Size of physical quantity– quantitative determination of a physical quantity inherent in a specific material object, system, phenomenon or process.
It is sometimes objected to the broad use of the word "size" by arguing that it refers only to length. However, we note that each body has a certain mass, as a result of which bodies can be distinguished by their mass, i.e. according to the size of the physical quantity we are interested in (mass). Looking at objects A And IN, one can, for example, argue that they differ from each other in length or size (for example, A > B). A more accurate estimate can only be obtained after measuring the length of these objects.
Often in the phrase “size of magnitude” the word “size” is omitted or replaced with the phrase “value of magnitude”.
In mechanical engineering, the term “size” is widely used, meaning by it the meaning of a physical quantity - the length characteristic of any part. This means that to express one concept “the value of a physical quantity” two terms (“size” and “value”) are used, which cannot contribute to the ordering of terminology. Strictly speaking, it is necessary to clarify the concept of “size” in mechanical engineering so that it does not contradict the concept of “size of a physical quantity” adopted in metrology. GOST 16263-70 provides a clear explanation on this issue.
A quantitative assessment of a specific physical quantity, expressed in the form of a certain number of units of a given quantity, is called "the value of a physical quantity".
An abstract number included in the “value” of a quantity is called a numerical value.
There is a fundamental difference between size and magnitude. The size of a quantity really exists, regardless of whether we know it or not. You can express the size of a quantity using any of the units of a given quantity, in other words, using a numerical value.
It is characteristic of a numerical value that when a different unit is used it changes, whereas physical size the value remains unchanged.
If we denote the measured quantity by x, the unit of quantity by x 1 , and their ratio by q 1, then x = q 1 x 1 .
The size of the quantity x does not depend on the choice of unit, which cannot be said about the numerical value of q, which is entirely determined by the choice of unit. If to express the size of a quantity x instead of the unit x 1 we use the unit x 2 , then the unchanged size x will be expressed by a different value:
x = q 2 x 2 , where n 2 n 1 .
If we use q= 1 in the above expressions, then the sizes of the units
x 1 = 1x 1 and x 2 = 1x 2 .
The sizes of different units of the same quantity are different. Thus, the size of a kilogram is different from the size of a pound; the size of a meter is from the size of a foot, etc.
1.6. Dimension of physical quantities
Dimension of physical quantities - this is the relationship between the units of quantities included in the equation that connects a given quantity with other quantities through which it is expressed.
The dimension of a physical quantity is denoted by dim A(from lat. dimension – dimension). Let us assume that the physical quantity A associated with X, Equation A = F(X, Y). Then the quantities X, Y, A can be represented in the form
X = x [X]; Y = y [Y];A = a [A],
Where A, X, Y - symbols denoting a physical quantity; a, x, y - numerical values of quantities (dimensionless); [A];[X]; [Y]- corresponding units of data of physical quantities.
The dimensions of the values of physical quantities and their units coincide. For example:
A = X/Y; dim(a) = dim(X/Y) = [X]/[Y].
Dimension - a qualitative characteristic of a physical quantity, giving an idea of the type, nature of the quantity, its relationship with other quantities, the units of which are taken as basic.
Physics, as a science that studies natural phenomena, uses standard research methods. The main stages can be called: observation, putting forward a hypothesis, conducting an experiment, substantiating the theory. During the observation, it is established distinctive features phenomena, the course of its course, possible reasons and consequences. A hypothesis allows us to explain the course of a phenomenon and establish its patterns. The experiment confirms (or does not confirm) the validity of the hypothesis. Allows you to establish a quantitative relationship between quantities during an experiment, which leads to an accurate establishment of dependencies. A hypothesis confirmed by experiment forms the basis of a scientific theory.
No theory can claim reliability if it has not received complete and unconditional confirmation during the experiment. Carrying out the latter is associated with measurements of physical quantities characterizing the process. - this is the basis of measurements.
What it is
Measurement concerns those quantities that confirm the validity of the hypothesis about patterns. Physical quantity is scientific characteristics physical body, the qualitative relation of which is common to many similar bodies. For each body, this quantitative characteristic is purely individual.
If we turn to the specialized literature, then in the reference book by M. Yudin et al. (1989 edition) we read that a physical quantity is: “a characteristic of one of the properties of a physical object (physical system, phenomenon or process), common in qualitative terms for many physical objects, but quantitatively individual for each object.”
Ozhegov's dictionary (1990 edition) states that a physical quantity is “the size, volume, extension of an object.”
For example, length is a physical quantity. Mechanics interprets length as the distance traveled, electrodynamics uses the length of the wire, and in thermodynamics a similar value determines the thickness of the walls of blood vessels. The essence of the concept does not change: the units of quantities can be the same, but the meaning can be different.
