Physical quantities. Physical quantity and its measurement
Physical quantity called physical property material object, process, physical phenomenon, characterized quantitatively.
The value of a physical quantity expressed by one or more numbers characterizing this physical quantity, indicating the unit of measurement.
The size of a physical quantity are the values of the numbers appearing in the meaning of the physical quantity.
Units of measurement of physical quantities.
The unit of measurement of a physical quantity is a fixed size value that is assigned a numeric value equal to one. It is used for the quantitative expression of physical quantities homogeneous with it. A system of units of physical quantities is a set of basic and derived units based on a certain system of quantities.
Only a few systems of units have become widespread. In most cases, many countries use the metric system.
Basic units.
Measure physical quantity - means to compare it with another similar physical quantity, taken as a unit.
The length of an object is compared with a unit of length, body weight - with a unit of weight, etc. But if one researcher measures the length in sazhens, and another in feet, it will be difficult for them to compare these two values. Therefore, all physical quantities around the world are usually measured in the same units. In 1963 it was adopted International system SI units (System international - SI).
For each physical quantity in the system of units, an appropriate unit of measurement must be provided. Standard units is its physical realization.
The length standard is meter- the distance between two strokes applied on a specially shaped rod made of an alloy of platinum and iridium.
Standard time is the duration of any correctly repeating process, which is chosen as the movement of the Earth around the Sun: the Earth makes one revolution per year. But the unit of time is not a year, but give me a sec.
For a unit speed take the speed of such a uniform rectilinear motion, at which the body moves 1 m in 1 s.
A separate unit of measurement is used for area, volume, length, etc. Each unit is determined when choosing one or another standard. But the system of units is much more convenient if only a few units are chosen as the main ones, and the rest are determined through the main ones. For example, if the unit of length is meter, then the unit of area is square meter, volume - cubic meter, speed - meter per second, etc.
Basic units The physical quantities in the International System of Units (SI) are: meter (m), kilogram (kg), second (s), ampere (A), kelvin (K), candela (cd) and mole (mol).
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Basic SI units |
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Value |
Unit |
Designation |
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Name |
Russian |
international |
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Strength electric current |
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Thermodynamic temperature |
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The power of light |
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Amount of substance |
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There are also SI derived units that have own names:
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SI derived units with their own names |
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Unit |
Derived unit expression |
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Value |
Name |
Designation |
Via other SI units |
Through basic and additional SI units |
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Pressure |
m -1 ChkgChs -2 |
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Energy, work, amount of heat |
m 2 ChkgChs -2 |
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Power, energy flow |
m 2 ChkgChs -3 |
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Quantity of electricity, electric charge |
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Electrical voltage, electrical potential |
m 2 ChkgChs -3 CHA -1 |
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Electrical capacitance |
m -2 Chkg -1 Hs 4 CHA 2 |
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Electrical resistance |
m 2 ChkgChs -3 CHA -2 |
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electrical conductivity |
m -2 Chkg -1 Hs 3 CHA 2 |
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Flux of magnetic induction |
m 2 ChkgChs -2 CHA -1 |
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Magnetic induction |
kghs -2 CHA -1 |
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Inductance |
m 2 ChkgChs -2 CHA -2 |
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Light flow |
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illumination |
m 2 ChkdChsr |
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Radioactive source activity |
becquerel |
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Absorbed radiation dose |
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ANDmeasurements. To obtain an accurate, objective and easily reproducible description of a physical quantity, measurements are used. Without measurements, a physical quantity cannot be quantified. Definitions such as "low" or "high" pressure, "low" or "high" temperature reflect only subjective opinions and do not contain comparison with reference values. When measuring a physical quantity, it is assigned a certain numerical value.
Measurements are made using measuring instruments. There is quite a large number of measuring instruments and fixtures, from the simplest to the most complex. For example, length is measured with a ruler or tape measure, temperature with a thermometer, width with calipers.
Measuring instruments are classified: according to the method of presenting information (indicating or recording), according to the method of measurement (direct action and comparison), according to the form of presentation of indications (analog and digital), etc.
The measuring instruments are characterized by the following parameters:
Measuring range- the range of values of the measured value, on which the device is designed during its normal operation (with a given measurement accuracy).
Sensitivity threshold- the minimum (threshold) value of the measured value, distinguished by the device.
