the adoption of the conditional prototype, the litter unit was not equal to a cubic decimeter. The value of this deviation (1l \u003d 1, 000028 DM 3) corresponds to the difference between the mass of the international prototype kilogram and a mass of the cubic decimeter of water. In 1964, the 12th General Conference on Measures and Weighs decided to equate the volume of 1 l to 1 dm 3.
It should be noted that at the time of establishing a metric system, there was no clear distinction between the concepts of mass and weight, so the international prototype kilogram was considered a reference unit of weight. However, when approving the international prototype kilogram at the 1st General Conference on Measures and Weighs in 1889, a kilogram was approved as a mass prototype.
A clear distinction of a kilogram as a mass unit and a kilogram as a unit of force was given in the decisions of the 3rd General Conference on Measures and Libades (1901g).
The state primary standard and calibration scheme for mass change means is determined by GOST 8.021 - 84. The state standard consists of a complex of measures and measuring instruments:
· National kilogram prototype - copies of No. 12 of the international prototype kilogram, which is a gircuit from a platinum-iridium alloy and intended for transmitting the size of a mass unit R1;
· The national prototype kilogram is a copy of No. 26 of the international prototype kilogram, which is a gircuit from a platinum-iridium alloy and intended for verifying the amount of a mass unit that is reproduced by the national prototype of a kilogram - Copies No. 12, and replacing the latter during its comparisons in the International Bureau of Measures and scales;
· R1 giri and a set of weights made from platinum-iridium alloy and intended for transmitting the size of a unit of mass standards - copies;
· Reference weights.
The nominal value of the mass reproduced by the standard is 1 kg. The state primary standard ensures the reproduction of a mass unit with an average quadratic deviation of the measurement result during comparison with an international kilogram prototype, not exceeding 2 * 10 -3 mg.
Reference scales, with the help of which the bulge of the mass of the mass is produced, with a weighing range of 2 * 10 -3 ... 1kg have a mean quadratic deviation of the observation result on scales 5 * 10 -4 ... 3 * 10 -2 mg.
Physical bodies use values \u200b\u200bcharacterizing space, time and considered body: length L, time T and weight m. Length L is defined as a geometrical distance between two points in space.
In the international system of units (C) per unit of length, a meter (M) was adopted.
\\ [\\ left \u003d m \\]
Initially, the meter was determined as a ten-millionth fraction of a quarter of the Earth Meridian. These creators of the metric system sought to achieve invariance and accurate reproducibility of the system. The standard of meter was a platinum alloy ruler with a 10% iridium, the cross section of which, to increase the flexural stiffness with a minimum volume of metal, a special X-shaped form was granted. In the groove of such a ruler there was a longitudinal flat surface, and the meter was determined as a distance between the centers of two strokes applied across the line at its ends, at a standard temperature of 0 $ () ^ \\ CIRC $ C. Currently, in view of the increased requirements for accuracy Measurements, the meter is defined as the length of the path flowing in a vacuum light for 1/299 792 458 share of a second. This definition was made in October 1983.
Time T between two events at a specified point of space is defined as the difference in the readings of the clock (the device whose work is based on a strictly periodic and uniform physical process).
In the international system of units (C) per unit of measurement of time, a second (C) is received.
\\ [\\ left \u003d c \\]
According to modern ideas, 1 second is a time interval equal to 9,192,631,770 radiation periods, corresponding to the transition between two ultra-thin levels of the main (quantum) state of the cesium-133 atom at rest at 0to K in the absence of perturbation by external fields. This definition was adopted in 1967 (clarification on the temperature and rest of the rest appeared in 1997).
The mass M body characterizes the effort to be applied to derive it from the equilibrium position, as well as the effort with which it can attract other bodies. This testifies to the dualism of the concept of mass - as body inertness measures and the measures of its gravitational properties. According to experiments, gravitational and inert body weight are equal to at least within the limits of measurement accuracy. Therefore, in addition to special cases, they are simply said about the mass - not specifying, inert or gravitational.
In the international system of units (s) per unit of measurement of the mass adopted kilograms.
$ \\ left \u003d kg \\ $
For the international prototype kilogram, a cylinder mass made from platinum-iridium alloy, a height and diameter of about 3.9 cm, stored in the Palace of Bretelle under Paris. The weight of this reference mass, equal to 1 kg at sea level on the geographical latitude of $ 45 () ^ \\ Circ $, is sometimes called kilogram-force. Thus, it can be used either as a measure of mass for the absolute system of units, or as a standard for the technical system of units in which one of the main units is a force unit. In practical dimensions, 1 kg can be considered equal to the weight of 1 l of clean water at a temperature of + 4 ° C.
