In 1875, the International Bureau of Weights and Measures was founded by the Metric Conference; its goal was to create a unified measurement system that would be used throughout the world. It was decided to take as a basis the metric system, which appeared during the French Revolution and was based on the meter and kilogram. Later, the standards of the meter and kilogram were approved. Over time, the system of units of measurement has evolved and currently has seven basic units of measurement. In 1960, this system of units received the modern name International System of Units (SI System) (Systeme Internatinal d "Unites (SI)). The SI system is not static; it is developing in accordance with the requirements that are currently imposed on measurements in science and technology.
Basic units of measurement of the International System of Units
The definition of all auxiliary units in the SI system is based on seven basic units of measurement. The main physical quantities in the International System of Units (SI) are: length ($l$); mass ($m$); time ($t$); electric current ($I$); Kelvin temperature (thermodynamic temperature) ($T$); amount of substance ($\nu $); luminous intensity ($I_v$).
The basic units in the SI system are the units of the above-mentioned quantities:
\[\left=m;;\ \left=kg;;\ \left=s;\ \left=A;;\ \left=K;;\ \ \left[\nu \right]=mol;;\ \left=cd\ (candela).\]
Standards of basic units of measurement in SI
Let us present the definitions of the standards of basic units of measurement as done in the SI system.
Meter (m) is the length of the path that light travels in a vacuum in a time equal to $\frac(1)(299792458)$ s.
Standard mass for SI is a weight in the shape of a straight cylinder, the height and diameter of which is 39 mm, consisting of an alloy of platinum and iridium weighing 1 kg.
One second (s) called a time interval that is equal to 9192631779 periods of radiation, which corresponds to the transition between two hyperfine levels of the ground state of the cesium atom (133).
One ampere (A)- this is the current strength passing in two straight infinitely thin and long conductors located at a distance of 1 meter, located in a vacuum, generating the Ampere force (the force of interaction of conductors) equal to $2\cdot (10)^(-7)N$ for each meter of conductor .
One kelvin (K)- this is the thermodynamic temperature equal to $\frac(1)(273.16)$ part of the triple point temperature of water.
One mole (mole)- this is the amount of a substance that has the same number of atoms as there are in 0.012 kg of carbon (12).
One candela (cd) equal to the intensity of light emitted by a monochromatic source with a frequency of $540\cdot (10)^(12)$Hz with an energy force in the direction of radiation $\frac(1)(683)\frac(W)(avg).$
Science is developing, measuring technology is being improved, and definitions of units of measurement are being revised. The higher the measurement accuracy, the greater the requirements for determining units of measurement.
SI derived quantities
All other quantities are considered in the SI system as derivatives of the basic ones. The units of measurement of derived quantities are defined as the result of the product (taking into account the degree) of the basic ones. Let us give examples of derived quantities and their units in the SI system.
The SI system also has dimensionless quantities, for example, reflection coefficient or relative dielectric constant. These quantities have dimension one.
The SI system includes derived units with special names. These names are compact forms of representing combinations of basic quantities. Let us give examples of SI units that have their own names (Table 2).
Each SI quantity has only one unit, but the same unit can be used for different quantities. Joule is a unit of measurement for the amount of heat and work.
SI system, units of measurement multiples and submultiples
The International System of Units has a set of prefixes for units of measurement that are used if the numerical values of the quantities in question are significantly greater or less than the unit of the system that is used without the prefix. These prefixes are used with any units of measurement; in the SI system they are decimal.
Let us give examples of such prefixes (Table 3).
When writing, the prefix and the name of the unit are written together, so that the prefix and the unit of measurement form a single symbol.
Note that the unit of mass in the SI system (kilogram) has historically already had a prefix. Decimal multiples and submultiples of the kilogram are obtained by connecting the prefix to the gram.
Non-system units
The SI system is universal and convenient in international communication. Almost all units that are not included in the SI system can be defined using SI terms. The use of the SI system is preferred in science education. However, there are some quantities that are not included in the SI, but are widely used. Thus, units of time such as minute, hour, day are part of culture. Some units are used for historical reasons. When using units that do not belong to the SI system, it is necessary to indicate how they are converted to SI units. An example of units is given in Table 4.
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, the distinctive features of the phenomenon, the course of its course, possible causes and consequences are established. 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. A physical quantity is a scientific characteristic of a 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.
