Definition physical quantity
Classification of physical quantities.
Classification of units of physical quantities.
SECTION 1. METROLOGY. Topic 3
Topic 3. Physical quantities as an object of measurement. SI system (SI)
1. Definition of a physical quantity.
2. International system of units of physical quantities SI.
Physical quantity (PV) – property physical object͵ common to many objects in a qualitative sense (this is a type of quantity), but individual in a quantitative sense (this is the size of a quantity).
System– are included in one of the accepted systems (these are all basic, derivative, multiple and submultiple units).
Off-system– are not included in any of the accepted systems of PV units (liter, nautical mile, carat, horsepower).
Multiple- ϶ᴛᴏ PV unit, the value of which is an integer number of times greater than the system or non-system unit (for example, a unit of length 1 km = 103 m, that is, a multiple of a meter).
Dolnaya- ϶ᴛᴏ PV unit, the value of which is an integer number of times less than a systemic or non-systemic unit (for example, a unit of length 1 mm = 10-3m, that is, it is a submachine unit).
Basic quantities are independent of each other and serve as the basis for establishing connections with other physical quantities, which are called derivatives from them. For example, in Einstein's formula E=mc2, mass is the basic unit, and energy is the derivative unit.
The set of basic and derived units is usually called a system of units of physical quantities. In 1960 ᴦ. The International System of Units (Systeme International d'Unites), designated SI, was adopted. It contains basic (meter, kilogram, second, ampere, kelvin, mole, candela), additional and derivative (radian, steradian) units of physical quantities.
In science, technology and everyday life, people deal with the various properties of the physical objects around us. Their description is made using physical quantities.
A physical quantity (PV) is a property of a physical object, common to many objects in a qualitative sense (this is a type of quantity - R), but individual in a quantitative sense (this is the size of a quantity - 10 Ohms).
In order to be able to establish for each object differences in the quantitative content of the property reflected by the physical quantity, the concepts of its size and value were introduced in metrology.
The size of the PV is the quantitative content in a given object of a property corresponding to the concept of PV - all bodies differ in mass, ᴛ.ᴇ. according to the size of this FV.
The PV value is an estimate of its size in the form of a certain number of units accepted for it. It is obtained as a result of measuring or calculating EF.
A PV unit is a PV of a fixed size, which is conditionally assigned a numerical value equal to 1.
Example: PV - mass,
The unit of this PV is 1kᴦ.
value - object mass = 5 kᴦ.
Classification of PV units
1. systemic and non-systemic
System - which are part of one of the accepted systems.
*these are all basic, derivative, multiple and submultiple units.
Extra-systemic - which are not included in any of the accepted systems of PV units:
liter ( unit of volume),
liter (unit of volume), nautical mile
carat (unit of mass in jewelry),
carat (unit of mass in jewelry) horsepower (obsolete
unit of power)
Definition of physical quantity - concept and types. Classification and features of the category "Determination of physical quantity" 2014, 2015.
INTRODUCTION
Physical quantity is a characteristic of one of the properties of a physical object ( physical system, phenomenon or process), common in qualitative terms 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 on a scale accepted for it. For example, 120 mm is the value linear magnitude; 75 kg is the value of body weight.
There are true and actual values of a physical quantity. The true value is a value that ideally reflects the property of an object. Real value- a value of a physical quantity found experimentally that is close enough to the true value that can be used instead.
Measurement of a physical quantity is a set of operations involving the use of a technical means that stores a unit or reproduces a scale of a physical quantity, which consists of 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 sizes of which only relations of order and equivalence 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 heating, etc.
The existence of such relationships is established theoretically or experimentally using special means comparison, as well as based on 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 occurs both between sizes and between differences in pairs of their sizes.
A typical example is the time interval scale. Thus, differences in time intervals are considered equal if the distances between the corresponding marks are equal.
The third type consists of additive physical quantities.
Additive physical quantities are quantities on the set of sizes of which not only the relations of order and equivalence, but also the operations of addition and subtraction are defined
Such quantities include, for example, length, mass, current strength and so on. They can be measured in parts, as well as reproduced using a multivalued measure based on the summation of individual measures.
The sum of the masses of two bodies is the mass of the body that is balanced on equal-armed scales by the first two.
The sizes of any two homogeneous PVs or any two sizes of the same PV can be compared with each other, i.e., you can 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 relations. It is easier to compare each of them with one size [Q] of a homogeneous PV, if we take it as a unit of PV size (abbreviated as a unit of PV). As a result of this 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 will be required (instead of C m 2), and a comparison of the sizes Q", Q", ... , Q (m) with each other can only be performed by calculations like
where n (i) / n (j) are abstract numbers.