In mechanics solid media The mains are also units of measurement of thermodynamic temperature and the amount of substance.
The unit of temperature measurement in the SI system serves Kelvin:
$ \\ left [t \\ right] \u003d to $.
1 Kelvin is 1 / 273.16 parts of the thermodynamic temperature of the triple point of water. The temperature is the characteristic of the energy that the molecules are possessed.
The amount of substance is measured in a moles: $ \\ left \u003d mol $
1 mol is equal to the number of substance of the system containing the same structural elementshow much contains atoms in carbon-12 weighing 0.012 kg. When using praying structural elements should be specified and may be atoms, molecules, ions, electrons and other particles or specified particle groups.
Other units of measurement of mechanical values \u200b\u200bare derived from the main, representing their linear combination.
The length derivatives are the area S and volume V. They characterize the areas of spaces, respectively, two and three measurements occupied by extended bodies.
Units of Measurement: Square - Meter Square, Volume - Cubic meter:
\\ [\\ left \u003d m ^ 2 \\ left \u003d m ^ 3 \\]
The unit of measuring the speed in C is a meter per second: $ \\ left \u003d m / c $
Unit of measurement of force in SI --NITON: $ \\ left \u003d H $ $ 1H \u003d 1 \\ FRAC (kg \\ cdot m) (C ^ 2) $
The same derivatives of measurement units are for all other mechanical values: density, pressure, pulse, energy, work, etc.
Derivatives are obtained from the main algebraic action, such as multiplication and division. Some of the derivatives of units in C are given their own names, for example, a unit of radians.
Consoles can be used before the names of units. They mean that the unit must be multiplied or divided into a certain integer, the degree of number 10. For example, the Kilo prefix means multiplication by 1000 (kilometer \u003d 1000 meters). Cons are also called decimal prefixes.
In the technical systems of measurements, instead of a unit of mass of the main one, a unit of force is considered. There are a number of other systems close to SI, but using other major units. For example, in the SGS system, which is generally accepted until the system appears, the main unit of measurement is gram, and the main unit of length is centimeter.
Measurements are based on the comparison of the same properties of material objects. For properties, with a quantitative comparison of which physical methods are used, a unified generalized concept is established in metrology - a physical value. Physical quantity- property, in general, in a qualitative attitude of many physical objects, but in quantitatively individual for each object, for example, length, weight, electrical conductivity and heat capacity of bodies, gas pressure in the vessel, etc. But the smell is not a physical value, as it is installed With the help of subjective sensations.
Measure for quantitative comparison of the same properties of objects unit of physical quantity - The physical value that by agreement is assigned a numerical value equal to 1. The units of physical quantities are assigned a complete and abbreviated symbol designation - dimension. For example, a mass - kilogram (kg), time - second (C), length - meter (M), force - Newton (H).
The value of the physical size - An assessment of the physical quantity in the form of a certain number of units adopted for it - characterizes the quantitative individuality of objects. For example, the diameter of the opening is 0.5 mm, the radius of the globe is 6378 km, the speed of the runner is 8 m / s, the speed of light is 3 10 5 m / s.
Measure It is called the foundation of the physical value with the help of special technical means. For example, measuring the shaft diameter with a caliper or micrometer, fluid temperature - a thermometer, gas pressure to a pressure gauge or a vacuum. The value of physical quantity x ^, The resulting measurement is determined by the formula x ^ \u003d ai Where but- numerical value (size) of physical quantity; And - a unit of physical quantity.
Since the values \u200b\u200bof physical quantities find an experimental way, they contain measurement errors. In this regard, there is a true and actual meaning of physical quantities. True value - The value of the physical quantity that the corresponding property of the object is ideally reflects in a qualitative and quantitative relationship. It is the limit to which the value of the physical quantity is approaching with an increase in measurement accuracy.
Value value - The value of the physical quantity found by experimentally and is so close to the true value, which for a specific purpose can be used instead. This value varies depending on the required measurement accuracy. With technical measurements, the value of the physical quantity found with the permissible error is taken for the actual value.
Measurement error There is a deviation of the measurement result from the true value of the measured value. Absolute errorthey call the measurement error, expressed in units of the measured value: Oh = x ^ - x, Where x- True value of the measured value. Relative error - Attitude absolute error Measurements to the true meaning of physical quantity: 6 \u003d ah / x. The relative error can also be expressed as a percentage.