The Russian measure of length is the arshin - the distance between the index and thumb. 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 entered. 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.
Various countries have tried to solve this problem. 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. A 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 is determined in the form of 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. The lack of 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.
This lesson will not be new for beginners. We have all heard from school such things as centimeter, meter, kilometer. And when it came to mass, they usually said gram, kilogram, ton.
Centimeters, meters and kilometers; grams, kilograms and tons have one common name - units of measurement of physical quantities.
In this lesson we will look at the most popular units of measurement, but we will not delve too deeply into this topic, since units of measurement go into the field of physics. Today we are forced to study part of physics because we need it for further study of mathematics.
Lesson contentUnits of length
The following units of measurement are used to measure length:
- millimeters;
- centimeters;
- decimeters;
- meters;
- kilometers.
millimeter(mm). Millimeters can even be seen with your own eyes if you take the ruler that we used at school every day
Small lines running one after another are millimeters. More precisely, the distance between these lines is one millimeter (1 mm):
centimeter(cm). On the ruler, each centimeter is marked with a number. For example, our ruler, which was in the first picture, had a length of 15 centimeters. The last centimeter on this ruler is marked with the number 15.
There are 10 millimeters in one centimeter. You can put an equal sign between one centimeter and ten millimeters, since they indicate the same length:
1 cm = 10 mm
You can see this for yourself if you count the number of millimeters in the previous figure. You will find that the number of millimeters (distances between lines) is 10.
The next unit of length is decimeter(dm). There are ten centimeters in one decimeter. An equal sign can be placed between one decimeter and ten centimeters, since they indicate the same length:
1 dm = 10 cm
You can verify this if you count the number of centimeters in the following figure:
You will find that the number of centimeters is 10.
The next unit of measurement is meter(m). There are ten decimeters in one meter. One can put an equal sign between one meter and ten decimeters, since they indicate the same length:
1 m = 10 dm
Unfortunately, the meter cannot be illustrated in the figure because it is quite large. If you want to see the meter live, take a tape measure. Everyone has it in their home. On a tape measure, one meter will be designated as 100 cm. This is because there are ten decimeters in one meter, and one hundred centimeters in ten decimeters:
1 m = 10 dm = 100 cm
100 is obtained by converting one meter to centimeters. This is a separate topic that we will look at a little later. For now, let's move on to the next unit of length, which is called the kilometer.
The kilometer is considered the largest unit of length. There are, of course, other higher units, such as megameter, gigameter, terameter, but we will not consider them, since a kilometer is enough for us to further study mathematics.
There are a thousand meters in one kilometer. You can put an equal sign between one kilometer and a thousand meters, since they indicate the same length:
1 km = 1000 m
Distances between cities and countries are measured in kilometers. For example, the distance from Moscow to St. Petersburg is about 714 kilometers.
International System of Units SI
The International System of Units SI is a certain set of generally accepted physical quantities.
The main purpose of the international system of SI units is to achieve agreements between countries.
We know that the languages and traditions of the countries of the world are different. There's nothing to be done about it. But the laws of mathematics and physics work the same everywhere. If in one country “twice two is four,” then in another country “twice two is four.”
The main problem was that for each physical quantity there are several units of measurement. For example, we have now learned that to measure length there are millimeters, centimeters, decimeters, meters and kilometers. If several scientists speaking different languages gather in one place to solve some problem, then such a large variety of units of length measurement can give rise to contradictions between these scientists.
One scientist will state that in their country length is measured in meters. The second may say that in their country the length is measured in kilometers. The third may offer his own unit of measurement.
Therefore, the international system of SI units was created. SI is an abbreviation for the French phrase Le Système International d’Unités, SI (which translated into Russian means the international system of units SI).
The SI lists the most popular physical quantities and each of them has its own generally accepted unit of measurement. For example, in all countries, when solving problems, it was agreed that length would be measured in meters. Therefore, when solving problems, if the length is given in another unit of measurement (for example, in kilometers), then it must be converted into meters. We'll talk about how to convert one unit of measurement to another a little later. For now, let's draw our international system of SI units.
Our drawing will be a table of physical quantities. We will include each studied physical quantity in our table and indicate the unit of measurement that is accepted in all countries. Now we have studied the units of length and learned that the SI system defines meters to measure length. So our table will look like this:
Mass units
Mass is a quantity indicating the amount of matter in a body. People call body weight weight. Usually when something is weighed they say “It weighs so many kilograms” , although we are not talking about weight, but about the mass of this body.