A distinctive feature of a physical quantity, say, from a mathematical one, is the presence of a unit of measurement. Meter, foot, arshin are examples of units of length.
Units
To measure a physical quantity, it must be compared with the quantity taken as a unit. Remember the wonderful cartoon “Forty-Eight Parrots”. To determine the length of the boa constrictor, the heroes measured its length in parrots, baby elephants, and monkeys. In this case, the length of the boa constrictor was compared with the height of other cartoon characters. The result depended quantitatively on the standard.
Quantities are a measure of its measurement in a certain system of units. Confusion in these measures arises not only due to imperfection and heterogeneity of measures, but sometimes also due to the relativity of units.
Russian measure of length - arshin - the distance between the index and thumb hands. However, everyone's hands are different, and the arshin measured by the hand of an adult man is different from the arshin measured by the hand of a child or woman. The same discrepancy in length measures concerns fathoms (the distance between the fingertips of hands spread out to the sides) and elbows (the distance from the middle finger to the elbow of the hand).
It is interesting that small men were hired as clerks in the shops. Cunning merchants saved fabric using slightly smaller measures: arshin, cubit, fathom.
Systems of measures
Such a variety of measures existed not only in Russia, but also in other countries. The introduction of units of measurement was often arbitrary; sometimes these units were introduced only because of the convenience of their measurement. For example, to measure atmospheric pressure mmHg was administered. Known in which a tube filled with mercury was used, it was possible to introduce such an unusual value.
The engine power was compared with (which is still practiced in our time).
Various physical quantities made the measurement of physical quantities not only complex and unreliable, but also complicating the development of science.
Unified system of measures
A unified system of physical quantities, convenient and optimized in every industrialized country, has become an urgent need. The idea of choosing as few units as possible was adopted as a basis, with the help of which other quantities could be expressed in mathematical relationships. Such basic quantities should not be related to each other; their meaning is determined unambiguously and clearly in any economic system.
They tried to solve this problem in various countries. The creation of a unified GHS, ISS and others) was undertaken repeatedly, but these systems were inconvenient either from a scientific point of view or in domestic and industrial use.
The task, posed at the end of the 19th century, was solved only in 1958. A unified system was presented at a meeting of the International Committee for Legal Metrology.
Unified system of measures
The year 1960 was marked by the historic meeting of the General Conference on Weights and Measures. Unique system, called “Systeme internationale d"unites” (abbreviated SI) was adopted by the decision of this honorable meeting. In the Russian version, this system is called the International System (abbreviation SI).
The basis is 7 main units and 2 additional ones. Their numerical value defined as a standard
Table of physical quantities SI
Name of main unit | Measured quantity | Designation |
|
International | Russian |
||
Basic units |
|||
kilogram | |||
Current strength | |||
Temperature | |||
Quantity of substance | |||
The power of light | |||
Additional units |
|||
Flat angle | |||
Steradian | Solid angle | ||
The system itself cannot consist of only seven units, since the variety of physical processes in nature requires the introduction of more and more new quantities. The structure itself provides not only for the introduction of new units, but also for their interrelation in the form of mathematical relationships (they are more often called dimensional formulas).
A unit of physical quantity is obtained using multiplication and division of the basic units in the dimensional formula. The absence of numerical coefficients in such equations makes the system not only convenient in all respects, but also coherent (consistent).
Derived units
The units of measurement that are formed from the seven basic ones are called derivatives. In addition to the basic and derived units, there was a need to introduce additional ones (radians and steradians). Their dimension is considered to be zero. Absence measuring instruments to determine them makes it impossible to measure them. Their introduction is due to their use in theoretical research. For example, the physical quantity “force” in this system is measured in newtons. Since force is a measure of the mutual action of bodies on each other, which is the reason for the variation in the speed of a body of a certain mass, it can be defined as the product of a unit of mass by a unit of speed divided by a unit of time:
F = k٠M٠v/T, where k is the proportionality coefficient, M is the unit of mass, v is the unit of speed, T is the unit of time.
SI gives the following formula for dimensions: H = kg٠m/s 2, where three units are used. And the kilogram, and the meter, and the second are classified as basic. The proportionality factor is 1.
It is possible to introduce dimensionless quantities, which are defined as a ratio of homogeneous quantities. These include, as is known, equal to the ratio of the friction force to the normal pressure force.