Since the true measurement value remains unknown, in practice you can find only an approximate estimate of the measurement error. At the same time, instead of the true value, the actual value of the physical quantity obtained during the measurement of the same value with higher accuracy is taken. For example, the error of measuring linear dimensions of the caliper is ± 0.1 mm, and micrometer - ± 0.004 mm.
Measurement accuracy can be quantified as the reverse value of the relative error module. For example, if the measurement error is ± 0.01, the measurement accuracy is 100.
In principle, you can imagine any large number of different systems of units, but only a few have received widespread. Worldwide for scientific and technical measurements and in most countries in industry and everyday life are used by the metric system.
Basic units.
In the system of units, an appropriate unit of measurement should be provided for each measured physical quantity. Thus, a separate unit of measurement is needed for length, area, volume, speed, etc., and each such unit can be determined by selecting one or another standard. But the system of units is significantly more convenient if only a few units are selected as the main, and the rest are determined through the main. So, if a number of length is a meter, the standard of which is stored in the state metrological service, then the unit of the area can be considered a square meter, a unit of volume - a cubic meter, a velocity unit - a meter per second, etc.
The convenience of such a system of units (especially for scientists and engineers who are much more common with measurements than other people) are that mathematical relationships between the main and derivative units of the system are simpler. At the same time, the unit of speed is the unit of distance (length) per unit of time, an acceleration unit is a unit of speed change per unit of time, a unit of force - a unit of acceleration unit of mass, etc. In mathematical record 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 relations between units. (Similar formulas allow you to identify units for such values \u200b\u200bas pressure or power of the electric current.) Such relations are common and are performed regardless of which units (meter, foot or arms) is measured and what units are selected for other values.
The technique for the basic unit of measurement of mechanical values \u200b\u200bis usually taken not a unit of mass, but a unit of force. Thus, if in the system, most used in physical research, the metal cylinder is taken for the standard of mass, then in the technical system it is considered as a standard of forces that balance the force acting on it. But since the strength of severity is not the same in different points on the surface of the Earth, it is necessary to indicate the location to accurately implement the reference. Historically, the location at sea level on the geographic latitude is 45 °. At the present time, such a standard is defined as the strength necessary in order to give the specified cylinder to a certain acceleration. True, in the technique of measurements are carried out, as a rule, not with such a high accuracy so that it is necessary to take care of the variations of gravity (if it comes to the graduation of measuring instruments).
Many confusion is associated with the concepts of mass, strength and weight. The fact is that there are units of all these three quantities wearing the same names. The mass is the inertial characteristics of the body, showing how difficult it is extended by the external force from the state of rest or uniform and straight movement. The unit of force is a force that, acting on a unit of mass, changes its speed per unit of speed per unit of time.
All bodies are attracted to each other. Thus, every body near the Earth is attracted to it. In other words, the Earth creates gravity acting on the body. This force is called its weight. The weight of weight, as indicated above, is not the same in different points on the surface of the Earth and at different heights above sea level due to differences in the gravitational attraction and in the manifestation of the earth's rotation. However, the total mass of this amount of the substance is unchanged; It is the same in interstellar space, and anywhere on Earth.
Exact experiments have shown that the strength of gravity acting on various bodies (that is, their weight) is proportional to their mass. Consequently, the masses can be compared on the scales, and the masses that are the same in one place will be the same and in any other place (if the comparison is carried out in vacuo to eliminate the effect of the outstanding air). If a certain body is weighed on spring weights, balancing the force of gravity by the strength of the stretched spring, the results of weight measurement will depend on the place where measurements are carried out. Therefore, spring scales need to be adjusted at each new place so that they correctly show the mass. The simplicity of the very weighing procedure was the reason that the strength of gravity acting on the reference mass was adopted for an independent unit of measurement in the technique. HEAT.
Metric system units.
The metric system is the general name of the international decimal system of units, the main units of which are meter and kilogram. In some differences in details, the elements of the system are the same all over the world.
History.
The metric system has grown out of the decisions taken National Assembly France in 1791 and 1795 to determine the meter as one ten million dollars of the plot of the earth's meridian from the North Pole to the equator.
Decree, published on July 4, 1837, the metric system was declared mandatory for use in all commercial transactions in France. She gradually displaced local and national systems in other European countries and was legally recognized as permissible in the UK and the United States. The agreement signed on May 20, 1875 seventeen countries was created an international organization designed to maintain and improve the metric system.
It is clear that, defining a meter as a ten-millionth fraction of a quarter of the earth's meridian, the creators of the metric system sought to achieve invariance and accurate reproducibility of the system. For the unit of mass they took a gram, determining it as a mass of one million cubic meter Waters with its maximum density. Since it would not be very convenient to carry out the geodesic measurements of the quarter of the earth's meridian. With each sale of the tissue meter, or to balance the basket of potatoes on the market with the corresponding amount of water, metal standards were created, with limit accuracy Reproducing these ideal definitions.