However, mass and weight are different concepts. Weight is the force with which the body acts on a horizontal support. Weight is measured in newtons. And mass is a quantity that shows the amount of matter in this body.
But there is nothing wrong with calling body weight weight. Even in medicine they say "person's weight" , although we are talking about the mass of a person. The main thing is to be aware that these are different concepts.
The following units of measurement are used to measure mass:
- milligrams;
- grams;
- kilograms;
- centners;
- tons.
The smallest unit of measurement is milligram(mg). You will most likely never use a milligram in practice. They are used by chemists and other scientists who work with small substances. It is enough for you to know that such a unit of measurement of mass exists.
The next unit of measurement is gram(G). It is customary to measure the amount of a particular product in grams when preparing a recipe.
There are a thousand milligrams in one gram. One can put an equal sign between one gram and a thousand milligrams, since they denote the same mass:
1 g = 1000 mg
The next unit of measurement is kilogram(kg). The kilogram is a generally accepted unit of measurement. It measures everything. The kilogram is included in the SI system. Let us also include one more physical quantity in our SI table. We will call it “mass”:
There are a thousand grams in one kilogram. You can put an equal sign between one kilogram and a thousand grams, since they denote the same mass:
1 kg = 1000 g
The next unit of measurement is hundredweight(ts). In centners it is convenient to measure the mass of a crop collected from a small area or the mass of some cargo.
There are one hundred kilograms in one centner. One can put an equal sign between one centner and one hundred kilograms, since they denote the same mass:
1 c = 100 kg
The next unit of measurement is ton(T). Large loads and masses of large bodies are usually measured in tons. For example, the mass of a spaceship or car.
There are one thousand kilograms in one ton. One can put an equal sign between one ton and a thousand kilograms, since they denote the same mass:
1 t = 1000 kg
Time units
There is no need to explain what time we think is. Everyone knows what time is and why it is needed. If we open the discussion to what time is and try to define it, we will begin to delve into philosophy, and we do not need this now. Let's start with the units of time.
The following units of measurement are used to measure time:
- seconds;
- minutes;
- watch;
- day.
The smallest unit of measurement is second(With). There are, of course, smaller units such as milliseconds, microseconds, nanoseconds, but we will not consider them, since at the moment this makes no sense.
Various parameters are measured in seconds. For example, how many seconds does it take for an athlete to run 100 meters? The second is included in the SI international system of units for measuring time and is designated as "s". Let us also include one more physical quantity in our SI table. We will call it “time”:
minute(m). There are 60 seconds in one minute. One minute and sixty seconds can be equated because they represent the same time:
1 m = 60 s
The next unit of measurement is hour(h). There are 60 minutes in one hour. An equal sign can be placed between one hour and sixty minutes, since they represent the same time:
1 hour = 60 m
For example, if we studied this lesson for one hour and we are asked how much time we spent studying it, we can answer in two ways: “we studied the lesson for one hour” or so “we studied the lesson for sixty minutes” . In both cases, we will answer correctly.
The next unit of time is day. There are 24 hours in a day. You can put an equal sign between one day and twenty-four hours, since they mean the same time:
1 day = 24 hours
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Electric current is characterized by quantities such as current, voltage and resistance that are interconnected. Before considering the question of how voltage is measured, it is necessary to find out exactly what this quantity is and what its role is in the formation of current.
How does tension work?
The general concept of electric current is the directed movement of charged particles. These particles are electrons, the movement of which occurs under the influence of an electric field. The more charges need to be moved, the more work is done by the field. This work is affected not only by current, but also by voltage.
The physical meaning of this value is that the work done by the current in any section of the circuit is correlated with the amount of charge that passes through this section. In the process of this work, a positive charge moves from a point where there is a small potential to a point with a high potential. Thus, voltage is defined as electromotive force, and work itself is energy.
The work done by an electric current is measured in joules (J), and the amount of electric charge is a coulomb (C). As a result, the voltage is a ratio of 1 J/C. The resulting unit of voltage is called a volt.