Type equality
called the basic measurement equation, where n [Q] is the value of the PV size (abbreviated as PV value). The PV value is a named number made up of the numerical value of the PV size (abbreviated as the numeric 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 is Q = n [Q] = 3.8 grams, with n = 0.7 and [Q] = 1 ampere the size of the current Q = n [Q ] = 0.7 ampere. 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” " and so on.
The size of the PV is most often determined by measuring it. Measuring the size of the PV (abbreviated as measuring the PV) consists of experimentally using special technical means find the value of the PV and evaluate the proximity of this value to the value that ideally reflects the size of this PV. The PV value found in this way will be called nominal.
The same size Q can be expressed different meanings with different numerical values depending on the choice of 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, from which
n 1 /n 2 = /,
i.e. numeric values PV is 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 in meters per second. This condition, which seems immutable at first glance, unfortunately, has not yet been met when measuring certain PVs (hardness, photosensitivity, etc.).
1. THEORETICAL PART
1.1 Concept of physical quantity
Weight objects of the surrounding world are characterized by their properties. Property is a philosophical category that expresses such an aspect of an object (phenomenon, process) that determines its difference or commonality with other objects (phenomena, processes) and is revealed in its relations to them. Property - quality category. For quantitative description various properties of processes and physical bodies the concept of quantity is introduced. Magnitude is a property of something that can be distinguished from other properties and assessed in one way or another, including quantitatively. A quantity does not exist on its own; it exists only insofar as there is an object with properties expressed by a given quantity.
Analysis of the quantities allows us to divide them (Fig. 1) into two types: quantities material form(real) and quantities ideal models realities (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. The physical quantity itself general case can be defined as a quantity characteristic of material objects (processes, phenomena) studied in natural (physics, chemistry) and technical sciences. Non-physical quantities include quantities inherent in social (non-physical) sciences - philosophy, sociology, economics, etc.
Rice. 1. Classification of quantities.
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 a certain number of times greater or less for one object than for another.
It is advisable to divide physical quantities into measured and estimated. The measured EF can be expressed quantitatively as a certain number established units of measurement. The ability to introduce and use 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. Estimation is understood as the operation of assigning a certain number to a given value, carried out according to established rules. Values are assessed using scales. A quantity scale is an ordered set of values of a quantity that serves as the initial basis for measuring a given quantity.
Non-physical quantities, for which a unit of measurement cannot in principle be introduced, can only be estimated. It should be noted that the assessment of non-physical quantities is not part of the tasks of theoretical metrology.
For a more detailed study of PVs, it is necessary to classify and identify their general metrological features separate groups. Possible classifications of PV are shown in Fig. 2.
According to the types of phenomena, PVs are divided into:
Real, i.e. quantities describing physical and physicochemical characteristics substances, materials and products made 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 measurement information signal is generated. In this case, passive PVs are converted into active ones, which are measured;
Energy, i.e. quantities describing energy characteristics 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 over time, this group includes various types spectral characteristics, correlation functions and other parameters.
According to affiliation various groups physical processes PVs are divided into spatiotemporal, mechanical, electrical and magnetic, thermal, acoustic, light, physicochemical, ionizing radiation, atomic and nuclear physics.
Rice. 2. Classifications of physical quantities
According to the degree of conditional independence from other quantities of this group, all PVs are divided into basic (conditionally independent), derivatives (conditionally dependent) and additional. Currently, the SI system uses seven physical quantities, chosen as the main ones: length, time, mass, temperature, force electric current, luminous intensity and amount of matter. Additional PVs include plane and solid angles. Based on the presence of dimension, PVs are divided into dimensional ones, i.e. having dimension and dimensionless.
1.2 Metric system of measures
The lack of rational justification for choosing PV units has led to their wide variety not only in different countries, but even in different areas of the same country. This created great difficulties, especially in international relations. The metric system of measures arose, i.e. a set of PV units recommended instead of those previously used.
The following units were adopted: length - meter (m), mass - kilogram (kg), volume - liter (l), time - second (s).
Decimal multiples and submultiples of PV units were also introduced, i.e. PV units, in 10 in whole degree times larger and smaller, and installed simple rules assigning names to multiples and submultiple units PV using prefixes: kilo, hecto, deca, deci, centi and milli [for example, centimeter (cm), millimeter (mm), decaliter (dal), etc.]
This gave the units metric system(metric PV units) a significant advantage over others existing at that time. In addition, metric units of PV made it possible not to use composite named numbers (for example, the length of 8 fathoms is 3 feet 5 inches) and greatly facilitated calculations.
1.3 Systems of units of physical quantities
Construction of units and systems of units. Previously, units of various PVs were installed, as a rule, independently of each other. The only exceptions were units of length, area and volume. The main feature of modern PV units is that dependencies are established between them. In this case, several basic units of PV are arbitrarily selected, and all the rest - derivative units of PV are obtained using dependencies (laws and definitions) connecting different PV, i.e. governing equations.