Soon it turned out that the metal standards of length can be compared with each other, making a much smaller error than with a comparison of any such standard with a quarter of the earth's meridian. In addition, it became clear that the accuracy of comparing metal standards of mass with each other is much higher than the accuracy of the comparison of any such standard with a mass of the corresponding volume of water.
In this regard, the International Commission on the meter in 1872 decided to accept for the standard "Archive" meter stored in Paris, "such what it is." In the same way, the members of the Commission took for the standard of mass. Archive platinum-iridium kilograms, "considering that a simple relation, established by the creators of the metric system, between the weight unit and the volume unit seems to be an existing kilogram with an accuracy sufficient for ordinary applications in industry and trade, and accurate Sciences need not in a simple numerical ratio of this kind, but in the maximum perfect definition of this relation. " In 1875, many countries of the world signed a meter agreement, and this Agreement established the procedure for coordinating metrological standards for the global scientific community through the International Bureau of Measures and Libra and the General Conference on Measures and Limits.
The new international organization immediately engaged in the development of international standards of length and mass and the transfer of their copies to all participating countries.
Standards of length and mass, international prototypes.
The international prototypes of standards of length and mass - meter and kilogram - were transferred to the storage of the International Bureau of measures and scales located in Sevra - suburb of Paris. The standard of meter was a platinum alloy ruler with a 10% iridium, the cross section of which, to increase the flexural stiffness with a minimum volume of metal, a special X-shaped form was granted. In the groove of such a ruler there was a longitudinal flat surface, and the meter was determined as a distance between the centers of two strokes, across the line at its ends, at the temperature of the standard equal to 0 ° C. For the international prototype kilogram, a mass of a cylinder was taken from the same platinum Iridiyevoy alloy as the standard standard, a height and diameter of about 3.9 cm. The weight of this reference mass equal to 1 kg at sea level on the geographic latitude of 45 °, sometimes called kilogram-force. Thus, it can be used either as a measure of mass for the absolute system of units, or as a standard for the technical system of units in which one of the main units is a force unit.
International prototypes were chosen from a significant batch of identical standards made at the same time. Other standards of this party were transferred to all participating countries as national prototypes (state primary standards), which are periodically returned to the International Bureau for comparison with international velarys. Comparisons held in different time Since then, they show that they do not detect deviations (from international standards), leaving the measurement accuracy.
International System SI.
The metric system was very favorably met by 19 V scientists. Partly because it was offered as an international system of units, partly for the reason that its units were theoretically assumed independently reproducible, and also due to its simplicity. Scientists began to withdraw new units for different physical quantities with whom they dealt with, based on the elementary laws of physics and linking these units with the units of the length and mass of the metric system. The latter has increasingly gained various European countries in which there were previously walking many units related to each other for different quantities.
Although in all countries who have adopted a metric unit of units, the standards of metric units were almost the same, various discrepancies have arisen in derived units between different countries and different disciplines. In the field of electricity and magnetism, two separate systems of derivatives appeared: electrostatic, based on the strength, with each other two electrical charges, and electromagnetic, based on the interaction of two hypothetical magnetic poles.
The situation is even more complicated with the advent of the so-called system. practical electrical units introduced in the middle of 19 V. British Association for Promoting Science Development to meet the queries of rapidly developing wired telegraph communications techniques. Such practical units do not coincide with the units of both above the systems, but from units of the electromagnetic system differ only by multipliers equal to whole degrees of ten.
Thus, for so ordinary electrical quantitiesAs a voltage, current and resistance, there were several options for the received units of measurement, and each scientist, an engineer, the teacher had to decide how much of these options it would be better to use. In connection with the development of electrical engineering in the second half of 19 and the first half of the 20th centuries. The practical units that began to dominate in this area have become more and more widely used.
To eliminate such confusion at the beginning of the 20th century. A proposal was put forward to combine practical electrical units with appropriate mechanical, based on metric units of length and mass, and to build some coherent (coherent) system. In 1960, the General Conference on measures and weights adopted a unified international system of units (SI), gave the definition of the main units of this system and prescribed the use of some derivatives of units, "not a predetermining question about others that can be added in the future." Thus, for the first time in history, an international coherent system of units was adopted in the history of international agreement. Currently, it is adopted as a legitimate system of units of measurement by most countries of the world.