To clearly explain the physical meaning of stress, you need to refer to the example of a hose filled with water. In this case, the volume of water will play the role of current strength, and its pressure will be equivalent to voltage. When water moves without a tip, it moves freely and in large quantities through the hose, creating low pressure. If you press the end of the hose with your finger, the volume will decrease while the water pressure increases. The jet itself will travel a much greater distance.
The same thing happens in electricity. The strength of the current is determined by the number or volume of electrons moving through the conductor. The voltage value is essentially the force with which those electrons are pushed through. It follows that, given the same voltage, a conductor that conducts a larger amount of current must also have a larger diameter.
Voltage unit
The voltage can be constant or variable, depending on the current. This value can be designated as the letter B (Russian designation) or V, corresponding to the international designation. To indicate alternating voltage, the “~” symbol is used, which is placed in front of the letter. For constant voltage there is a “-” sign, but in practice it is almost never used.
When considering the question of how voltage is measured, it should be remembered that there are not only volts for this. Larger quantities are measured in kilovolts (kV) and megavolts (mV), which means 1 thousand and 1 million volts, respectively.
How to measure voltage and current
In principle, one can imagine any large number of different systems of units, but only a few are widely used. All over the world, the metric system is used for scientific and technical measurements and in most countries in industry and everyday life.
Basic units.
In the system of units, for each measured physical quantity there must be a corresponding unit of measurement. Thus, a separate unit of measurement is needed for length, area, volume, speed, etc., and each such unit can be determined by choosing one or another standard. But the system of units turns out to be much more convenient if in it only a few units are selected as basic ones, and the rest are determined through the basic ones. So, if the unit of length is a meter, the standard of which is stored in the State Metrological Service, then the unit of area can be considered a square meter, the unit of volume is a cubic meter, the unit of speed is a meter per second, etc.
The convenience of such a system of units (especially for scientists and engineers, who deal with measurements much more often than other people) is that the mathematical relationships between the basic and derived units of the system turn out to be simpler. In this case, a unit of speed is a unit of distance (length) per unit of time, a unit of acceleration is a unit of change in speed per unit of time, a unit of force is a unit of acceleration per unit of mass, etc. In mathematical notation it looks like this: v = l/t, a = v/t, F = ma = ml/t 2. The presented formulas show the “dimension” of the quantities under consideration, establishing relationships between units. (Similar formulas allow you to determine units for quantities such as pressure or electric current.) Such relationships are of a general nature and are valid regardless of what units (meter, foot or arshin) the length is measured in and what units are chosen for other quantities.
In technology, the basic unit of measurement of mechanical quantities is usually taken not as a unit of mass, but as a unit of force. Thus, if in the system most commonly used in physical research, a metal cylinder is taken as a standard of mass, then in a technical system it is considered as a standard of force that balances the force of gravity acting on it. But since the force of gravity is not the same at different points on the Earth's surface, location specification is necessary to accurately implement the standard. Historically, the location was sea level at a latitude of 45°. Currently, such a standard is defined as the force necessary to give the specified cylinder a certain acceleration. True, in technology, measurements are usually not carried out with such high accuracy that it is necessary to take care of variations in gravity (if we are not talking about the calibration of measuring instruments).
There is a lot of confusion surrounding the concepts of mass, force and weight. The fact is that there are units of all these three quantities that have the same names. Mass is an inertial characteristic of a body, showing how difficult it is to remove it from a state of rest or uniform and linear motion by an external force. A unit of force is a force that, acting on a unit of mass, changes its speed by one unit of speed per unit of time.
All bodies attract each other. Thus, any body near the Earth is attracted to it. In other words, the Earth creates the force of gravity acting on the body. This force is called its weight. The force of weight, as stated above, is not the same at different points on the surface of the Earth and at different altitudes above sea level due to differences in gravitational attraction and in the manifestation of the Earth's rotation. However, the total mass of a given amount of substance is unchanged; it is the same both in interstellar space and at any point on Earth.
Precise experiments have shown that the force of gravity acting on different bodies (i.e. their weight) is proportional to their mass. Consequently, masses can be compared on scales, and masses that turn out to be the same in one place will be the same in any other place (if the comparison is carried out in a vacuum to exclude the influence of displaced air). If a certain body is weighed on a spring scale, balancing the force of gravity with the force of an extended spring, then the results of measuring the weight will depend on the place where the measurements are taken. Therefore, spring scales must be adjusted at each new location so that they correctly indicate the mass. The simplicity of the weighing procedure itself was the reason that the force of gravity acting on the standard mass was adopted as an independent unit of measurement in technology. HEAT.