Table of physical quantities derived from basic ones
Unit name | Measured quantity | Dimensional formula |
kg٠m 2 ٠s -2 |
||
pressure | kg٠ m -1 ٠s -2 |
|
magnetic induction | kg ٠А -1 ٠с -2 |
|
electrical voltage | kg ٠m 2 ٠s -3 ٠A -1 |
|
Electrical resistance | kg ٠m 2 ٠s -3 ٠A -2 |
|
Electric charge | ||
power | kg ٠m 2 ٠s -3 |
|
Electrical capacity | m -2 ٠kg -1 ٠c 4 ٠A 2 |
|
Joule to Kelvin | Heat capacity | kg ٠m 2 ٠s -2 ٠К -1 |
Becquerel | Activity of a radioactive substance | |
Magnetic flux | m 2 ٠kg ٠s -2 ٠A -1 |
|
Inductance | m 2 ٠kg ٠s -2 ٠A -2 |
|
Absorbed dose | ||
Equivalent radiation dose | ||
Illumination | m -2 ٠kd ٠av -2 |
|
Light flow | ||
Strength, weight | m ٠kg ٠s -2 |
|
Electrical conductivity | m -2 ٠kg -1 ٠s 3 ٠A 2 |
|
Electrical capacity | m -2 ٠kg -1 ٠c 4 ٠A 2 |
Non-system units
The use of historically established quantities that are not included in the SI or differ only by a numerical coefficient is allowed when measuring quantities. These are non-systemic units. For example, mm of mercury, x-ray and others.
Numerical coefficients are used to introduce submultiples and multiples. Prefixes correspond to a specific number. Examples include centi-, kilo-, deca-, mega- and many others.
1 kilometer = 1000 meters,
1 centimeter = 0.01 meters.
Typology of quantities
We will try to indicate several basic features that allow us to establish the type of value.
1. Direction. If the action of a physical quantity is directly related to the direction, it is called vector, others - scalar.
2. Availability of dimension. The existence of a formula for physical quantities makes it possible to call them dimensional. If all units in a formula have a zero degree, then they are called dimensionless. It would be more correct to call them quantities with a dimension equal to 1. After all, the concept of a dimensionless quantity is illogical. The main property - dimension - has not been canceled!
3. If possible, addition. An additive quantity, the value of which can be added, subtracted, multiplied by a coefficient, etc. (for example, mass) is a physical quantity that is summable.
4. In relation to the physical system. Extensive - if its value can be compiled from the values of the subsystem. An example would be area measured in square meters. Intensive - a quantity whose value does not depend on the system. These include temperature.
The concept of a physical quantity is common in physics and metrology and is used to describe material systems of objects.
Physical quantity, as mentioned above, this is a characteristic that is common in a qualitative sense for many objects, processes, phenomena, and in a quantitative sense - individual for each of them. For example, all bodies have their own mass and temperature, but the numerical values of these parameters are different for different bodies. The quantitative content of this property in an object is the size of the physical quantity, numerical estimate of its size called the value of a physical quantity.
A physical quantity that expresses the same quality in a qualitative sense is called homogeneous (of the same name ).
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 meaning - this is the meaning in an ideal way reflecting qualitatively and quantitatively the corresponding properties of the object.
Real value - this is a value found experimentally and so close to the true one that it can be taken instead.
Physical quantities are classified according to a number of characteristics. The following are distinguished: classifications:
1) in relation to measurement information signals, physical quantities are: active - quantities that can be converted into a measurement information signal without the use of auxiliary energy sources; passive new - quantities that require the use of auxiliary energy sources, through which a measurement information signal is created;
2) on the basis of additivity, physical quantities are divided into: additive , or extensive, which can be measured in parts, and also 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 magnitude or measurement by indirect measurements. (Additivity (Latin additivus - added) is a property of quantities, consisting in the fact that the value of a quantity corresponding to the whole object is equal to the sum of the values of quantities corresponding to its parts).
Evolution of development systems physical units.
Metric system- the first system of units of physical quantities
was adopted in 1791 by the French National Assembly. It included units of length, area, volume, capacity and weight , which were based on two units - meter and kilogram . It was different 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 for 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, calling it an absolute system. He took as a basis three quantities independent of each other - mass, length, time .
For the main units he accepted these quantities 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 on the principle proposed by Gauss, and based on the metric system of 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 basic 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;
MKGSS 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: meter - a unit of length, kilogram - force - a unit of force, 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 G. Giorgi.
International relations in the field of science and economics required the unification of units of measurement, the creation of a unified system of units of physical quantities, covering various branches of the measurement field and preserving the principle of coherence, i.e. equality of the coefficient of proportionality to unity in the equations of connection between physical quantities.
SystemSI. In 1954, the commission to develop a unified International
system of units proposed a draft system of units, which was approved in 1960. XI General Conference on Weights and Measures. International system units (abbreviated SI) took its name from the initial letters of the French name System International.
The International System of Units (SI) includes seven main ones (Table 1), two additional ones and a number of non-systemic units of measurement.