Sensitivity- relates the value of the measured parameter and the corresponding change in instrument readings.
Accuracy- the ability of the device to indicate the true value of the measured indicator.
Stability- the ability of the device to maintain a given measurement accuracy for a certain time after calibration.
Physical quantity - a property of physical objects that is qualitatively common to many objects, but quantitatively individual for each of them. The qualitative side of the concept of "physical quantity" determines its kind (for example, electrical resistance as common property conductors of electricity), and quantitative - its "size" (the value of the electrical resistance of a particular conductor, for example R \u003d 100 Ohm). The numerical value of the measurement result depends on the choice of the unit of the physical quantity.
Physical quantities are assigned letter symbols used in physical equations expressing relationships between physical quantities that exist in physical objects.
The size of a physical quantity - quantitative certainty of the value inherent in a particular object, system, phenomenon or process.
The value of a physical quantity- an estimate of the size of a physical quantity in the form of a certain number of units of measurement accepted for it. Numerical value of a physical quantity- an abstract number expressing the ratio of the value of a physical quantity to the corresponding unit of a given physical quantity (for example, 220 V is the value of the voltage amplitude, and the number 220 itself is a numerical value). It is the term "value" that should be used to express the quantitative side of the property in question. It is incorrect to say and write "current value", "voltage value", etc., since current and voltage are quantities themselves (the terms "current value", "voltage value" will be correct).
With the chosen assessment of a physical quantity, it is characterized by true, real and measured values.
The true value of a physical quantity name the value of a physical quantity that would ideally reflect the corresponding property of the object in qualitative and quantitative terms. It is impossible to determine it experimentally due to inevitable measurement errors.
This concept is based on two main postulates of metrology:
§ the true value of the determined quantity exists and it is constant;
§ the true value of the measured quantity cannot be found.
In practice, they operate with the concept of a real value, the degree of approximation of which to true value depends on the accuracy of the measuring instrument and the error of the measurements themselves.
The actual value of a physical quantity name its value, found experimentally and so close to the true value that for a certain purpose it can be used instead.
Under measured value understand the value of the quantity, counted by the indicator device of the measuring instrument.
Unit of physical quantity - the value of a fixed size, which is conventionally assigned a standard numerical value equal to one.
Units of physical quantities are divided into basic and derivatives and combined into systems of units of physical quantities. The unit of measurement is set for each of the physical quantities, taking into account the fact that many quantities are interconnected by certain dependencies. Therefore, only a part of physical quantities and their units are determined independently of others. Such quantities are called main. Other physical quantities - derivatives and they are found using physical laws and dependencies through the main ones. The set of basic and derived units of physical quantities, formed in accordance with accepted principles, is called system of units of physical quantities. The unit of the basic physical quantity is basic unit systems.
International system of units (SI system; SI - French. Systeme International) was adopted by the XI General Conference on Weights and Measures in 1960.
The SI system is based on seven basic and two additional physical units. Basic units: meter, kilogram, second, ampere, kelvin, mole and candela (Table 1).
Table 1. Units of the International SI system
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Name |
Dimension |
Name |
Designation |
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international |
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Main |
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kilogram |
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The strength of the electric current |
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Temperature |
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Amount of substance |
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The power of light |
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Additional |
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flat corner |
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Solid angle |
steradian |
Meter is equal to the distance traveled by light in vacuum in 1/299792458 of a second.
Kilogram- a unit of mass, defined as the mass of the international prototype of the kilogram, representing a cylinder made of an alloy of platinum and iridium.
Second is equal to 9192631770 periods of radiation corresponding to the energy transition between two levels of the hyperfine structure of the ground state of the cesium-133 atom.
Ampere- the strength of an unchanging current, which, passing through two parallel rectilinear conductors of infinite length and negligible circular cross-sectional area, located at a distance of 1 m from one another in a vacuum, would cause an interaction force equal to 210 -7 N (newton) on each section of the conductor 1 m long.
Kelvin- a unit of thermodynamic temperature equal to 1/273.16 of the thermodynamic temperature of the triple point of water, that is, the temperature at which the three phases of water - vapor, liquid and solid - are in dynamic equilibrium.
mole- the amount of a substance containing so much structural elements, how much is contained in carbon-12 weighing 0.012 kg.
Candela- the strength of the light given direction a source emitting monochromatic radiation with a frequency of 54010 12 Hz (wavelength about 0.555 microns), whose energy radiation strength in this direction is 1/683 W / sr (sr - steradian).
