What are called physical quantities. Basic physical quantities and units of their measurement

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Books

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• Hydraulics 4th ed., trans. and additional Textbook and workshop for academic baccalaureate, Eduard Mikhailovich Kartashov. The textbook outlines the basic physical and mechanical properties of liquids, issues of hydrostatics and hydrodynamics, gives the basics of the theory of hydrodynamic similarity and mathematical modeling ...

Physical quantity

Physical quantity - physical property a material object, a physical phenomenon, a process that can be characterized quantitatively.

The value of a physical quantity- one or more (in the case of a tensor physical quantity) numbers characterizing this physical quantity, indicating the unit of measurement, on the basis of which they were obtained.

The size of a physical quantity- the values ​​of the numbers appearing in the value of a physical quantity.

For example, a car can be characterized as physical quantity like mass. Wherein, meaning this physical quantity will be, for example, 1 ton, and size- the number 1, or meaning will be 1000 kilograms, and size- the number 1000. The same car can be characterized using a different physical quantity- speed. Wherein, meaning this physical quantity will be, for example, a vector of a certain direction 100 km / h, and size- number 100.

Dimension of a physical quantity- unit of measurement, appearing in the value of a physical quantity. As a rule, a physical quantity has many different dimensions: for example, length has a nanometer, millimeter, centimeter, meter, kilometer, mile, inch, parsec, light year, etc. Some of these units of measurement (without taking into account their decimal factors) can be included in various systems of physical units - SI, CGS, etc.

Often a physical quantity can be expressed in terms of other, more fundamental physical quantities. (For example, force can be expressed in terms of the mass of a body and its acceleration). Which means respectively, and the dimension such a physical quantity can be expressed in terms of the dimensions of these more general quantities. (The dimension of force can be expressed in terms of the dimensions of mass and acceleration). (Often such a representation of the dimension of a certain physical quantity in terms of the dimensions of other physical quantities is an independent task, which in some cases has its own meaning and purpose.) The dimensions of such more general quantities are often already basic units one or another system of physical units, that is, those that themselves are no longer expressed through others, even more general quantities.

Example.
If the physical quantity power is written as

Tue is an abbreviation one of units of measurement of this physical quantity (watts). Litera to is the symbol for the decimal factor "kilo" of the International System of Units (SI).

Dimensional and dimensionless physical quantities

• Dimensional physical quantity- a physical quantity, to determine the value of which it is necessary to apply some unit of measurement of this physical quantity. The vast majority of physical quantities are dimensional.
• Dimensionless physical quantity- a physical quantity, to determine the value of which it is enough only to indicate its size. For example, relative permittivity is a dimensionless physical quantity.

Additive and non-additive physical quantities

• Additive physical quantity- physical quantity, different meanings which can be summed, multiplied by a numerical coefficient, divided by each other. For example, the physical quantity mass is an additive physical quantity.
• Non-additive physical quantity- a physical quantity for which summation, multiplication by a numerical coefficient or division by each other does not have its values physical sense. For example, the physical quantity temperature is a non-additive physical quantity.

Extensive and intensive physical quantities

The physical quantity is called

• extensive, if the magnitude of its value is the sum of the magnitudes of the values ​​of this physical quantity for the subsystems that make up the system (for example, volume, weight);
• intensive if the value of its value does not depend on the size of the system (for example, temperature, pressure).

Some physical quantities, such as angular momentum, area, force, length, time, are neither extensive nor intensive.

Derived quantities are formed from some extensive quantities:

• specific quantity is the quantity divided by the mass (for example, specific volume);
• molar quantity is the quantity divided by the amount of the substance (for example, molar volume).

Scalar, vector, tensor quantities

In the most general case we can say that a physical quantity can be represented by a tensor of a certain rank (valence).

System of units of physical quantities

The system of units of physical quantities is a set of units of measurement of physical quantities, in which there is a certain number of so-called basic units of measurement, and the remaining units of measurement can be expressed through these basic units. Examples of systems of physical units - International System of Units (SI), CGS.

Symbols for physical quantities

Literature

• RMG 29-99 Metrology. Basic terms and definitions.
• Burdun G. D., Bazakutsa V. A. Units of physical quantities. - Kharkiv: Vishcha school,.

Physical quantity called the physical property of a material object, process, physical phenomenon, characterized quantitatively.

The value of a physical quantity expressed by one or more numbers characterizing this physical quantity, indicating the unit of measurement.

The size of a physical quantity are the values ​​of the numbers appearing in the meaning of the physical quantity.

Units of measurement of physical quantities.