Physical quantities whose units are accepted as basic are called fundamental PVs, and the units of which are derivatives are called derivative PVs.
The set of basic and derived units of physical activity, covering all or some areas of physics, is called a system of units of physical activity.
Let us consider examples of establishing derivative units of PV with length L, mass M and time T chosen as the main PV, i.e. with the selected basic units of PV [L], [M] and [T].
Example 1: Establishing a unit of area. Let's choose some simple geometric figure, for example a circle. The size of the area s of a circle is proportional to the second power of the size of its diameter d: s = k S d 2, where k S is the proportionality coefficient. We will take this equation as the determining one. Putting the size of the diameter of a circle equal to a unit of length, i.e. d = [L], we obtain [s] = k S [L] 2. The choice of the proportionality coefficient k S is arbitrary. Let k S = l, then [s] = [L] 2, i.e., the area of a circle whose diameter is equal to a unit length is chosen as the unit area. If [L] = 1 m, then [s] = 1 m 2. The area of a circle in this case must be calculated using the formula s = d 2 , and the area of a square with side b - using the formula s = (4/p)b 2 .
Usually, instead of such a round unit of area, a more convenient one is used square unit, which is the area of a square with side equal to one length.
If, when establishing a round unit of area, k S = p/4 had been taken, then it would have coincided with the usual square unit.
Example 2. Setting the speed unit. As a defining equation, we take the equation showing that the size of the speed and uniform motion the more than larger size l distance traveled and by what smaller size time spent on this path T:
where k u is the proportionality coefficient.
Assuming l = [L], T = [T], we obtain the unit of speed [u]=k u k u [L] [T] -1. If for reasons of convenience we set k u = l, then the unit of speed will be [u] = [L] [T] -1. With [L] = 1 mi [T] = 1s according to the last formula [u] = 1 m/s.
Example 3: Setting the acceleration unit. As the defining equation, we take the definition of acceleration as the derivative of speed with respect to time: a = du/dT. Assuming du = [u], dT = [T], we obtain the unit of acceleration: [a] = 
With [L] = 1 m and [T] = 1s [a] = 1 m/s 2.
Example 4: Establishing a unit of force. Let us choose as the defining equation of the law of universal gravitation
f = where m 1 and m 2 are the sizes of body masses;
r is the size of the distance between the centers of these masses;
k f - proportionality coefficient.
Assuming m 1 = m 2 [M], r = [L], we obtain the unit of force
or with k f =1 [f] = [M] 2 [L] -2. With [L] = 1 m and [M] = 1 kg according to the last formula [f] = 1 kg 2 / m 2.
Choosing the equation of Newton's second law f = = k f ma as the defining one, we obtain, similarly to the previous one, a unit of force in the form [f] = k f [M] * [a] = k f [M] [L] [T] -2, or in the form [f] = [M] [L] [T] -2. With [M] = 1 kg, [L] = 1 m and [T] = 1s according to the last formula [f] = 1 kg m/s 2.
Both units of force obtained are equal, but the second is widespread, and the first is rarely used (mainly in astronomy).
From the considered examples it is clear that with the selected main PVs - length L, mass M and time T, the derivative unit [x] of some PV x is found through the units [L], [M] and [T] according to the formula:
[x] = k x [L] pL [M] pM [T] pT ,
where k x is an arbitrarily selected proportionality coefficient;
p L, p M and p T are positive or negative numbers.
These numbers show how the derivative unit of the PV changes with the change in the main one. For example, with a change in the basic unit [L] by q times, the derived unit [x] will change by q pL times. Since k x does not affect the change in [x], the nature of the change in the unit [x] with the change in the units [L], [M] and [T] is usually expressed using dimensional formulas in which k x = 1. In the case under consideration the dimension formula has the form
dimx = L pL M pL T pT ,
where the right side is called the dimension of the PV unit; left side– designation of this dimension (dimension);
p L, p M and p T are dimension indicators.
From the dimension formula it is clear how the size of the derivative of the PV changes with the change in the size of the main PV with the selected defining equation. The right side of this formula is also called the dimension of the PV.
Let us consider the general case when there are several basic functional functions A, B, C, D, ..., whose units are [A], [B], [C], [D], ..... Then, obviously, establishing the derivative unit of PV x will be reduced to the choice of any defining equation connecting x with other (basic and derivative) PVs, to reducing this equation to the form:
x = k x A pA B pB C pC D pD …,
where p A, p B, p C, p D, ... are indicators of dimension, and to replacing the main PVs with their units:
[x] = k x [A] pA [B] pB [C] pC [D] pD …
The dimension formula in this case will look like:
dim x = A pA B pB C pC D pD …
It is known that the derived unit PV x has a dimension p A relative to the basic unit PV A, dimension p B relative to the basic unit PV B, etc. (or that the derivative of the PV has a dimension p A relative to the main PV A, a dimension p B relative to the main PV B, etc.). So, having considered the dimension of speed (example 2) LT -1, or L 1 M 0 T -1, we can say that speed has dimension 1 relative to length, zero dimension relative to mass and dimension -1 relative to time (unit of speed has dimension 1 relative units of length, etc.).