The international system of units (C) is a coordinated system in which for any physical quantity, such as length, time or force, one and only one unit of measurement is envisaged. Some of the units are given special names, an example is the unit of pressure Pascal, while the names of others are formed from the names of those units, from which they are manufactured, for example, a speed unit - meter per second. The main units together with two additional geometric nature are presented in Table. 1. Derivatives for which special names have been taken in Table. 2. Of all derivatives of the mechanical units, the Newton force is most important, the Joule energy unit and the Watt power unit. Newton is defined as a force that gives a mass of one kilogram an acceleration equal to one meter per second in a square. Joule is equal to work that is performed when the point of the application of the force equal to one Newton is moved to a distance of one meter in the direction of force. Watt is a power at which work in one joule is performed in one second. The electric and other derivatives will be stated below. Official definitions of basic and additional units are as follows.
The meter is the length of the path flowing in a vacuum with light for 1/299 792 458 share of a second. This definition was made in October 1983.
A kilogram is equal to the mass of the international kilogram prototype.
Second - duration 9 192 631,770 periods of radiation oscillations corresponding to the transitions between the two levels of the ultra-thin structure of the main state of the cesium-133 atom.
Kelvin is 1 / 273,16 parts of the thermodynamic temperature of the triple point of water.
Mol is equal to the amount of substance, which contains as many structural elements as atoms in the carbon isotope-12 weighing 0.012 kg.
Radine - flat angle between two circle radius, the length of the arc between which is equal to the radius.
Steeradian is equal to a bodily corner with a vertex in the center of the sphere, cutting the area on its surface equal to the square of the square with a side equal to the sphere radius.
To form decimal multiple and dolly units, a number of consoles and multipliers are prescribed in Table. 3.
|
Table 3. Prefixes and multipliers of decimal multiple and dolle units of the international system |
|||||
| ex | deci | ||||
| Peta | Santi | ||||
| Tera | Milli | ||||
| Giga | micro |
mK |
|||
| mega | Nano | ||||
| kilo | pico | ||||
| hecto | Femto | ||||
| dese |
yes |
Atto | |||
Thus, a kilometer (km) is 1000 m, and a millimeter - 0.001 m. (These consoles are applicable to all units, such as in kilowatts, milliamperes, etc.)
It was originally assumed that one of the main units should be grams, and this was reflected in the names of the units of mass, but at present the main unit is a kilogram. Instead of the name of Megagrams, the word "ton" is used. In physical disciplines, for example, for measuring the wavelength of visible or infrared light, a million meter (micrometer) is often used. In spectroscopy, wavelengths are often expressed in angstroms (Å); An angstrom is equal to one tenth nanometer, i.e. 10 - 10 m. For radiation with a smaller wavelength, such as X-ray, scientific publications It is allowed to use the pitchos and an X-unit (1 X-unit. \u003d 10 -13 m). A volume equal to 1000 cubic centimeters (one cubic decimeter) is called a liter (L).
Mass, length and time.
All basic units of SI system, except a kilogram, are currently determined through physical constants or phenomena, which are considered unchanged and with high accuracy reproducible. As for a kilogram, a way to implement it has not yet been found with the degree of reproducibility, which is achieved in the comparison procedures of various mass standards with the international kilogram prototype. Such a comparison can be carried out by weighing on spring scales, the error of which does not exceed 1CH 10 -8. Standards of multiple and dolle units for a kilogram are installed by combined weighing on scales.
Since the meter is determined through the speed of light, it can be reproduced independently in any well-equipped laboratory. Thus, the interference method of the bar and end measures of length, which enjoy in workshops and laboratories, can be checked by conducting a comparison directly with the wavelength of light. The error under such methods under optimal conditions does not exceed one billion (1h 10 -9). With the development of laser technology, such measurements are very simplified, and their range expanded significantly.
In the same way, in accordance with its modern definition, it can be independently implemented in the competent laboratory on the installation with an atomic bundle. The beam atoms are excited by a high-frequency generator configured to atomic frequency, and the electronic circuit measures the time, counting periods of oscillations in the generator circuit. Such measurements can be carried out with an accuracy of 1CH 10 -12 - much higher than it was possible with the previous definitions of seconds based on the rotation of the Earth and its treatment around the Sun. Time and its reverse value - frequency - are unique in that ways that their standards can be transmitted on the radio. Thanks to this, anyone who has the appropriate radio reception equipment, can receive the exact time and reference frequency signals, which are almost not different from accuracy from transmitted to the air.
Mechanics.
Temperature and heat.