The unit of measurement of a physical quantity is the fixed size value assigned to numerical value equal to one. It is used for the quantitative expression of physical quantities homogeneous with it. A system of units of physical quantities is a set of basic and derived units based on a certain system of quantities.

Only a few have become widespread systems of units. In most cases, many countries use the metric system.

Basic units.

Measure physical quantity - means to compare it with another similar physical quantity, taken as a unit.

The length of an object is compared with a unit of length, body weight - with a unit of weight, etc. But if one researcher measures the length in sazhens, and another in feet, it will be difficult for them to compare these two values. Therefore, all physical quantities around the world are usually measured in the same units. In 1963, the International System of Units SI (System international - SI) was adopted.

For each physical quantity in the system of units, an appropriate unit of measurement must be provided. Standard units is its physical realization.

The length standard is meter- the distance between two strokes applied on a specially shaped rod made of an alloy of platinum and iridium.

Standard time is the duration of any correctly repeating process, which is chosen as the movement of the Earth around the Sun: the Earth makes one revolution per year. But the unit of time is not a year, but give me a sec.

For a unit speed take the speed of such uniform rectilinear motion, at which the body makes a movement of 1 m in 1 s.

A separate unit of measurement is used for area, volume, length, etc. Each unit is determined when choosing one or another standard. But the system of units is much more convenient if only a few units are chosen as the main ones, and the rest are determined through the main ones. For example, if the unit of length is meter, then the unit of area is square meter, volume - cubic meter, speed - meter per second, etc.

Basic units physical quantities in international system units (SI) are: meter (m), kilogram (kg), second (s), ampere (A), kelvin (K), candela (cd) and mole (mole).

There are also derived SI units, which have their own names:

Andmeasurements. To obtain an accurate, objective and easily reproducible description of a physical quantity, measurements are used. Without measurements, a physical quantity cannot be quantified. Definitions such as "low" or "high" pressure, "low" or "high" temperature reflect only subjective opinions and do not contain comparison with reference values. When measuring a physical quantity, it is assigned a certain numerical value.

Measurements are made using measuring devices. There is quite a large number of measuring instruments and fixtures, from the simplest to the most complex. For example, length is measured with a ruler or tape measure, temperature with a thermometer, width with calipers.

Measuring instruments are classified: according to the method of presenting information (indicating or recording), according to the method of measurement (direct action and comparison), according to the form of presentation of indications (analog and digital), etc.

The measuring instruments are characterized by the following parameters:

Measuring range- the range of values ​​of the measured quantity, on which the device is designed during its normal operation (with a given measurement accuracy).

Sensitivity threshold- the minimum (threshold) value of the measured value, distinguished by the device.

Sensitivity- relates the value of the measured parameter and the corresponding change in instrument readings.

Accuracy- the ability of the device to indicate the true value of the measured indicator.

Stability- the ability of the device to maintain a given measurement accuracy for a certain time after calibration.

Physical quantity- this is a property that is qualitatively common to many objects (systems, their states and processes occurring in them), but quantitatively individual for each object.

Individuality in quantitative terms should be understood in the sense that a property can be for one object a certain number of times more or less than for another.

As a rule, the term "quantity" is used in relation to properties or their characteristics that can be quantified, that is, measured. There are properties and characteristics that have not yet been learned to quantify, but seek to find a way to quantify them, such as smell, taste, etc. Until we learn how to measure them, we should not call them quantities, but properties.

The standard contains only the term "physical quantity", and the word "quantity" is given as a short form of the main term, which is allowed to be used in cases that exclude the possibility of different interpretations. In other words, it is possible to call a physical quantity briefly a quantity, if it is obvious without an adjective that we are talking about a physical quantity. In the following text of this book short form the term "quantity" is used only in the indicated sense.

In metrology, the word "value" is given a terminological meaning by imposing a restriction in the form of the adjective "physical". The word "value" is often used to express the size of a given physical quantity. They say: pressure value, speed value, voltage value. This is wrong, since pressure, speed, voltage in the correct sense of these words are quantities, and it is impossible to talk about the magnitude of a quantity. In the above cases, the use of the word "value" is superfluous. Indeed, why talk about a large or small "value" of pressure, when you can say: large or small pressure, etc..

A physical quantity displays the properties of objects that can be expressed quantitatively in accepted units. Any measurement implements the operation of comparing the homogeneous properties of physical quantities on the basis of "greater-less". As a result of the comparison, each size of the measured quantity is assigned a positive real number:

x = q [x] , (1.1)

where q - the numerical value of the quantity or the result of the comparison; [X] - unit of magnitude.