If p A = p B = p C = p D = ... = 0, then the derivative of the PV x is called the dimensionless PV, and its unit [x] is called the dimensionless PV unit.
An example of a dimensionless derivative unit of PV is the unit [φ] of a plane angle φ – radian. When establishing this unit, the equation φ = = k φ (l/r) was adopted as the defining one, showing that the size of the angle φ is greater, the greater the size of the length l of the arc subtending it and the smaller the size of the length r of the radius of this arc. The equation assumes k φ = 1, l = [L], r= [L]. Therefore [φ] = = [L] 0 and dim φ = L 0 .
If, when establishing a derived PV unit in its expression through the basic PV units, one assumes k x = 1, then it is called a coherent derived PV unit. A system of PV units, all of whose derived units are coherent, is called a coherent system of PV units.
The dimensions of the derived PV units x, y and z are interconnected in the following way. If z = k 1 xy, then
dimz - dimх * dimу. (1.2)
If z = k 2 then
dimz - dimх/diму. (1.3)
If z = k 3 x n, then
dimz - (dim x) n . (1.4)
We used equalities (1.2) and (1.3) when establishing the units of acceleration and force, and equality (1.4) is a consequence of equality (1.2).
Dimension formulas can be written only for such PVs, the measurement of which satisfies the condition of uniqueness of measurements. The dimensions of different PVs can coincide (for example, moment of force and work), and the dimensions of the same PV in different systems ax units of PV can differ (see example 4, where different constitutive equations led us to different dimensions of force units and, therefore, to different dimensions of force). Therefore, dimensions are not given full presentation about FV. However, the discrepancy between the dimensions of the left and right sides of any formula or any equation indicates that this formula or this equation is erroneous. In addition, the concept of dimension makes it easier to solve many problems. If it is known in advance which PVs are involved in the process under study, then using dimensional analysis it is possible to establish the nature of the relationship between the sizes of these PVs. At the same time, solving a problem often turns out to be much simpler than if it were done in other ways.
It is important that in the mathematical formulation physical phenomena By PV symbols we mean not the PVs themselves and not their sizes, but the values of the PVs, i.e. named numbers. For example, in the equation f = k f ma, expressing Newton’s second law, the symbols m and a mean not the PVs themselves (mass and acceleration) and not the dimensions of mass and acceleration, which cannot be multiplied by each other, but the values of mass and acceleration, i.e. that is, named numbers that reflect the dimensions of mass and acceleration, and for which the multiplication operation makes sense.
1.4 Systems of units
The first system of PV units was essentially the metric PV units mentioned above. However, it was only in 1832 that K. Gauss proposed henceforth to build systems of PV units as a collection of basic and derived units. In the system he built, the main units of PV were millimeter, milligram and second.
Subsequently, other systems of PV units appeared, also based on metric PV units, but with different basic units. The most famous of these systems are the following.
GHS system (1881). The basic units of PV are centimeter, gram, second. The system has become widespread in physics. Subsequently, some versions of this system were created for electric and magnetic PVs.
MTS system (1919). The basic units of PV are meter, ton (1000 kg), second. This system was not widely used.
MKGSS system ( late XIX V). The basic units of PV are meter, kilogram-force, second. This system has become widespread in technology.
ISSA system (1901). It is sometimes called the Georgie system (named after its creator). The basic units of PV are meter, kilogram, second and ampere. This system is currently included integral part into the new international system of PV units.
All basic and derived units of any system of PV units are called system units PV (in relation to this system). Along with systemic ones, there are also so-called non-systemic units, i.e. those that are not included in the system of PV units. All non-systemic PV units can be divided into two groups: 1) not included in any of the known systems, for example: unit of length - x-unit, unit of pressure - millimeter of mercury, unit of energy - electron-volt; 2) which are non-systemic only in relation to some systems, for example: the unit of length - centimeter - non-systemic for all systems except the GHS; unit of mass - ton - non-systemic for all systems except MTS; unit of electrical capacity - centimeter - non-systemic for all systems except SGSE.
The presence of different systems of PV units, as well as large number non-systemic PV units creates inconveniences associated with the calculations required when moving from one PV units to others. In connection with the growth of scientific and technical ties between countries, the unification of PV units has become necessary. As a result, a new International System of VF Units was created.
International system of units. In 1960, the XI General Conference on Weights and Measures approved International system units of PV SI ·.
In the USSR and in the CMEA member countries, SI was introduced into the CMEA standard STSEV 1052 - 78 “Metrology. Units of physical quantities" Information about the basic units of PV SI is given in table. 1.