Additional units SI systems are only for the formation of units angular velocity and angular acceleration. Additional physical quantities of the SI system include flat and solid angles.
Radian (glad) is the angle between two radii of a circle whose arc length is equal to this radius. In practical cases, the following units of measurement of angular values are often used:
degree - 1 _ \u003d 2p / 360 rad \u003d 1.745310 -2 rad;
minute - 1 "= 1 _ / 60 = 2.9088 10 -4 rad;
second - 1 "= 1" / 60 = 1 _ / 3600 = 4.848110 -6 rad;
radian - 1 rad \u003d 57 _ 17 "45" \u003d 57.2961 _ \u003d (3.4378 10 3) "= (2.062710 5)".
Steradian (Wed) is a solid angle with a vertex in 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.
Measure solid angles using planar angles and calculation
where b- solid angle; c- flat angle at the top of the cone formed inside the sphere by a given solid angle.
Derived units of the SI system are formed from basic and additional units.
In the field of measurements of electrical and magnetic quantities, there is one basic unit - ampere (A). Through the ampere and the power unit - watt (W), common for electrical, magnetic, mechanical and thermal quantities, all other electrical and magnetic units can be determined. However, today there are no sufficiently accurate means of reproducing a watt by absolute methods. Therefore, electrical and magnetic units are based on units of current and the unit of capacitance, the farad, derived from the ampere.
Physical quantities derived from the ampere also include:
§ unit of electromotive force (EMF) and electric voltage - volt (V);
§ unit of frequency - hertz (Hz);
§ unit of electrical resistance - ohm (Ohm);
§ unit of inductance and mutual inductance of two coils - henry (H).
In table. Tables 2 and 3 show the derived units most commonly used in telecommunication systems and radio engineering.
Table 2. SI derived units
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Value |
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Name |
Dimension |
Name |
Designation |
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international |
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Energy, work, amount of heat |
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Strength, weight |
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Power, energy flow |
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The amount of electricity |
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Electrical voltage, electromotive force (EMF), potential |
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Electrical capacitance |
L -2 M -1 T 4 I 2 |
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Electrical resistance |
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electrical conductivity |
L -2 M -1 T 3 I 2 |
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Magnetic induction |
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Flux of magnetic induction |
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Inductance, mutual inductance |
Table 3. SI units used in measurement practice
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Value |
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Name |
Dimension |
unit of measurement |
Designation |
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international |
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Electric current density |
ampere per square meter |
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Electric field strength |
volt per meter |
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Absolute permittivity |
L 3 M -1 T 4 I 2 |
farad per meter |
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Specific electrical resistance |
ohm per meter |
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Total power of the electrical circuit |
volt-ampere |
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Reactive power of an electrical circuit |
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Magnetic field strength |
ampere per meter |
Abbreviated designations of units, both international and Russian, named after great scientists, are written in capital letters, for example, ampere - A; om - Om; volt - V; farad - F. For comparison: meter - m, second - s, kilogram - kg.
In practice, the use of integer units is not always convenient, since measurements result in very large or very small values. Therefore, in the SI system, its decimal multiples and submultiples are established, which are formed using multipliers. Multiple and submultiple units of quantities are written together with the name of the main or derived unit: kilometer (km), millivolt (mV); megaohm (MOhm).
Multiple unit of physical quantity- a unit that is an integer number of times larger than the system unit, for example, kilohertz (10 3 Hz). Sub-multiple unit of physical quantity- a unit that is an integer number of times less than the system unit, for example microhenry (10 -6 Gn).
The names of multiple and submultiple units of the SI system contain a number of prefixes corresponding to multipliers (Table 4).
Table 4. Multipliers and prefixes for the formation of decimal multiples and submultiples of SI units
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Factor |
Prefix |
Prefix designation |
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international |
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The concept of a physical quantity is common in physics and metrology and is used to describe the material systems of objects.
Physical quantity, as mentioned above, this is a characteristic that is qualitatively common for a variety of objects, processes, phenomena, and quantitatively - individual for each of them. For example, all bodies have their own mass and temperature, but numerical values these options for different bodies different. The quantitative content of this property in the object is the size of the physical quantity, numerical assessment of its size called the value of the physical quantity.