Table 1 - International system of units
|
Physical quantities that have an officially approved standard |
Unit |
Abbreviated unit designation physical quantity |
|
|
international |
|||
|
kilogram | |||
|
Electric current strength | |||
|
Temperature | |||
|
Illuminance unit | |||
|
Quantity of substance | |||
Source: Tyurin N.I. Introduction to metrology. M.: 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;
a 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;
ampere is equal to the strength of a constant current, which, when passing through two parallel straight conductors of infinite length and is negligible small area circular cross-section, located at a distance of 1 m from each other in a vacuum, causes an interaction force on each section of a conductor 1 m long;
candela is equal to the luminous intensity in a given direction of a source emitting ion-protective radiation, the energetic luminous intensity of which in this direction is 1/683 W/sr;
a 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 in a system containing the same number of structural elements as there are atoms in C 12 weighing 0.012 kg 2.
Additional units International system of units for measuring plane 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 equal to 57°17"48"3;
steradian (sr) - a solid angle whose vertex is located at the center of the sphere and which cuts out on the surface sphere area, equal to the area of a square with side length equal to the radius spheres.
Additional SI units are used to form the units of angular velocity, angular acceleration and some other quantities. The radian and steradian are used for theoretical constructions and calculations, since most practical values of angles in radians that are important for practice are expressed as transcendental numbers.
Non-system units:
A tenth of a white is taken as a logarithmic unit - decibel (dB);
Diopter - luminous intensity for optical instruments;
Reactive power-var (VA);
Astronomical unit (AU) - 149.6 million km;
A light year is the distance a ray of light travels in 1 year;
Capacity - liter (l);
Area - hectare (ha).
Logarithmic units are divided into absolute, which represent the decimal logarithm of the ratio of a physical quantity to a normalized value, and relative, formed as a decimal logarithm of the ratio of any two homogeneous (same) quantities.
Non-SI units include 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 unity. In this case, the derived unit is called coherent.
Dimension is a qualitative display of measured quantities. The value of a quantity is obtained as a result of its measurement or calculation in accordance with basic equation frommeasurements:Q = q * [ Q]
where Q - quantity value; q- numerical value of the measured quantity in conventional units; [Q] - the unit chosen for measurement.
If the defining equation includes a numerical coefficient, then to form a derived unit, such numerical values of the initial quantities should be substituted into the right side of the Equation so that the numerical value of the derived unit being determined is equal to one.
(For example, 1 ml is taken as a unit of measurement for the mass of a liquid, so on the packaging it is indicated: 250 ml, 750, etc., but if 1 liter is taken as a unit of measurement, then the same amount of liquid will be indicated 0.25 liters. , 075l. respectively).
As one of the ways to form multiples and submultiples, the decimal multiplicity between major and minor units, adopted in the metric system of measures, is used. In table 1.2 provides factors and prefixes for the formation of decimal multiples and submultiples and their names.
Table 2 - Factors and prefixes for the formation of decimal multiples and submultiples and their names
|
Factor |
Console |
Prefix designation |
|
|
international |
|||
(Exabyte is a unit of measurement of the amount of information, equal to 1018 or 260 bytes. 1 EeV (exaelectronvolt) = 1018 electronvolt = 0.1602 joule)
It should be taken into account that when forming multiple and submultiple units of area and volume using prefixes, dual reading may arise depending on where the prefix is added. For example, 1 m2 can be used as 1 square meter and as 100 square centimeters, which is far from the same thing, because 1 square meter that's 10,000 square centimeters.
According to international rules, multiples and submultiples of area and volume should be formed by adding prefixes to the original units. Degrees refer to those units that are obtained by attaching prefixes. For example, 1 km 2 = 1 (km) 2 = (10 3 m) 2 == 10 6 m 2.
To ensure the uniformity of measurements, it is necessary to have identical units in which all measuring instruments of the same physical quantity are calibrated. Unity of measurements is achieved by storing, accurately reproducing established units of physical quantities and transferring their sizes to all working measuring instruments using standards and reference measuring instruments.
Reference - a measuring instrument that ensures the storage and reproduction of a legal unit of physical quantity, as well as the transfer of its size to other measuring instruments.
The creation, storage and use of standards, monitoring their condition are subject to uniform rules established by GOST “GSI. Standards of units of physical quantities. Procedure for development, approval, registration, storage and application.”
By subordination standards are divided into primary and secondary and have the following classification.
Primary standard ensures storage, reproduction of units and transmission of dimensions with the highest accuracy in the country achievable in this field of measurement:
- special primary standards- are intended to reproduce the unit in conditions in which direct transmission of the unit size from the primary standard with the required accuracy is technically infeasible, for example, for low and high voltages, microwave and HF. They are approved as state standards. In view of the special importance of state standards and to give them the force of law, GOST is approved for each state standard. The State Committee for Standards creates, approves, stores and applies state standards.