Two essentially derived SI units of PV: the plane angle unit is the radian ( Russian designation rad, international - rad) and the unit of solid angle - steradian (Russian designation cf, international - sr) - are not officially considered derivatives and are called additional units FV SI. The reason for their isolation is that they are established according to the defining equations j = l/r and y = S/R 2, where j is a plane angle, the vertex of which coincides with the center of an arc of length l and radius r; y is a solid angle whose vertex coincides with the center of a sphere of radius R, and which cuts out an area S on the surface of the sphere. Units
[j] = 0 and [y] = 
are dimensionless and, therefore, do not depend on the choice of basic units of the PV system.
Derived PV SI units are formed from basic and additional ones according to the rules for the formation of coherent PV units.
Basic units of physical quantities SI Table 1.
For example: angular acceleration– radian per second squared (rad/s 2), tension magnetic field– ampere per meter (A/m), brightness – candela per square meter(cd/m2).
SI PV units with special names are given in table. 2.
The international system has the following advantages over other systems of PV units: it is universal, i.e. it covers all areas of physics; coherent; its PV units are practically convenient in most cases and were widely used in the past.
Units approved for use in the CMEA countries. The above advantages of SI as a whole do not yet allow us to say that its PV units are in all cases more acceptable than any others. For example, to measure large gaps of time, a month and a century may turn out to be more convenient units than a second; for measuring long distances, the light year and parsec may turn out to be more convenient units than the meter, etc.
Derived units of physical quantities SI, having special names. Table 2.
2. CALCULATION PART
Task. An observation result of X = 100V was obtained using a voltmeter of accuracy class 4, U n = 150V. Determine the range in which the true value is located, the relative and absolute error.
Solution. k = 
Relative error: 
True value: X u = (100 ± 6) V.
All technological activities human is associated with the measurement of various physical quantities.
A set of physical quantities represents a certain system in which individual quantities are interconnected by a system of equations.
For each physical quantity, a unit of measurement must be established. An analysis of the interrelations of physical quantities shows that independently of each other it is possible to establish units of measurement for only a few physical quantities, and express the rest through them. Number is independent established values is equal to the difference between the number of quantities included in the system and the number of independent equations of connection between quantities.
For example, if the speed of a body is determined by the formula v=L/t, then only two quantities can be established independently, and the third can be expressed through them.
Physical quantities whose units are established independently of others are called fundamental quantities, and their units are called fundamental units.
The dimension of a physical quantity is an expression in the form of a power monomial, composed of products of symbols of basic physical quantities in various degrees and reflecting the relationship of a given quantity with physical quantities accepted in a given system of quantities as basic and with a proportionality coefficient equal to unity.
The powers of the symbols of the basic quantities included in a monomial can be integer, fractional, positive and negative. In accordance with international standard ISO 31/0, the dimension of quantities should be indicated by the sign dim. In the LMT system, the dimension of X will be:
dimX = L l M m T t ,
where L.M.T are symbols of quantities taken as basic (length, mass, time, respectively);
l, m, t - integer or fractional, positive or negative real numbers, which are indicators of dimension.
The dimension of a physical quantity is more general characteristics than the equation that determines the quantity, since the same dimension can be inherent in quantities that have different qualitative aspects.
For example, the work of force F is determined by the equation A = Fl; kinetic energy of a moving body - by the equation E k =mv 2 /2, and the dimensions of both are the same.
With dimensions you can perform the operations of multiplication, division, exponentiation and root extraction.
The indicator of the dimension of a physical quantity is an indicator of the power to which the dimension of the basic physical quantity, included in the dimension of the derivative physical quantity, is raised.
Dimensions are widely used in forming derived units and checking the homogeneity of equations. If all exponents of a dimension are equal to zero, then such a physical quantity is called dimensionless. All relative values(ratio of quantities of the same name) are dimensionless.
Physical quantity (PV) is a property that is qualitatively common to many physical objects (their states and processes occurring in them), but quantitatively individual for each of them.
Qualitatively general properties characterized by the genus FV. Qualitatively common can be PVs that have different names (different names): either length, width, height, depth, distance, or electromotive force, electrical voltage, electric potential, or work, energy, amount of heat. Such PVs are said to be of the same kind, or homogeneous. Physical quantities that are not homogeneous are called heterogeneous, or inhomogeneous.
Quantitatively individual property characterized by the size of the PV. For example, speed, temperature, viscosity are properties inherent in the most various objects, but for some objects of this property more, others have less. Consequently, the dimensions of speed, temperature, and viscosity for some physical objects are greater than for others.
BIBLIOGRAPHY
1. Kuznetsov V.A., Yalunina G.V. Fundamentals of metrology. Tutorial. – M.: Publishing house. Standards, 1995. – 280 p.
2. Pronenko V.I., Yakirin R.V. Metrology in industry. – Kyiv: Technology, 1979. – 223 p.
3. Laktionov B.I., Radkevich Ya.M. Metrology and interchangeability. – M.: Moscow State Publishing House mining university, 1995. – 216 p.