A physical quantity that expresses the same qualitative property is called homogeneous (of the same name ).
The main task of measurements - obtaining information about the values of a physical quantity in the form of a certain number of units accepted for it.
The values of physical quantities are divided into true and real.
true value is a value that ideally reflects qualitatively and quantitatively the corresponding properties of the object.
Actual value is a value found experimentally and so close to the true that it can be taken instead.
Physical quantities are classified according to a number of features. There are the following classification:
1) in relation to the signals of measuring information, physical quantities are: active - quantities that, without the use of auxiliary energy sources, can be converted into a signal of measuring information; liability nye - quantities that require the use of auxiliary energy sources, through which a signal of measuring information is created;
2) on the basis of additivity, physical quantities are divided into: additive , or extensive, which can be measured in parts, as well as accurately reproduced using a multi-valued measure based on the summation of the sizes of individual measures; not additive, or intensive, which are not directly measured, but are converted into a measurement of a quantity or a measurement by indirect measurements. (Additivity (lat. additivus - added) is a property of quantities, consisting in the fact that the value of the quantity corresponding to the whole object is equal to the sum of the values of the quantities corresponding to its parts).
Development evolution systems of physical units.
Metric- the first system of units of physical quantities
was adopted in 1791 by the National Assembly of France. She included units of length, area, volume, capacity and weight , which were based on two units - meter and kilogram . It differed from the system of units used now, and was not yet a system of units in the modern sense.
Absolute systemunits of physical quantities.
The method of constructing a system of units as a set of basic and derived units was developed and proposed in 1832 by the German mathematician K. Gauss, who called it an absolute system. As a basis, he took three quantities independent of each other - mass, length, time .
For the main units these values he took milligram, millimeter, second , assuming that the remaining units can be determined using them.
Later, a number of systems of units of physical quantities appeared, built according to the principle proposed by Gauss, and based on metric system measures, but differing in basic units.
In accordance with the proposed Gauss principle, the main systems of units of physical quantities are:
GHS system, in which the base units are the centimeter as a unit of length, the gram as a unit of mass, and the second as a unit of time; was installed in 1881;
ICSS system. The use of the kilogram as a unit of weight, and later as a unit of force in general, led at the end of the 19th century. to the formation of a system of units of physical quantities with three basic units: a meter - a unit of length, a kilogram - force - a unit of force, a second - a unit of time;
5. MKSA system- the basic units are meter, kilogram, second and ampere. The foundations of this system were proposed in 1901 by the Italian scientist J. Giorgi.
International relations in the field of science and economics required the unification of units of measurement, the creation unified system units of physical quantities, covering various branches of the measurement area and preserving the principle of coherence, i.e. equality to unity of the coefficient of proportionality in the equations of connection between physical quantities.
SystemSI. In 1954, the commission for the development of a unified International
system of units proposed a draft system of units, which was approved in 1960. XI General Conference on Weights and Measures. The International System of Units (abbreviated as SI) took its name from the initial letters of the French name System International.
The International System of Units (SI) includes seven main (Table 1), two additional and a number of non-system units of measurement.
Table 1 - International system of units
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Physical quantities having an officially approved standard |
Unit of measurement |
Unit abbreviation physical quantity |
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international |
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kilogram | |||
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The strength of the electric current | |||
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Temperature | |||
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Illumination unit | |||
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Amount of substance | |||
Source: Tyurin N.I. Introduction to metrology. Moscow: Standards Publishing House, 1985.
Basic units measurements physical quantities in accordance with the decisions of the General Conference on Weights and Measures are defined as follows:
meter - the length of the path that light travels in a vacuum in 1/299,792,458 of a second;
the kilogram is 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 Cs 133 atom;
the ampere is equal to the strength of the unchanging current, which, when passing through two parallel straight conductors of infinite length and negligible circular cross-sectional area, located at a distance of 1 m from one another in a vacuum, causes an interaction force on each section of the conductor 1 m long;
candela is equal to the intensity of light in a given direction of a source that emits ionoprotective radiation, the energy intensity of which in this direction is 1/683 W/sr;
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 substance of a system containing as many structural elements as there are atoms in C 12 weighing 0.012 kg 2.