Mechanical units do not allow solving all scientific and technical tasks Without attracting any other relations. Although the work performed when moving the mass against the action of force, and kinetic energy Some mass in nature is equivalent to thermal energy of the substance, it is more convenient to consider the temperature and heat as separate values \u200b\u200bthat are independent of mechanical.
Thermodynamic temperature scale.
The unit of thermodynamic temperature of Kelvin (K), called Kelvin, is determined by the triple water point, i.e. The temperature at which water is in equilibrium with ice and ferry. This temperature is adopted equal to 273.16 K than and the thermodynamic temperature scale is determined. This scale proposed by Kelvin is based on the second principle of thermodynamics. If there are two heat reservoirs with a constant temperature and a reversible heat machine transmitting heat from one of them to another in accordance with the carno cycle, the ratio of thermodynamic temperatures of two tanks is given by equality T. 2 /T. 1 = –Q. 2 Q. 1, where Q. 2 I. Q. 1 - the amount of heat transmitted to each of the tanks (the "minus" sign indicates that one of the heat reservoirs is selected). Thus, if the temperature of a warmer reservoir is 273.16 K, and the heat, selected from it, twice as much heat transmitted to another tank, the temperature of the second tank is 136.58 K. If the temperature of the second tank is 0 k, then In general, it will not be transferred heat, since all gas energy was transformed into mechanical energy at the adiabatic expansion site in the cycle. This temperature is called absolute zero. Thermodynamic temperature used usually in scientific researchcoincides with the temperature in the equation of the state of the perfect gas PV = RTwhere P. - pressure, V.- Volume I. R. - Gas constant. The equation shows that for the perfect gas, the product of the pressure on the pressure is proportional to the temperature. None for one of the real gases is not accurately implemented. But if you contribute to virial forces, then the expansion of gases allows you to reproduce the thermodynamic temperature scale.
International temperature scale.
In accordance with the determination outlined above, the temperature can be obtained with very high accuracy (about 0.003 k near the triple point) to measure gas thermometry. The heat-insulated chamber is placed a platinum resistance thermometer and a gas tank. When the camera is heated, the electrical resistance of the thermometer increases and the gas pressure in the reservoir increases (in accordance with the equation of the state), and during cooling there is a reverse picture. Measuring simultaneously resistance and pressure, it is possible to marvel the thermometer by gas pressure, which is proportional to the temperature. Thermometer is then placed in a thermostat in which liquid water can be maintained in equilibrium with its solid and steam phases. Having measured its electrical resistance at this temperature, the thermodynamic scale is obtained, since the temperature of the triple point is attributed to the value of 273.16 K.
There are two international temperature scales - Kelvin (K) and Celsius (C). Temperature on the Celsius scale is obtained from the temperature on the Kelvin scale with subtraction from the last 273.15 K.
Accurate temperature measurements by gas thermometry require a lot of work and time. Therefore, in 1968 an international practical temperature scale (MTTH) was introduced. Using this scale, thermometers different types can be graded in the laboratory. This scale was established using a platinum resistance thermometer, thermocouples and a radiation pyrometer used in temperature ranges between some pairs of constant reference points (temperature references). MTTSH was supposed to comply with the most possible accuracy to the thermodynamic scale, but as it turned out later, its deviations are very significant.
Temperature scale Fahrenheit.
The temperature scale of Fahrenheit, which is widely used in conjunction with the British technical system of units, as well as in non-aggravated measurements in many countries, is customary to determine on two permanent reference points - ice melting temperature (32 ° F) and water boiling (212 ° F) Normal (atmospheric) pressure. Therefore, to get the temperature on the Celsius scale from the temperature on the Fahrenheit scale, you need to deduct from the last 32 and multiply the result by 5/9.
Units of heat.
Since the heat is one of the forms of energy, it can be measured in Joules, and this metric unit was adopted by an international agreement. But since once the amount of heat was determined by changing the temperature of a certain amount of water, the unit was widespread, called calorie and equal to the amount of heat required to increase the temperature of one gram of water at 1 ° C. Due to the fact that the water heat capacity depends on temperature , I had to clarify the value of calories. There were at least two different calories - "thermochemical" (4,1840 J) and "steam" (4,1868 J). "Calorior", which enjoys in the diettics, in fact there is a kilocaloria (1000 calories). Caloea is not a unit of SI system, and in most areas of science and technology, it has been separated from use.
Electricity and magnetism.
All generally accepted electrical and magnetic measurement units are based on the metric system. In agreement with modern definitions of electrical and magnetic units, they are all derived units derived from certain physical formulas from metric units of length, masses and time. Since most of the electric and magnetic values \u200b\u200bare not so easy to measure, using the mentioned standards, it was considered that it was more convenient to establish the derivatives for some of the specified values \u200b\u200bof the experiments, while others measure, using such references.