It would be more correct to say “dimensionless unit of PV”, since the dimension is equal to zero, not the size. However, the term “dimensionless PV unit” is widely used. The same applies to the term “dimensionless PV”.
SGSE is one of the varieties of the GHS system.
· SI stands for Systeme International. Instead of SI, you can write SI (System International).
Physical quantity (PV) is a property that is common in quality
notably to many physical objects, but quantitatively
respect individual for each physical object.
Measurement – a set of operations performed to determine
dividing the quantitative value of a quantity.
Qualitative characteristics of measured quantities . Quality
The main characteristic of physical quantities is the dimensional
ness. It is denoted by the symbol dim, which comes from the word
dimension, which, depending on the context, can be translated
both as size and as dimension.
Measuring scales. Measurement scale- this is ordered
nary set of values of a physical quantity that serves
basis for its measurement.
Classification of measurements
Measurements can be classified according to the following criteria:
1. By method of obtaining information:
- straight – these are measurements in which the desired value of fi-
sical magnitude is obtained directly;
- indirect is a measurement in which the definition of distortion
possible value of a physical quantity is found based on the results
tats of direct measurements of other physical quantities, functional
but related to the desired value;
- cumulative are simultaneous measurements of non-
how many quantities of the same name for which the desired value of
the identities are determined by solving the system of equations obtained
when measuring these quantities in various combinations;
- joint are measurements taken simultaneously
two or more non-identical quantities to determine the
dependencies between them.
2. According to the amount of measurement information:
One-time;
Multiple.
3. In relation to basic units:
Absolute;
Relative.
4. According to the nature of the dependence of the measured value on time,
static;
dynamic.
5. Depending on the physical nature of the measured quantities
measurements are divided into types:
Measurement of geometric quantities;
Measurement of mechanical quantities;
Measurement of parameters of flow, flow rate, level, volume
Pressure measurement, vacuum measurements;
Measurement of physical and chemical composition and properties of substances;
Thermophysical and temperature measurements;
Time and frequency measurement;
Measurement of electrical and magnetic quantities;
Radioelectronic measurements;
Measurement of acoustic quantities;
Optical-physical measurements;
Measurement of characteristics of ionizing radiation and nuclei -
nal constants.
Measurement methods
Measurement method is a technique or set of techniques
comparison of the measured quantity with its unit in accordance with the re-
standardized measurement principle.
Measuring principle is a physical phenomenon or effect that
underlying the measurements. For example, the phenomenon of electric
resonance in the oscillatory circuit is the basis for measuring
frequency of the electrical signal using the resonant method.
Methods for measuring specific physical quantities are very
varied. IN in general terms distinguish between the direct method
assessments and method of comparison with the measure.
Direct assessment method is that the meaning
the measured value is determined directly from the reference
device of the measuring device.
Comparison method with measure is that the measured weight
the identity is compared with the value reproduced by the measure.
The method of comparison with a measure has a number of varieties. This is me-
contrast method, zero method, substitution method, differential
rational method, coincidences.
Contrasting method is that the measured
magnitude and magnitude reproduced by the measure are simultaneously reproducible
act on the comparison device, with the help of which the
The relationship between these quantities is determined. For example, change
weight bearing on lever scales balanced with weights, or
measuring DC voltage on the compensator compared
interaction with the known EMF of a normal element.
Null method is that the net effect
the impact of the measured quantity and measure on the comparison device up to
drive to zero. For example, electrical resistance measurements
bridge with its full balancing.
Substitution method is that the measured value
The rank is replaced by a measure with a known value. For example,
weighing with alternate placement of the measured mass and weights
on the same pan of scales (Borda method).
Differential method is that the measured
the quantity is compared with a homogeneous quantity that has a known
value, slightly different from the measured value
magnitude, and at which the difference between these two is measured
quantities. For example, measuring frequency with a digital frequency counter
rum with a heterodyne frequency carrier.
Match method is that the difference between
measurable quantity and value, reproducible measure, measurable
are recorded using coincidences of scale marks or periodic signals
catch For example, measuring rotation speed with a strobe light.
It is necessary to distinguish between the measurement method and the execution technique.
measurements.
Measurement procedure – this is an established co-
a set of operations and rules during measurement, the implementation of which
ensures obtaining measurement results with guaranteed
accuracy in accordance with the accepted method.
Measuring instruments
Measuring instrument (SI) is a technical tool that uses
designed for measurements and having standardized metrological
characteristics.__
Measure is an SI intended for reproduction
physical quantity of a given size. For example, a weight is a measure
masses, a quartz oscillator is a measure of frequency, a ruler is a measure of length.