Unit of physical quantity- a physical quantity, which, by definition, is given a value equal to one. It can also be said that the unit of a physical quantity is its value, which is taken as a basis for comparing physical quantities of the same kind with it in their quantitative assessment.

Equation (1.1) is the basic measurement equation. The numerical value of q is found as follows

therefore, it depends on the accepted unit of measurement .

1. Systems of units of physical quantities

When carrying out any measurements, the measured value is compared with another value that is homogeneous with it, taken as a unit. To build a system of units, several physical quantities are chosen arbitrarily. They are called basic. The values ​​determined through the main ones are called derivatives. The set of basic and derived quantities is called a system of physical quantities.

AT general view relationship between derived quantity Z and basic can be represented by the following equation:

Z = L  M  T  I    J  ,

where L, M, T,I, ,J- basic quantities; , , , , ,  - indicators of dimension. This formula is called the dimension formula. The system of quantities can consist of both dimensional and dimensionless quantities. Dimensional is a quantity in the dimension of which at least one of the basic quantities is raised to a power that is not equal to zero. A dimensionless quantity is a quantity in whose dimension the basic quantities are included in a degree equal to zero. A dimensionless quantity in one system of quantities can be a dimensional quantity in another system. The system of physical quantities is used to build a system of units of physical quantities.

The unit of a physical quantity is the value of this quantity, taken as the basis for comparing with it the values ​​of quantities of the same kind in their quantitative assessment. It is assigned a numerical value of 1 by definition.

Units of basic and derived quantities are called basic and derived units, respectively, their totality is called a system of units. The choice of units within a system is somewhat arbitrary. However, as the basic units, they choose those that, firstly, can be reproduced with the highest accuracy, and secondly, are convenient in the practice of measurements or their reproduction. The units of quantities included in the system are called system units. In addition to system units, non-system units are also used. Non-system units are units that are not part of the system. They are convenient for certain areas of science and technology or regions and therefore have become widespread. Non-systemic units include: power unit - horsepower, energy unit - kilowatt-hour, time units - hour, day, temperature unit - degree Celsius and many others. They arose during the development of measurement technology to meet practical needs or were introduced for the convenience of using them in measurements. For the same purposes, multiple and submultiple units of quantities are used.

A multiple unit is one that is an integer number of times greater than a system or off-system unit: kilohertz, megawatt. A fractional unit is one that is an integer number of times less than a system or off-system unit: milliampere, microvolt. Strictly speaking, many off-system units can be considered as multiples or submultiples.

In science and technology, relative and logarithmic quantities and their units are also widely used, which characterize the amplification and attenuation of electrical signals, modulation coefficients, harmonics, etc. Relative values ​​can be expressed in dimensionless relative units, in percent, in ppm. The logarithmic value is the logarithm (usually decimal in radio electronics) of the dimensionless ratio of two quantities of the same name. The unit of the logarithmic value is bel (B), defined by the ratio:

N = lg P 1/ / P 2 = 2 lg F 1 / F 2 , (1.2)

where P 1 ,P 2 - energy quantities of the same name (values ​​of power, energy, power density flux, etc.); F 1 , F 2 - power quantities of the same name (voltage, current strength, intensity electromagnetic field etc.).

As a rule, a submultiple unit from a bel is used, called a decibel, equal to 0.1 B. In this case, in formula (1.2), an additional factor of 10 is added after the equal signs. For example, the voltage ratio U 1 / U 2 \u003d 10 corresponds to a logarithmic unit of 20 dB .

There is a tendency to use natural systems of units based on universal physical constants (constants) that could be taken as basic units: the speed of light, Boltzmann's constant, Planck's constant, electron charge, etc. . The advantage of such a system is the constancy of the basis of the system and the high stability of the constants. In some standards, such constants are already used: the standard of the unit of frequency and length, the standard of the unit of constant voltage. But the sizes of units of quantities based on constants, at the present level of development of technology, are inconvenient for practical measurements and do not provide the necessary accuracy in obtaining all derived units. However, such advantages of the natural system of units as indestructibility, invariability in time, and independence from location stimulate work on studying the possibility of their practical application.

For the first time, a set of basic and derived units that form a system was proposed in 1832 by K. F. Gauss. As the basic units in this system, three arbitrary units are accepted - length, mass and time, respectively equal to a millimeter, a milligram and a second. Later, other systems of units of physical quantities were proposed, based on the metric system of measures and differing in basic units. But all of them, while satisfying some experts, aroused objections from others. This required the creation of a new system of units. To some extent, it was possible to resolve the existing contradictions after the adoption in 1960 by the XI General Conference on Weights and Measures of the International System of Units, abbreviated as SI (SI). In Russia, it was first adopted as preferable (1961), and then after the entry into force of GOST 8.417-81 “GSI. Units of Physical Quantities" - and as mandatory in all areas of science, technology, the national economy, as well as in all educational institutions.