Additional units International system of units for measuring flat and solid angles:
radian (rad) - a flat angle between two radii of a circle, the arc between which is equal in length to the radius. In degrees, a radian is 57°17"48"3;
steradian (sr) - solid angle, the vertex of which is located in the center of the sphere and which cuts out on the surface sphere area, equal to the area of a square with sides equal in length to the radius of the sphere.
Additional SI units are used to form units of angular velocity, angular acceleration, and some other quantities. The radian and steradian are used for theoretical constructions and calculations, since most of the practical values of angles in radians are expressed in transcendental numbers.
Off-system units:
A tenth of a bela is taken as a logarithmic unit - decibel (dB);
Diopter - light intensity for optical instruments;
Reactive power-var (VA);
Astronomical unit (au) - 149.6 million km;
A light year is the distance that a ray of light travels in 1 year;
Capacity - liter (l);
Area - hectare (ha).
Logarithmic units are subdivided into absolute, which represent decimal logarithm the ratio of the physical quantity to the normalized value, and relative, formed as a decimal logarithm of the ratio of any two homogeneous (of the same name) quantities.
The non-SI units are degrees and minutes. The remaining units are derived.
Derived units SI are formed using the simplest equations that relate quantities and in which the numerical coefficients are equal to one. In this case, the derived unit is called coherent.
Dimension is a qualitative display of the measured values. The value of a quantity is obtained as a result of its measurement or calculation in accordance with master equation frommeasurements:Q = q * [ Q]
where Q - the value of the quantity; q- numerical value of the measured value in conventional units; [Q] - the unit selected for measurement.
If the defining equation includes a numerical coefficient, then to form a derived unit, the right side of the Equation should be substituted with such numerical values of the initial quantities so that the numerical value of the derived unit being determined is equal to one.
(For example, 1 ml is taken as a unit for measuring the mass of a liquid, therefore it is indicated on the package: 250 ml, 750, etc., but if 1 l is taken as a unit of measurement, then the same amount of liquid will be indicated 0.25 l. , 075 liters respectively).
As one of the ways to form multiples and submultiples, the decimal multiplicity between larger and smaller units, adopted in the metric system of measures, is used. In table. 1.2 provides multipliers and prefixes for the formation of decimal multiples and submultiples and their names.
Table 2 - Multipliers and prefixes for the formation of decimal multiples and submultiples and their names
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Factor |
Prefix |
Prefix designation |
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international |
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(Exabyte is a unit of measurement of the amount of information, equal to 1018 or 260 bytes. 1 EeV (exaelectronvolt) = 1018 electronvolts = 0.1602 joules)
It should be borne in mind that when forming multiple and submultiple units of area and volume with the help of prefixes, a dual reading may occur, depending on where the prefix is added. For example, 1 m 2 can be used as 1 square meter and as 100 square centimeters, which is far from the same thing, because 1 square meter is 10,000 square centimeters.
According to international rules, multiples and submultiples of area and volume units should be formed by adding prefixes to the original units. Degrees refer to those units that are obtained as a result of the addition of prefixes. For example, 1 km 2 \u003d 1 (km) 2 \u003d (10 3 m) 2 \u003d= 10 6 m 2.
To ensure the uniformity of measurements, the identity of the units in which all measuring instruments of the same physical quantity are calibrated is necessary. The unity of measurements is achieved by storing, accurately reproducing the established units of physical quantities and transferring their sizes to all working measuring instruments using standards and exemplary measuring instruments.
Reference - a measuring instrument that ensures the storage and reproduction of a legalized unit of physical quantity, as well as the transfer of its size to other measuring instruments.
The creation, storage and use of standards, control of their condition are subject to uniform rules established by GOST “GSI. Standards of units of physical quantities. The order of development, approval, registration, storage and application.
By subordination standards are subdivided into primary and secondary and have the following classification.
primary standard provides storage, reproduction of the unit and transmission of dimensions with the highest accuracy in the country, achievable in this area of measurement:
- special primary standards- designed to reproduce the unit under conditions in which direct transmission of the unit size from the primary standard with the required accuracy is technically unfeasible, for example, for low and high voltages, microwave and high frequency. They are approved as state standards. In view of the special importance of state standards and in order to give them the force of law, GOST is approved for each state standard. Creates, approves, stores and applies state standards State Committee for Standards.
secondary standard reproduces the unit under special conditions and replaces the primary standard under these conditions. It is created and approved to ensure the least wear of the state standard. Secondary standards in turn divided according to purpose:
Copy standards - designed to transfer the sizes of units to working standards;
Comparison standards - designed to check the safety of the state standard and to replace it in case of damage or loss;
Witness standards - are used to compare standards that, for one reason or another, cannot be directly compared with each other;
Working standards - reproduce the unit from the secondary standards and serve to transfer the size to the standard of a lower rank. Secondary standards are created, approved, stored and used by ministries and departments.
unit reference - one means or a set of measuring instruments that ensure the storage and reproduction of the unit in order to transfer its size to the lower-level measuring instruments according to the verification scheme, made according to a special specification and officially approved in the prescribed manner as a standard.