Multivalued measures:
Smoothly adjustable;
Measure sets;
Stores measures.
A single-valued measure reproduces the physical quantity of a single-valued
th size.
A multivalued measure reproduces a number of values of one and the same
the same physical quantity.
Transducer is an SI intended
to generate a measurement information signal in the form,
convenient for transfer, further transformation, but
not amenable to direct perception by the operator.
Measuring device is an SI intended for
generating a measurement information signal in a form convenient
for operator perception. For example, a voltmeter, frequency meter,
oscilloscope, etc.
Measuring setup is a set of functional
combined SI and auxiliary devices designed
to measure one or more physical quantities and
located in one place. Typically, measuring
installations are used for checking measuring instruments.
Measuring system – a set of functional
combined measures, measuring instruments, measuring
converters, computers and other technical means,
located at different points of the controlled object, etc. With
the purpose of measuring one or more physical quantities,
characteristic of this object, and the generation of measuring signals
V different circuits. It differs from a measuring setup in that
which produces measurement information in a form convenient
for automatic processing and transmission.
2.2 Units of physical quantities
2.3. International PV System (SI)
2.4. Physical quantities of technological processes in food production
2.1 Physical quantities and scales
Physical quantity(PV) is one of the properties of a physical object (physical system, phenomenon or process), common in qualitative terms for 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.
It is advisable to divide 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 an important distinguishing feature of measured EF. However, there are properties such as taste, smell, etc., for which units of measurement cannot be entered. Such quantities can be estimated, for example, using magnitude scales– an ordered sequence of its values, adopted by agreement based on the results of precise measurements.
By type of phenomena FV is divided into:
- real, i.e. describing the physical and physico-chemical properties of substances, materials and products made from them. This group includes mass, density, specific surface area, etc.
energy, i.e. quantities describing the energy characteristics of the processes of transformation, transmission and use of energy. These include, for example, current, voltage, power. These are active quantities that 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.
By belonging to various groups of physical processes Physics are divided into spatiotemporal, mechanical, thermal, electrical and magnetic, acoustic, light, physicochemical, ionizing radiation, atomic and nuclear physics.
By degree of conditional independence from other quantities of this group PVs are divided into basic (conditionally independent), derivative (conditionally dependent) and additional. Basic physical quantity– a physical quantity included in a system of quantities and conventionally accepted as independent of other quantities of this system. First of all, the quantities that characterize the basic properties of the material world were chosen as the main ones: 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 letter of the Latin or Greek alphabet: length - L, mass - M, time - T, electric current - I, temperature - O, amount of substance - N, light intensity - J. These symbols are included in the name of the system of physical quantities.
Derived physical quantity– a physical quantity included in a system of quantities and determined through the basic quantities of this system. For example, a derived physical quantity is density, defined through the mass and volume of a body.
Additional physical quantities include plane and solid angles.
A set of basic and derivative PVs, formed in accordance with accepted principles, is called system of physical quantities.
By presence of dimension PVs are divided into dimensional ones, i.e. having dimension and dimensionless.
In cases where it is necessary to emphasize that we mean the quantitative content of a physical quantity in a given object, the concept p should be used PV size(size of quantity) – quantitative determination of the physical function inherent in a specific material object, system, phenomenon, process.
PV value(Q) – expression of the size of a physical quantity in the form of a certain number of units accepted for it. The value of a physical quantity is obtained as a result of measurement or calculation, for example, 12 kg is the value of body weight.
Numerical value of PV (q) - an abstract number included in the value of a quantity
The equation
is called the fundamental measurement equation.
There is a fundamental difference between size and magnitude. The size of a quantity does not depend on whether we know it or not. We can express the size using any of the units of a given quantity and numerical value (except for the unit of mass - kg, you can use, for example, g). Dimensions different units of the same size are different.
The relationship between the basic and derived quantities of the system is expressed using dimensional equations.
Dimension of a physical quantity(dimQ) is an expression in the form of a power monomial, which reflects the relationship of a quantity with the basic units of the system and in which the proportionality coefficient is taken equal to one. The dimension of a quantity is the product of basic physical quantities raised to the appropriate powers
dimQ = L α M β N γ I η , (2.2)
where L, M, N, I – symbols basic PVs, and α, β, γ, η are real numbers.
Indicator of the dimension of a physical quantity– an indicator of the degree to which the dimension of the basic physical quantity included in the dimension of the derivative physical quantity is raised. Dimension indicators can take on different values: integers or fractions, positive or negative.
The concept of “dimension” applies to both basic and derived physical quantities. The dimension of the main quantity in relation to itself is equal to one and does not depend on other quantities, i.e. the formula for the dimension of the main quantity coincides with its symbol, for example: the length dimension is L, the mass dimension is M, etc.