Units SI system.
The following is a list of electrical and magnetic units of the SI system.
Ampere, unit of power of electric current - one of the six basic units of the SI system. Ampere is the power of an unchanged current, which, when passing along two parallel straight-line conductors of an infinite length with a negligible area of \u200b\u200ba circular cross section, located in a vacuum at a distance of 1 m one from the other, would cause 1 m long of the interaction force in each site 10h 10 - 7 N.
Volt, unit of potential difference and electromotive power. Volt is an electrical voltage on the section of the electrical circuit with a constant current force of 1 A with an expendable power of 1 W.
Pendant, unit of electricity (electric charge). The pendant is the amount of electricity passing through the cross section of the conductor at a constant current force 1 and in time 1 s.
Faraday, unit of electrical capacity. Farrad - capacitance of the capacitor, on the plates of which, when charging 1 CL, an electrical voltage occurs 1 V.
Henry, an inductance unit. Henry is equal to the inductance of the contour, in which self-induction EMF arises in 1 V with a uniform change in the current strength in this circuit by 1 and for 1 s.
Weber, unit of magnetic flux. Weber - magnetic flow, While descending, it is up to zero in an inclined loop with a resistance of 1 ohms, an electric charge is flowing equal to 1 CL.
Tesla, unit of magnetic induction. Tesla - magnetic induction of homogeneous magnetic fieldin which the magnetic flux through a flat platform of 1 m 2, perpendicular to the induction lines is 1 WB.
Practical standards.
Light and illumination.
Units of the forces of light and illumination cannot be determined on the basis of only mechanical units. It is possible to express the stream of energy in the light wave in W / m 2, and the intensity of the light wave is in the / 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, but also the sensitivity of the human eye to the spectral distribution of this intensity.
The international agreement for the unit of Light forces was adopted by Kandela (previously called a candle) equal to the power of light in this direction of the source emitting a monochromatic radiation of the frequency of 540h 10 12 Hz ( l. \u003d 555 nm), energy force light radiation which in this direction is 1/683 W / cf. This approximately corresponds to the power of the spermacet candlelight, which once served as the standard.
If the power of the source light is equal to one candela in all directions, then the full light stream is equal to 4 p. lumens. Thus, if this source is in the center of the sphere with a radius of 1 m, the illumination of the inner surface of the sphere is equal to one lumena per square meter, i.e. One suite.
X-ray and gamma radiation, radioactivity.
X-ray (P) is an outdated unit of exposure dose of X-ray, gamma and photonic radiation, equal to the amount of radiation, which, taking into account the second-electron radiation, forms at 0.001,93 g of air of ions carrying a charge equal to one unit of the charge of the SSS of each sign. In the system system, the absorbed dose of radiation is Gray, equal to 1 J / kg. The benchmark of the absorbed dose of radiation is the installation with ionization chambers, which measure the ionization produced by radiation.
Value - This is what can be measured. Concepts such as length, area, volume, weight, time, speed, etc. are called values. The value is measurement resultsIt is determined by the number expressed in certain units. Units in which the value is measured, called units of measure.
For the designation of the magnitude, the number is written, and next to the name of the unit in which it was measured. For example, 5 cm, 10 kg, 12 km, 5 min. Each value has countless values, for example, the length can be equal to: 1 cm, 2 cm, 3 cm, etc.
The same value can be expressed in different units, such as kilograms, grams and tons - these are weight measurement units. The same value in different units is expressed by different numbers. For example, 5 cm \u003d 50 mm (length), 1 h \u003d 60 min (time), 2 kg \u003d 2000 g (weight).
Measure any value - it means to find out how many times it contains another value of the same kind, adopted per unit of measurement.
For example, we want to find out the exact length of some room. So we need to measure this length using another length, which is well known to us, for example, with a meter. To do this, we postpone the meter on the length of the room as many times as possible. If it meets the length of the room is exactly 7 times, then its length is 7 meters.
As a result, the measurement of the magnitude is obtained or named number, for example, 12 meters, or several named numbers, for example 5 meters of 7 centimeters, the totality of which is called compound nominated number.
Measures
In each state, the government has established certain units of measure for different quantities. Accurately calculated unit of measure, taken as a sample, is called etalon or exemplary unit. Made exemplary meters, kilograms, centimeters, etc., on which units for everyday use are made. Units included and approved by the state are called measures.