Reproduction of units, depending on the technical and economic requirements, is carried out by two ways:
- centralized- using a single state standard for the whole country or a group of countries. All basic units and most of the derivatives are reproduced centrally;
- decentralized- applicable to derived units, the size of which cannot be transferred by direct comparison with the standard and provide the necessary accuracy.
The standard establishes a multi-stage procedure for transferring the dimensions of a unit of a physical quantity from the state standard to all working means of measuring a given physical quantity using secondary standards and exemplary means of measuring various categories from the highest first to the lowest and from exemplary means to workers.
The transfer of size is carried out by various verification methods, mainly known measurement methods. Transferring the size in a stepwise way is accompanied by a loss of accuracy, however, multi-stepping allows you to save standards and transfer the size of a unit to all working measuring instruments.
Study of physical phenomena and their laws, as well as the use of these laws in practical human activity is associated with the measurement of physical quantities.
A physical quantity is a property that is qualitatively common to many physical objects (physical systems, their states and processes occurring in them), but quantitatively individual for each object.
A physical quantity is, for example, mass. Different physical objects have mass: all bodies, all particles of matter, particles of the electromagnetic field, etc. Qualitatively, all specific realizations of mass, i.e., the masses of all physical objects, are the same. But the mass of one object can be a certain number of times greater or less than the mass of another. And in this quantitative sense, mass is a property that is individual for each object. Physical quantities are also length, temperature, electric field strength, oscillation period, etc.
Specific realizations of the same physical quantity are called homogeneous quantities. For example, the distance between the pupils of your eyes and the height of the Eiffel Tower are concrete realizations of the same physical quantity - length, and therefore are homogeneous quantities. The mass of this book and the mass of the Earth's satellite Kosmos-897 are also homogeneous physical quantities.
Homogeneous physical quantities differ from each other in size. The size of a physical quantity is
quantitative content in this object of a property corresponding to the concept of "physical quantity".
The sizes of homogeneous physical quantities of various objects can be compared with each other if the values of these quantities are determined.
The value of a physical quantity is an estimate of a physical quantity in the form of a certain number of units accepted for it (see p. 14). For example, the value of the length of a certain body, 5 kg is the value of the mass of a certain body, etc. An abstract number included in the value of a physical quantity (in our examples 10 and 5) is called a numerical value. In the general case, the value X of a certain quantity can be expressed as the formula
where is the numerical value of the quantity, its unit.
It is necessary to distinguish between the true and actual values of a physical quantity.
The true value of a physical quantity is the value of the quantity that would ideally reflect the corresponding property of the object in qualitative and quantitative terms.
The actual value of a physical quantity is the value of the quantity found experimentally and so close to the true value that it can be used instead of it for a given purpose.
Finding the value of a physical quantity empirically using special technical means called measurement.
The true values of physical quantities are, as a rule, unknown. For example, no one knows the true values of the speed of light, the distance from the Earth to the Moon, the mass of an electron, a proton, and others. elementary particles. We do not know the true value of our height and body weight, we do not know and cannot find out the true value of the air temperature in our room, the length of the table at which we work, etc.
However, using special technical means, it is possible to determine the actual
all these and many other values. At the same time, the degree of approximation of these actual values to the true values of physical quantities depends on the perfection of the technical means of measurement used in this case.
Measuring instruments include measures, measuring instruments, etc. A measure is understood as a measuring instrument designed to reproduce a physical quantity of a given size. For example, a weight is a measure of mass, a ruler with millimeter divisions is a measure of length, a measuring flask is a measure of volume (capacity), a normal element is a measure of electromotive force, a quartz oscillator is a measure of the frequency of electrical oscillations, etc.