Secondary standard reproduces the unit in special conditions and replaces the primary standard under these conditions. It is created and approved to ensure the least wear and tear on the state standard. Secondary standards in turn divided according to purpose:
Copy standards - designed to transfer unit sizes 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 - used for comparison of standards that, for one reason or another, cannot be directly compared with each other;
Working standards - reproduce a unit from secondary standards and serve to transfer the size to a standard of a lower rank. Secondary standards are created, approved, stored and used by ministries and departments.
Unit standard - one instrument or set of measuring instruments that provide storage and reproduction of a unit for the purpose of transferring its size to subordinate measuring instruments in the verification scheme, made according to a special specification and officially approved in 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 entire country or 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 conveyed 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 working ones.
Size transfer is carried out by various verification methods, mainly by well-known measurement methods. Transferring a size in a stepwise manner is accompanied by a loss of accuracy, however, multi-stepping allows you to save standards and transfer the unit size to all working measuring instruments.
The study of physical phenomena and their patterns, as well as the use of these patterns in practical activities human 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, tension electric field, oscillation period, etc.
Specific implementations of the same physical quantity are called homogeneous quantities. For example, the distance between the pupils of your eyes and the height Eiffel Tower there are specific realizations of the same physical quantity - length and therefore are homogeneous quantities. The mass of this book and the mass of the Earth satellite “Cosmos-897” are also homogeneous physical quantities.
Homogeneous physical quantities differ from each other in size. The size of a physical quantity is
the quantitative content in a given object of a property corresponding to the concept of “physical quantity”.
The sizes of homogeneous physical quantities of different objects can be compared with each other if the values of these quantities are determined.
The value of a physical quantity is an assessment 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 general, 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 a 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 a quantity found experimentally and so close to the true value that it can be used instead for a given purpose.
Finding the value of a physical quantity experimentally using special technical means is called measurement.
The true values of physical quantities are usually 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
the values of all these and many other quantities. Moreover, the degree of approximation of these actual values to the true values of physical quantities depends on the perfection of the technical measuring instruments used.
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 by observation. Measuring instruments include a dynamometer, ammeter, pressure gauge, etc.
There are direct and indirect measurements.
Direct measurement is a measurement in which the desired value of a quantity is found directly from experimental data. Direct measurements include, for example, measuring 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 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, the thermal expansion of bodies or the thermoelectric effect is used, 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 measurement principle. Measurement principles are not covered in this manual. Metrology deals with the study of principles and methods of measurement, types of measuring instruments, measurement errors and other issues related to measurements.
A physical quantity is one of the properties of a physical object (phenomenon, process), which is qualitatively common to many physical objects, while differing in quantitative value.
The purpose of measurements is to determine the value of a physical quantity - a certain number of units accepted for it (for example, the result of measuring the mass of a product is 2 kg, the height of a building is 12 m, etc.).
Depending on the degree of approximation to objectivity, true, actual and measured values of a physical quantity are distinguished.
This is a value that ideally reflects the corresponding property of an object in qualitative and quantitative terms. Due to the imperfection of measurement tools and methods, it is practically impossible to obtain the true values of quantities. They can only be imagined theoretically. And the values obtained during measurement only approach the true value to a greater or lesser extent.
This is a value of a quantity found experimentally that is so close to the true value that it can be used instead for a given purpose.
This is the value obtained by measurement using specific methods and measuring instruments.
9. Classification of measurements according to the dependence of the measured value on time and according to sets of measured values.
According to the nature of the change in the measured value - static and dynamic measurements.
Dynamic measurement - a measurement of a quantity whose size changes over time. A rapid change in the size of the measured quantity requires its measurement with the most precise definition moment in time. For example, measuring the distance to the Earth's surface level from hot air balloon or DC voltage measurement electric current. Essentially, a dynamic measurement is a measurement of the functional dependence of the measured quantity on time.
Static measurement - measurement of a quantity that is taken into account in accordance with the assigned measurement task and does not change throughout the measurement period. For example, measuring the linear size of a manufactured product when normal temperature can be considered static, since temperature fluctuations in the workshop at the level of tenths of a degree introduce a measurement error of no more than 10 μm/m, which is insignificant compared to the manufacturing error of the part. Therefore, in this measurement task, the measured quantity can be considered unchanged. When calibrating a line length measure against the state primary standard, thermostatting ensures the stability of maintaining the temperature at the level of 0.005 °C. Such temperature fluctuations cause a thousand times smaller measurement error - no more than 0.01 μm/m. But in this measurement task it is essential, and taking into account temperature changes during the measurement process becomes a condition for ensuring the required measurement accuracy. Therefore, these measurements should be carried out using the dynamic measurement technique.
Based on existing sets of measured values on electrical ( current, voltage, power) , mechanical ( mass, number of products, effort); , thermal power(temperature, pressure); , physical(density, viscosity, turbidity); chemical(compound, Chemical properties, concentration) , radio engineering etc.