Metric system of units.
The metric system is the general name for the international decimal system of units, the basic units of which are the meter and the kilogram. Although there are some differences in details, the elements of the system are the same throughout the world.
Story.
The metric system grew out of regulations adopted by the French National Assembly in 1791 and 1795 defining the meter as one ten-millionth of the portion of the earth's meridian from the North Pole to the equator.
By decree issued on July 4, 1837, the metric system was declared mandatory for use in all commercial transactions in France. It gradually replaced local and national systems in other European countries and was legally accepted as acceptable in the UK and USA. An agreement signed on May 20, 1875 by seventeen countries created an international organization designed to preserve and improve the metric system.
It is clear that by defining the meter as a ten-millionth part of a quarter of the earth's meridian, the creators of the metric system sought to achieve invariance and accurate reproducibility of the system. They took the gram as a unit of mass, defining it as the mass of one millionth of a cubic meter of water at its maximum density. Since it would not be very convenient to carry out geodetic measurements of a quarter of the earth's meridian with each sale of a meter of cloth or to balance a basket of potatoes at the market with the appropriate amount of water, metal standards were created that reproduced these ideal definitions with extreme accuracy.
It soon became clear that metal length standards could be compared with each other, introducing much less error than when comparing any such standard with a quarter of the earth's meridian. In addition, it became clear that the accuracy of comparing metal mass standards with each other is much higher than the accuracy of comparing any such standard with the mass of the corresponding volume of water.
In this regard, the International Commission on the Meter in 1872 decided to accept the “archival” meter stored in Paris “as it is” as the standard of length. Similarly, the members of the Commission accepted the archival platinum-iridium kilogram as the standard of mass, “considering that the simple relationship established by the creators of the metric system between the unit of weight and the unit of volume is represented by the existing kilogram with an accuracy sufficient for ordinary applications in industry and commerce, and the exact Sciences do not need a simple numerical relationship of this kind, but an extremely perfect definition of this relationship.” In 1875, many countries around the world signed a meter agreement, and this agreement established a procedure for coordinating metrological standards for the world scientific community through the International Bureau of Weights and Measures and the General Conference on Weights and Measures.
The new international organization immediately began developing international standards for length and mass and transmitting copies of them to all participating countries.
Standards of length and mass, international prototypes.
The international prototypes of the standards of length and mass - the meter and the kilogram - were deposited with the International Bureau of Weights and Measures, located in Sèvres, a suburb of Paris. The meter standard was a ruler made of a platinum alloy with 10% iridium, the cross-section of which was given a special X-shape to increase bending rigidity with a minimum volume of metal. In the groove of such a ruler there was a longitudinal flat surface, and the meter was defined as the distance between the centers of two strokes applied across the ruler at its ends, at a standard temperature of 0 ° C. The mass of a cylinder made of the same platinum was taken as the international prototype of the kilogram. iridium alloy, the same as the standard meter, with a height and diameter of about 3.9 cm. The weight of this standard mass, equal to 1 kg at sea level at latitude 45°, is sometimes called kilogram-force. Thus, it can be used either as a standard of mass for an absolute system of units, or as a standard of force for a technical system of units in which one of the basic units is the unit of force.
The international prototypes were selected from a large batch of identical standards produced simultaneously. Other standards of this batch were transferred to all participating countries as national prototypes (state primary standards), which are periodically returned to the International Bureau for comparison with international standards. Comparisons made at various times since then show that they do not show deviations (from international standards) beyond the limits of measurement accuracy.
International SI system.
The metric system was very favorably received by scientists of the 19th century. partly because it was proposed as an international system of units, partly because its units were theoretically assumed to be independently reproducible, and also because of its simplicity. Scientists began to develop new units for the various physical quantities they dealt with, based on the elementary laws of physics and linking these units to the metric units of length and mass. The latter increasingly conquered various European countries, in which previously many unrelated units for different quantities were in use.
Although all countries that adopted the metric system of units had nearly the same standards for metric units, various discrepancies in derived units arose between different countries and different disciplines. In the field of electricity and magnetism, two separate systems of derived units emerged: electrostatic, based on the force with which two electric charges act on each other, and electromagnetic, based on the force of interaction between two hypothetical magnetic poles.