A measuring device is a measuring instrument designed to generate a signal of measuring information in a form accessible to direct perception observation. Measuring instruments include dynamometer, ammeter, manometer, etc.
There are direct and indirect measurements.
A direct measurement is a measurement in which the desired value of a quantity is found directly from experimental data. Direct measurements include, for example, the measurement of mass on an equal-arm scale, temperature - with a thermometer, length - with a scale ruler.
Indirect measurement is a measurement in which the desired value of a quantity is found on the basis of a known relationship between it and the quantities subjected to direct measurements. Indirect measurements are, for example, finding the density of a body by its mass and geometric dimensions, finding the electrical resistivity of a conductor by its resistance, length and cross-sectional area.
Measurements of physical quantities are based on various physical phenomena. For example, to measure temperature, use thermal expansion bodies or thermoelectric effect, to measure the mass of bodies by weighing - the phenomenon of gravity, etc. The set of physical phenomena on which measurements are based is called the principle of measurement. Measurement principles are not covered in this manual. Metrology deals with the study of the principles and methods of measurements, types of measuring instruments, measurement errors and other issues related to measurements.
INTRODUCTION
A physical quantity is a characteristic of one of the properties of a physical object (physical system, phenomenon or process), which is qualitatively common to many physical objects, but quantitatively individual for each object.
Individuality is understood in the sense that the value of a quantity or the size of a quantity can be for one object a certain number of times greater or less than for another.
The value of a physical quantity is an estimate of its size in the form of a certain number of units accepted for it or a number according to the scale adopted for it. For example, 120 mm is the value of a linear value; 75 kg is the value of body weight.
There are true and real values of a physical quantity. A true value is a value that ideally reflects a property of an object. Real value - the value of a physical quantity, found experimentally, close enough to the true value that can be used instead.
The measurement of a physical quantity is a set of operations for the use of a technical means that stores a unit or reproduces a scale of a physical quantity, which consists in comparing (explicitly or implicitly) the measured quantity with its unit or scale in order to obtain the value of this quantity in the form most convenient for use.
There are three types of physical quantities, the measurement of which is carried out according to fundamentally different rules.
The first type of physical quantities includes quantities on the set of dimensions of which only the order and equivalence relations are defined. These are relationships like "softer", "harder", "warmer", "colder", etc.
Quantities of this kind include, for example, hardness, defined as the ability of a body to resist the penetration of another body into it; temperature, as the degree of body heat, etc.
The existence of such relations is established theoretically or experimentally using special means comparisons, as well as on the basis of observations of the results of the impact of a physical quantity on any objects.
For the second type of physical quantities, the relation of order and equivalence takes place both between sizes and between differences in pairs of their sizes.
A typical example is the scale of time intervals. So, the differences of time intervals are considered equal if the distances between the corresponding marks are equal.
The third type is additive physical quantities.
Additive physical quantities are called quantities, on the set of sizes of which not only the order and equivalence relations are defined, but also the operations of addition and subtraction
Such quantities include, for example, length, mass, current strength, etc. They can be measured in parts, and also reproduced using a multi-valued measure based on the summation of individual measures.
The sum of the masses of two bodies is the mass of such a body, which is balanced on the first two equal-arm scales.
The dimensions of any two homogeneous PV or any two sizes of the same PV can be compared with each other, i.e., find how many times one is larger (or smaller) than the other. To compare m sizes Q", Q", ... , Q (m) with each other, it is necessary to consider C m 2 of their relationship. It is easier to compare each of them with one size [Q] of a homogeneous PV, if we take it as a unit of the PV size, (abbreviated as a PV unit). As a result of such a comparison, we obtain expressions for the dimensions Q", Q", ... , Q (m) in the form of some numbers n", n", .. . ,n (m) PV units: Q" = n" [Q]; Q" = n"[Q]; ...; Q(m) = n(m)[Q]. If the comparison is carried out experimentally, then only m experiments are required (instead of C m 2), and the comparison of the sizes Q", Q", ... , Q (m) with each other can be performed only by calculations like
where n (i) / n (j) are abstract numbers.