Classification of measurements according to the method of obtaining the result (by type).
According to the method of obtaining measurement results, they are distinguished: direct, indirect, cumulative and joint measurements.
Direct measurements are those in which the desired value of the measured quantity is found directly from experimental data.
Indirect measurements are those in which the desired value of the measured quantity is found on the basis of a known relationship between the measured quantity and quantities determined using direct measurements.
Cumulative measurements are those in which several quantities of the same name are simultaneously measured and the determined value is found by solving a system of equations that is obtained on the basis of direct measurements of quantities of the same name.
Joint measurements are the measurements of two or more quantities of different names to find the relationship between them.
Classification of measurements according to the conditions that determine the accuracy of the result and the number of measurements to obtain the result.
According to the conditions that determine the accuracy of the result, measurements are divided into three classes:
1. Measurements of the highest possible accuracy achievable with the existing level of technology.
These include, first of all, standard measurements associated with the highest possible accuracy of reproduction of established units of physical quantities, and, in addition, measurements of physical constants, primarily universal ones (for example, the absolute value of acceleration free fall, gyromagnetic ratio of the proton, etc.).
This class also includes some special measurements that require high accuracy.
2. Control and verification measurements, the error of which, with a certain probability, should not exceed a certain specified value.
These include measurements performed by laboratories for state supervision of the implementation and compliance with standards and the state of measuring equipment and factory measurement laboratories, which guarantee the error of the result with a certain probability not exceeding a certain predetermined value.
3. Technical measurements in which the error of the result is determined by the characteristics of the measuring instruments.
Examples of technical measurements are measurements carried out during production in machine-building plants, on switchboards distribution devices power stations, etc.
Based on the number of measurements, measurements are divided into single and multiple.
A single measurement is a measurement of one quantity made once. In practice, single measurements have a large error; therefore, to reduce the error, it is recommended to perform measurements of this type at least three times, and take their arithmetic average as the result.
Multiple measurements are measurements of one or more quantities performed four or more times. A multiple measurement is a series of single measurements. The minimum number of measurements at which a measurement can be considered multiple is four. The result of multiple measurements is the arithmetic average of the results of all measurements taken. With repeated measurements, the error is reduced.
Classification of random measurement errors.
Random error is a component of measurement error that changes randomly during repeated measurements of the same quantity.
1) Rough - does not exceed the permissible error
2) A miss is a gross error, depends on the person
3) Expected - obtained as a result of the experiment during creation. conditions
Concept of metrology
Metrology– the science of measurements, methods and means of ensuring their unity and methods of achieving the required accuracy. It is based on a set of terms and concepts, the most important of which are given below.
Physical quantity- a property that is qualitatively common to many physical objects, but quantitatively individual for each object. Physical quantities are length, mass, density, force, pressure, etc.
Unit of physical quantity is considered to be the quantity that, by definition, is assigned a value equal to 1. For example, mass 1 kg, force 1 N, pressure 1 Pa. IN various systems units Units of the same size may differ in size. For example, for a force of 1 kgf ≈ 10 N.
Physical quantity value– numerical assessment of the physical size of a specific object in accepted units. For example, the mass of a brick is 3.5 kg.
Technical Dimension– determination of the values of various physical quantities using special technical methods and means. During laboratory tests, the values are determined geometric dimensions, mass, temperature, pressure, force, etc. All technical measurements must meet the requirements of unity and accuracy.
Direct measurement– experimental comparison of a given value with another, taken as unit, by means of reading on the instrument scale. For example, measuring length, mass, temperature.
Indirect measurements– results obtained using the results of direct measurements by calculations using known formulas. For example, determining the density and strength of a material.
Unity of measurements– a state of measurements in which their results are expressed in legal units and measurement errors are known with a given probability. Unity of measurements is necessary in order to be able to compare the results of measurements taken in different places, at different times, using a variety of instruments.
Accuracy of measurements– quality of measurements, reflecting the closeness of the results obtained to the true value of the measured value. Distinguish between true and actual values of physical quantities.
True meaning physical quantity ideally reflects the corresponding properties of the object in qualitative and quantitative terms. The true value is free from measurement errors. Since all values of a physical quantity are found empirically and they contain measurement errors, the true value remains unknown.
Real value physical quantities are found experimentally. It is so close to the true value that for certain purposes it can be used instead. At technical measurements value of a physical quantity found with an acceptable technical requirements error is taken as the actual value.
Measurement error– deviation of the measurement result from the true value of the measured value. Since the true value of the measured quantity remains unknown, in practice the measurement error is only approximately estimated by comparing the measurement results with the value of the same quantity obtained with an accuracy several times higher. Thus, the error in measuring the dimensions of a sample with a ruler, which is ± 1 mm, can be estimated by measuring the sample with a caliper with an error of no more than ± 0.5 mm.