To find the dimension of a derivative of a physical quantity in a certain system of quantities, one should substitute their dimension into the right side of the defining equation of this quantity instead of the designation of quantities. So, for example, substituting into the defining equation of the speed of uniform motion V = l/t instead of dl the dimension of length L and instead of dt the dimension of time T, we obtain - dim Q = L/T = LT – 1.
The following operations can be performed on dimensions: multiplication, division, exponentiation and root extraction.
Dimensional physical quantity– a physical quantity in the dimension of which at least one of the basic physical quantities is raised to a power, not equal to zero. If all exponents of the dimension of quantities are equal to zero, then such a physical quantity is called dimensionless. All relative quantities are dimensionless, that is, the ratio of quantities of the same name. For example, relative density r is a dimensionless quantity. Indeed, r = L -3 M/L -3 M = L 0 M 0 = 1.
The value of a physical quantity can be true, actual and measured. True value of PV(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 true value of a certain quantity exists, it is constant and can be correlated with the concept of absolute truth. It 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 actual 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. Measured value of a physical quantity– the value of a physical quantity obtained using a specific technique.
In practical activities, it is necessary to carry out measurements of various physical quantities. Various manifestations (quantitative or qualitative) of any property form sets, the mapping of whose elements onto an ordered set of numbers or, more generally, conventional signs form scales for measuring these properties.
Physical quantity scale is an ordered set of PV values that serves as the initial basis for measuring a given quantity. In accordance with the logical structure of the manifestation of properties, five main types of measurement scales are distinguished: names, order, conventional intervals, ratios.
Naming scale (classification scale). Such scales are used to classify empirical objects whose properties appear only in relation to equivalence; these properties cannot be considered physical quantities, therefore scales of this type are not PV scales. This is the simplest type of scale, based on assigning numbers to the qualitative properties of objects, playing the role of names. In naming scales, in which the assignment of a reflected property to a particular equivalence class is carried out using the human senses, this is the most adequate result, chosen by the majority of experts. At the same time, it is of great importance right choice classes of an equivalent scale - they must be distinguished by observers and experts assessing this property. The numbering of objects on a scale of names is carried out according to the principle: “do not assign the same number to different objects.” Numbers assigned to objects can only be used to determine the probability or frequency of occurrence of that object, but cannot be used for summation or other mathematical operations. Since these scales are characterized only by equivalence relations, they do not contain the concepts of zero, “more or less” and units of measurement. An example of naming scales are widespread color atlases intended for color identification.
If the property of a given empirical object manifests itself in relation to equivalence and ascending or descending order of the quantitative manifestation of the property, then for it a construction can be constructed scale of order (ranks). It is monotonically increasing or decreasing and allows you to establish a greater/lesser ratio between quantities characterizing the specified property. In order scales, zero exists or does not exist, but in principle it is impossible to introduce units of measurement, since a proportionality relation has not been established for them and, accordingly, there is no way to judge how many times more or less specific manifestations of a property are.
In cases where the level of knowledge of a phenomenon does not allow one to accurately establish the relationships that exist between the values of a given characteristic, or the use of a scale is convenient and sufficient for practice, use conditional (empirical) scale according torow. This is a PV scale, the initial values of which are expressed in conventional units, for example, the Engler viscosity scale, the 12-point Beaufort scale for measuring the strength of sea wind.
Interval scales (difference scale are a further development of order scales and are used for objects whose properties satisfy the relations of equivalence, order and additivity. The interval scale consists of identical intervals, has a unit of measurement and an arbitrarily chosen beginning - zero point. Such scales include chronology according to various calendars, in which either the creation of the world, or the Nativity of Christ, etc. is taken as the starting point. The Celsius, Fahrenheit and Reaumur temperature scales are also interval scales.
Relationship scale describe the properties of empirical objects that satisfy the relations of equivalence, order and additivity (scales of the second kind are additive), and in some cases proportionality (scales of the first kind are proportional). Their examples are the scale of mass (second kind), thermodynamic temperature (first kind).
In ratio scales, there is an unambiguous natural criterion for the zero quantitative manifestation of a property and a unit of measurement. From a formal point of view, the ratio scale is an interval scale with a natural origin. All arithmetic operations are applicable to the values obtained on this scale, which has important when measuring EF. For example, the scale scale, starting from zero, can be graduated in different ways, depending on the required weighing accuracy.
Absolute scales. By absolute we mean scales that have all the features of ratio scales, but additionally have a natural unambiguous definition of the unit of measurement and do not depend on the adopted system of units of measurement. Such scales correspond to relative values: gain, attenuation, etc. To form many derived units in the SI system, dimensionless and counting units of absolute scales are used.
Note that the scales of names and order are called notmetric (conceptual), and interval and ratio scales - metric (material). Absolute and metric scales belong to the category of linear. The practical implementation of measurement scales is carried out by standardizing both the scales and measurement units themselves, and, if necessary, the methods and conditions for their unambiguous reproduction.