Seven are chosen as the main ones in the International System of Units (SI). following units: meter, kilogram, second, ampere, Kelvin, candela, mole.

The international system of units includes two additional units - for measuring flat and solid angles. These units cannot be introduced into the category of basic ones, since they are determined by the ratio of two quantities. At the same time, they are not derived units, since they do not depend on the choice of basic units.

Radian (rad) - the angle between two radii of a circle, the arc between which is equal in length to the radius.

Steradian (sr) is a solid angle whose vertex is located in the center of the sphere and which cuts out on the surface. spheres an area equal to the area of ​​a square with a side length equal to the radius of the sphere.

In accordance with the Law on Ensuring the Uniformity of Measurements in the Russian Federation, units of the International System of Units adopted by the General Conference on Weights and Measures recommended by the International Organization of Legal Metrology are allowed to be used in the prescribed manner.

The names, designations and rules for writing units of quantities, as well as the rules for their application on the territory of the Russian Federation, are established by the government of the Russian Federation, with the exception of cases provided for by legislative acts of the Russian Federation.

The Government of the Russian Federation may allow for use, along with units of quantities of the International System of Units, non-systemic units of quantities.

The study of physical phenomena and their laws, as well as the use of these laws 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 realizations 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 one and the same physical quantity - length, and therefore they are homogeneous quantities. The mass of this book and the mass of the Earth's satellite Kosmos-897 are also homogeneous physical quantities.

Homogeneous physical quantities differ from each other in size. The size of a physical quantity is

quantitative content in this object of a property corresponding to the concept of "physical quantity".

The sizes of homogeneous physical quantities of various objects can be compared with each other if the values ​​of these quantities are determined.

The value of a physical quantity is an estimate of a physical quantity in the form of a certain number of units accepted for it (see p. 14). For example, the value of the length of a certain body, 5 kg is the value of the mass of a certain body, etc. An abstract number included in the value of a physical quantity (in our examples 10 and 5) is called a numerical value. In the general case, the value X of a certain quantity can be expressed as the formula

where is the numerical value of the quantity, its unit.

It is necessary to distinguish between the true and actual values ​​of a physical quantity.

The true value of a physical quantity is the value of the quantity that would ideally reflect the corresponding property of the object in qualitative and quantitative terms.

The actual value of a physical quantity is the value of the quantity found experimentally and so close to the true value that it can be used instead of it for a given purpose.

Finding the value of a physical quantity empirically using special technical means called measurement.

The true values ​​of physical quantities are, as a rule, unknown. For example, no one knows the true values ​​of the speed of light, the distance from the Earth to the Moon, the mass of an electron, a proton, and others. elementary particles. We do not know the true value of our height and body weight, we do not know and cannot find out the true value of the air temperature in our room, the length of the table at which we work, etc.

However, using special technical means, it is possible to determine the actual

all these and many other values. At the same time, the degree of approximation of these actual values ​​to the true values ​​of physical quantities depends on the perfection of the technical means of measurement used in this case.

Measuring instruments include measures, measuring instruments, etc. A measure is understood as a measuring instrument designed to reproduce a physical quantity of a given size. For example, a weight is a measure of mass, a ruler with millimeter divisions is a measure of length, a measuring flask is a measure of volume (capacity), a normal element is a measure electromotive force, quartz oscillator - 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 for direct perception by observation. Measuring instruments include dynamometer, ammeter, manometer, etc.

There are direct and indirect measurements.

A direct measurement is a measurement in which the desired value of a quantity is found directly from experimental data. Direct measurements include, for example, the measurement of mass on an equal-arm scale, temperature - with a thermometer, length - with a scale ruler.

Indirect measurement is a measurement in which the desired value of a quantity is found on the basis of a known relationship between it and the quantities subjected to direct measurements. Indirect measurements are, for example, finding the density of a body by its mass and geometric dimensions, finding the specific electrical resistance conductor by its resistance, length and cross-sectional area.

Measurements of physical quantities are based on various physical phenomena. For example, to measure temperature, use thermal expansion bodies or thermoelectric effect, to measure the mass of bodies by weighing - the phenomenon of gravity, etc. The set of physical phenomena on which measurements are based is called the principle of measurement. Measurement principles are not covered in this manual. Metrology deals with the study of the principles and methods of measurements, types of measuring instruments, measurement errors and other issues related to measurements.