Absolute error expressed in units of the measured quantity.
Relative error- the ratio of the absolute error to the actual value of the measured value.
Measuring instruments – technical means, used in measurements and having standardized metrological properties. Measuring instruments are divided into measures and measuring instruments.
Measure– a measuring instrument designed to reproduce a physical quantity of a given size. For example, a weight is a measure of mass.
Measuring device– a measuring instrument that serves to reproduce measurement information in a form accessible to perception by an observer. The simplest measuring instruments are called measuring instrument. For example, a ruler, a caliper.
The main metrological indicators of measuring instruments are:
The scale division value is the difference in the values of the measured quantity, corresponding to two adjacent scale marks;
The initial and final values of the scale are the smallest and highest value measured value indicated on the scale;
Measurement range is the range of values of the measured value for which permissible errors are normalized.
Measurement error– the result of mutual superposition of errors caused by for various reasons: the error of the measuring instruments themselves, the errors that arise when using the device and reading the measurement results and errors from non-compliance with the measurement conditions. When enough large number measurements, the arithmetic mean of the measurement results approaches the true value, and the error decreases.
Systematic error- an error that remains constant or changes naturally with repeated measurements and arises for well-known reasons. For example, the shift of the instrument scale.
Random error is an error in which there is no natural connection with previous or subsequent errors. Its appearance is caused by many random reasons, the influence of which on each measurement cannot be taken into account in advance. The reasons leading to the appearance of a random error include, for example, heterogeneity of the material, irregularities during sampling, and errors in instrument readings.
If during measurements a so-called gross error, which significantly increases the error expected under given conditions, then such measurement results are excluded from consideration as unreliable.
The unity of all measurements is ensured by the establishment of units of measurement and the development of their standards. Since 1960, the International System of Units (SI) has been in force, which replaced the complex set of systems of units and individual non-system units developed on the basis of the metric system of measures. In Russia, the SI system has been adopted as standard, and its use in the field of construction has been regulated since 1980.
Lecture 2. PHYSICAL QUANTITIES. UNITS OF MEASUREMENT
2.1 Physical quantities and scales
2.2 Units of physical quantities
2.3. International System of Units (SI System)
2.4 Physical quantities of technological processes
food production
2.1 Physical quantities and scales
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 of them.
Individual in quantitative terms should be understood in such a way that the same property for one object can be a certain number of times greater or less than for another.
Typically, the term "physical quantity" is used to refer to properties or characteristics that can be quantified. Physical quantities include mass, length, time, pressure, temperature, etc. All of them determine the general ones in qualitative terms physical properties, their quantitative characteristics may be different.
It is advisable to distinguish physical quantities into measured and assessed. Measured EF can be expressed quantitatively in the form of a certain number of established units of measurement. The possibility of introducing and using the latter is important hallmark measured PV.
However, there are properties such as taste, smell, etc., for which units cannot be entered. Such quantities can be estimated. Values are assessed using scales.
By accuracy of the result There are three types of values of physical quantities: true, actual, measured.
True value of a physical quantity(true value of a quantity) - the value of a physical quantity that, in qualitative and quantitative terms, would ideally reflect the corresponding property of the object.
The postulates of metrology include
The true value of a certain quantity exists and it is constant
The true value of the measured quantity cannot be found.
The true value of a physical quantity can only be obtained as a result of an endless process of measurements with endless improvement of methods and measuring instruments. For each level of development of measuring technology, we can only know the actual value of a physical quantity, which is used instead of the true one.
Real value of a physical quantity– the value of a physical quantity found experimentally and so close to the true value that it can replace it for the given measurement task. A typical example illustrating the development of measurement technology is the measurement of time. At one time, the unit of time, the second, was defined as 1/86400 of the average solar day with an error of 10 -7 . Currently, the second is determined with an error of 10 -14 , i.e., we are 7 orders of magnitude closer to the true value of determining time at the reference level.
The actual value of a physical quantity is usually taken to be the average arithmetic series values obtained from equal-precision measurements, or a weighted arithmetic mean for unequal-precision measurements.
Measured value of a physical quantity– the value of a physical quantity obtained using a specific technique.
By type of PV phenomena divided into the following groups :
- real , those. describing physical and physicochemical characteristics substances. Materials and products made from them. These include mass, density, etc. These are passive PVs, because to measure them, it is necessary to use auxiliary energy sources, with the help of which a signal of measurement information is generated.
- energy – describing the energy characteristics of the processes of transformation, transmission and use of energy (energy, voltage, power. These quantities are active. They can be converted into measurement information signals without the use of auxiliary energy sources;
- characterizing the flow of time processes . This group includes various kinds of spectral characteristics, correlation functions, etc.