Type equality
is called the basic measurement equation, where n [Q] is the value of the size of the PV (abbreviated as the value of the PV). The PV value is a named number, composed of the numerical value of the PV size, (abbreviated as the numerical value of the PV) and the name of the PV unit. For example, with n = 3.8 and [Q] = 1 gram, the size of the mass Q = n [Q] = 3.8 grams, with n = 0.7 and [Q] = 1 ampere, the size of the current strength Q = n [Q ] = 0.7 amperes. Usually, instead of “the size of the mass is 3.8 grams”, “the size of the current is 0.7 amperes”, etc., they say and write more briefly: “the mass is 3.8 grams”, “the current is 0.7 amperes " etc.
The dimensions of the PV are most often found as a result of their measurement. The measurement of the size of the PV (abbreviated as the measurement of the PV) consists in the fact that by experience, using special technical means, the value of the PV is found and the proximity of this value to the value that ideally reflects the size of this PV is estimated. The PV value found in this way will be called nominal.
The same Q dimension can be expressed different values with different numerical values depending on the choice of the PV unit (Q = 2 hours = 120 minutes = 7200 seconds = = 1/12 days). If we take two different units and , then we can write Q = n 1 and Q = n 2, whence
n 1 / n 2 \u003d /,
i.e., the numerical values of the PV are inversely proportional to its units.
From the fact that the size of the PV does not depend on its chosen unit, the condition for the unambiguity of measurements follows, which consists in the fact that the ratio of two values of a certain PV should not depend on which units were used in the measurement. For example, the ratio of the speeds of a car and a train does not depend on whether these speeds are expressed in kilometers per hour or meters per second. This condition, which at first glance seems indisputable, unfortunately, cannot yet be met when measuring some PVs (hardness, photosensitivity, etc.).
1. THEORETICAL PART
1.1 The concept of a physical quantity
Weight objects of the surrounding world are characterized by their properties. Property is a philosophical category that expresses such a side of an object (phenomenon, process) that determines its difference or commonality with other objects (phenomena, processes) and is found in its relationship to them. The property is a quality category. For a quantitative description of various properties of processes and physical bodies, the concept of quantity is introduced. A value is a property of something that can be distinguished from other properties and evaluated in one way or another, including quantitatively. The value does not exist by itself, it takes place only insofar as there is an object with properties expressed by this value.
An analysis of the values allows us to divide them (Fig. 1) into two types: the values material form(real) and values of ideal models of reality (ideal), which relate mainly to mathematics and are a generalization (model) of specific real concepts.
Real quantities, in turn, are divided into physical and non-physical. A physical quantity in the most general case can be defined as a quantity inherent in material objects (processes, phenomena) studied in the natural (physics, chemistry) and technical sciences. Non-physical quantities should include quantities inherent in the social (non-physical) sciences - philosophy, sociology, economics, etc.
Rice. 1. Classification of quantities.
The document RMG 29-99 interprets a physical quantity as one of the properties of a physical object, which is qualitatively common for many physical objects, but quantitatively individual for each of them. Individuality in quantitative terms is understood in the sense that a property can be for one object a certain number of times more or less than for another.
Physical quantities it is advisable to divide into measured and evaluated. Measured FIs can be expressed quantitatively as a certain number of established units of measure. The possibility of introducing and using such units is important hallmark measured PV. Physical quantities for which, for one reason or another, a unit of measurement cannot be introduced, can only be estimated. Evaluation is understood as the operation of assigning a certain number to a given value, carried out according to established rules. Evaluation of the value is carried out using scales. A magnitude scale is an ordered set of magnitude values that serves as the initial basis for measuring a given magnitude.
Non-physical quantities, for which a unit of measurement cannot in principle be introduced, can only be estimated. It should be noted that the estimation of non-physical quantities is not included in the tasks of theoretical metrology.
For a more detailed study of PV, it is necessary to classify, to identify the general metrological features of their individual groups. Possible classifications of FI are shown in fig. 2.
According to the types of phenomena, PVs are divided into:
Real, i.e. quantities describing physical and physiochemical properties substances, materials and products from them. This group includes mass, density, electrical resistance, capacitance, inductance, etc. Sometimes these PVs are called passive. To measure them, it is necessary to use an auxiliary energy source, with the help of which a signal of measuring information is formed. In this case, passive PV are converted into active ones, which are measured;
Energy, i.e. quantities describing the energy characteristics of the processes of transformation, transmission and use of energy. These include current, voltage, power, energy. These quantities are called active.
They can be converted into measurement information signals without the use of auxiliary energy sources;
Characterizing the course of processes in time, This group includes different kind spectral characteristics, correlation functions and other parameters.