Measures are called uniformIf they serve to measure the values \u200b\u200bof the same kind. So, grams and kilograms are homogeneous measures, as they serve to measure weight.
Units
Below are the units of measurement of different quantities that are often found in Mathematics tasks:
Weight / Mass Measures
- 1 ton \u003d 10 centners
- 1 centner \u003d 100 kilograms
- 1 kilogram \u003d 1000 grams
- 1 gram \u003d 1000 milligrams
- 1 kilometer \u003d 1000 meters
- 1 meter \u003d 10 decimeters
- 1 decimeter \u003d 10 centimeters
- 1 centimeter \u003d 10 millimeters
- 1 square kilometer \u003d 100 hectares
- 1 hectare \u003d 10,000 square meters. metram
- 1 square meter \u003d 10,000 square meters. Santimeters
- 1 square centimeter \u003d 100 square meters. millimeters
- 1 cubic. meter \u003d 1000 cubic meters. Decimeters
- 1 cubic. Decimeter \u003d 1000 cubic meters. Santimeters
- 1 cubic. Santimeter \u003d 1000 cubic meters. millimeters
Consider such a magnitude as liter. A liter is used to measure the capacity of blood vessels. A liter is a volume that is equal to one cubic decimeter (1 liter \u003d 1 cubic meter. Decimeter).
Time measures
- 1st century (century) \u003d 100 years
- 1 year \u003d 12 months
- 1 month \u003d 30 days
- 1 week \u003d 7 days
- 1 day \u003d 24 hours
- 1 hour \u003d 60 minutes
- 1 minute \u003d 60 seconds
- 1 second \u003d 1000 milliseconds
In addition, use such time measurement units as a quarter and decade.
- quarter - 3 months
- decade - 10 days
The month is accepted in 30 days, if you do not need to determine the number and name of the month. January, March, May, July, August, October and December - 31 days. February in a simple year - 28 days, February in leap year - 29 days. April, June, September, November - 30 days.
The year is (approximately) the time during which the Earth makes a complete turn around the sun. It is customary to consider every three consecutive years to 365 days, and the next fourth is the next - in 366 days. Year containing 366 days called leap, and the years containing 365 days - simple. By the fourth year, one extra day is added for the following reason. The time of circulation of the Earth around the Sun contains in itself not exactly 365 days, but 365 days and 6 hours (approximately). Thus, the simple year is shorter than the true year for 6 hours, and 4 of the ordinary year in short, 4 true years for 24 hours, i.e. on one day. Therefore, each fourth year add one day (February 29).
On the other types of magnitude you will learn as the last study of various sciences.
Abbreviated names of Mer.
Abbreviated names of measures are taken to record no point:
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Weight / Mass Measures
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Square measures (square measures)
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Time measures
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Vessel capacity measure
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Measuring instruments
For measuring different quantities, special measuring instruments are used. Some of them are very simple and are intended for simple measurements. Such instruments include a measuring ruler, roulette, measuring cylinder, etc. Other measuring instruments are more complex. Such devices include stopwalls, thermometers, electronic scales, etc.
Measuring instruments, as a rule, have a measuring scale (or briefly). This means that bar divisions are applied on the instrument, and the corresponding value is written next to each bar division. The distance between two strokes, near which the value is written, can be additionally divided into several smaller divisions, these divisions are most often indicated by numbers.
To determine what value of the value corresponds to each small division, it is not difficult. For example, the figure below shows the measuring ruler:
Figures 1, 2, 3, 4, etc. indicate distances between strokes, which are divided into 10 identical divisions. Consequently, each division (the distance between the nearest strokes) corresponds to 1 mm. This value is called price division scale Measuring instrument.
Before proceeding with the measurement of the value, the price of dividing the scale of the instrument used should be determined.
In order to determine the fission price, it is necessary:
- Find the two nearest touches of the scale, near which the values \u200b\u200bare written.
- The deduction from the larger value is less and the resulting number is divided into the number of divisions between them.
As an example, we will determine the division of the thermometer scale depicted in the picture on the left.
Take two strokes, about which the numeric values \u200b\u200bof the measured value (temperature) are applied.
For example, touches with notation 20 ° C and 30 ° C. The distance between these strokes is divided into 10 divisions. Thus, the price of each division will be equal to:
(30 ° C - 20 ° C): 10 \u003d 1 ° C
Consequently, the thermometer shows 47 ° C.
Measure various values \u200b\u200bin everyday life You have to constantly each of us. For example, to come in time to school or to work, it is necessary to measure the time that will be spent on the road. Meteorologists for weather prediction measure temperature, atmospheric pressure, wind speed, etc.