According to the degree of conditional dependence on other values of PV divided into basic and derivative
Basic physical quantity– a physical quantity included in a system of quantities and conventionally accepted as independent of other quantities of this system.
The choice of physical quantities accepted as basic and their number is carried out arbitrarily. First of all, the values that characterize the basic properties were chosen as the main ones. material world: length, mass, time. The remaining four basic physical quantities are chosen in such a way that each of them represents one of the branches of physics: current strength, thermodynamic temperature, amount of matter, light intensity.
Each basic physical quantity of a system of quantities is assigned a symbol in the form of a lowercase Latin letter or Greek alphabet: length - L, mass - M, time - T, electric current - I, temperature - O, amount of substance - N, luminous intensity - J. These symbols are included in the name of the system of physical quantities. Thus, the system of physical quantities of mechanics, the main quantities of which are length, mass and time, is called the “LMT system”.
Derived physical quantity– a physical quantity included in a system of quantities and determined through the basic quantities of this system.
1.3 Physical quantities and their measurements
Physical quantity – one of the properties of a physical object (physical system, phenomenon or process), common in qualitative terms for many physical objects, but quantitatively individual for each of them. We can also say that a physical quantity is a quantity that can be used in the equations of physics, and by physics here we mean science and technology in general.
Word " magnitude" is often used in two senses: as a general property to which the concept of more or less is applicable, and as the quantity of this property. In the latter case, we would have to talk about the “magnitude of a quantity,” so in what follows we will talk about quantity precisely as a property of a physical object, and in the second sense, as the meaning of a physical quantity.
Recently, the division of quantities into physical and non-physical , although it should be noted that not yet strict criterion for such a division of quantities. At the same time, under physical understand quantities that characterize the properties of the physical world and are used in physical sciences and technology. There are units of measurement for them. Physical quantities, depending on the rules of their measurement, are divided into three groups:
Quantities characterizing the properties of objects (length, mass);
quantities characterizing the state of the system (pressure,
temperature);
Quantities characterizing processes (speed, power).
TO non-physical refer to quantities for which there are no units of measurement. They can characterize both the properties of the material world and concepts used in social sciences, economics, and medicine. In accordance with this division of quantities, it is customary to distinguish between measurements of physical quantities and non-physical measurements . Another expression of this approach is two different understandings of the concept of measurement:
measurement in in the narrow sense as an experimental comparison
one measurable quantity with another known quantity
the same quality adopted as a unit;
measurement in in a broad sense how to find matches
between numbers and objects, their states or processes according to
known rules.
The second definition appeared in connection with the recent widespread use of measurements of non-physical quantities that appear in biomedical research, in particular in psychology, economics, sociology and other social sciences. In this case, it would be more correct to talk not about measurement, but about estimating quantities , understanding assessment as establishing the quality, degree, level of something in accordance with established rules. In other words, this is an operation of attributing, by calculating, finding or determining a number, a quantity characterizing the quality of an object, according to established rules. For example, determining the strength of wind or earthquake, grading figure skaters or assessing students' knowledge on a five-point scale.
Concept assessment quantities should not be confused with the concept of estimating quantities, associated with the fact that as a result of measurements we actually do not receive the true value of the measured quantity, but only its assessment, to one degree or another close to this value.
The concept discussed above measurement", which presupposes the presence of a unit of measurement (measure), corresponds to the concept of measurement in the narrow sense and is more traditional and classical. In this sense, it will be understood below - as a measurement of physical quantities.
Below are about basic concepts , related to a physical quantity (hereinafter, all basic concepts in metrology and their definitions are given according to the above-mentioned recommendation on interstate standardization RMG 29-99):
- size of a physical quantity - quantitative certainty of a physical quantity inherent in a specific material object, system, phenomenon or process;
- physical quantity value - expression of the size of a physical quantity in the form of a certain number of units accepted for it;
- true value of a physical quantity - the value of a physical quantity that ideally characterizes the corresponding physical quantity in qualitative and quantitative terms (can be correlated with the concept of absolute truth and is obtained only as a result of an endless process of measurements with endless improvement of methods and measuring instruments);
actual value of a physical quantity the value of a physical quantity obtained experimentally and so close to the true value that it can be used instead of it in the given measurement task;
unit of measurement of physical quantity a physical quantity of a fixed size, which is conventionally assigned a numerical value equal to 1, and used for the quantitative expression of physical quantities similar to it;
system of physical quantities a set of physical quantities formed in accordance with accepted principles, when some quantities are taken as independent, while others are defined as functions of these independent quantities;
main physical quantity – a physical quantity included in a system of quantities and conventionally accepted as independent of other quantities of this system.
derived physical quantity – a physical quantity included in a system of quantities and determined through the basic quantities of this system;
system of units of physical units a set of basic and derived units of physical quantities, formed in accordance with the principles for a given system of physical quantities.