The situation became even more complicated with the advent of the so-called system. practical electrical units introduced in the mid-19th century. by the British Association for the Advancement of Science to meet the demands of rapidly developing wire telegraph technology. Such practical units do not coincide with the units of both systems mentioned above, but differ from the units of the electromagnetic system only by factors equal to whole powers of ten.
Thus, for such common electrical quantities as voltage, current and resistance, there were several options for accepted units of measurement, and each scientist, engineer, and teacher had to decide for himself which of these options was best for him to use. In connection with the development of electrical engineering in the second half of the 19th and first half of the 20th centuries. Practical units were increasingly used and eventually came to dominate the field.
To eliminate such confusion at the beginning of the 20th century. a proposal was put forward to combine practical electrical units with corresponding mechanical ones based on metric units of length and mass, and build some kind of coherent system. In 1960, the XI General Conference on Weights and Measures adopted a unified International System of Units (SI), defined the basic units of this system and prescribed the use of certain derived units, “without prejudice to others that may be added in the future.” Thus, for the first time in history, an international coherent system of units was adopted by international agreement. It is now accepted as a legal system of units of measurement by most countries in the world.
The International System of Units (SI) is a harmonized system that provides one and only one unit of measurement for any physical quantity, such as length, time, or force. Some of the units are given special names, an example is the unit of pressure pascal, while the names of others are derived from the names of the units from which they are derived, for example the unit of speed - meter per second. The basic units, together with two additional geometric ones, are presented in Table. 1. Derived units for which special names are adopted are given in table. 2. Of all the derived mechanical units, the most important are the unit of force newton, the unit of energy the joule and the unit of power the watt. Newton is defined as the force that imparts an acceleration of one meter per second squared to a mass of one kilogram. A joule is equal to the work done when the point of application of a force equal to one Newton moves a distance of one meter in the direction of the force. A watt is the power at which one joule of work is done in one second. Electrical and other derived units will be discussed below. The official definitions of major and minor units are as follows.
A meter is the length of the path traveled by light in a vacuum in 1/299,792,458 of a second. This definition was adopted in October 1983.
A kilogram is equal to the mass of the international prototype of the kilogram.
A second is the duration of 9,192,631,770 periods of radiation oscillations corresponding to transitions between two levels of the hyperfine structure of the ground state of the cesium-133 atom.
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 a substance that contains the same number of structural elements as atoms in the carbon-12 isotope weighing 0.012 kg.
A radian is a plane angle between two radii of a circle, the length of the arc between which is equal to the radius.
The steradian is equal to the solid angle with its vertex at the center of the sphere, cutting out on its surface an area equal to the area of a square with a side equal to the radius of the sphere.
To form decimal multiples and submultiples, a number of prefixes and factors are prescribed, indicated in the table. 3.
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Table 3. Prefixes and multipliers of the international system of units |
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| exa | deci | ||||
| peta | centi | ||||
| tera | Milli | ||||
| giga | micro |
mk |
|||
| mega | nano | ||||
| kilo | pico | ||||
| hecto | femto | ||||
| soundboard |
Yes |
atto | |||
Thus, a kilometer (km) is 1000 m, and a millimeter is 0.001 m. (These prefixes apply to all units, such as kilowatts, milliamps, etc.)
It was originally intended that one of the base units should be the gram, and this was reflected in the names of the units of mass, but nowadays the base unit is the kilogram. Instead of the name megagram, the word “ton” is used. In physics disciplines, such as measuring the wavelength of visible or infrared light, a millionth of a meter (micrometer) is often used. In spectroscopy, wavelengths are often expressed in angstroms (Å); An angstrom is equal to one tenth of a nanometer, i.e. 10 - 10 m. For radiation with a shorter wavelength, such as X-rays, in scientific publications it is allowed to use a picometer and an x-unit (1 x-unit = 10 –13 m). A volume equal to 1000 cubic centimeters (one cubic decimeter) is called a liter (L).
Mass, length and time.
All basic SI units, except the kilogram, are currently defined in terms of physical constants or phenomena that are considered immutable and reproducible with high accuracy. As for the kilogram, a way to implement it with the degree of reproducibility that is achieved in procedures for comparing various mass standards with the international prototype of the kilogram has not yet been found. Such a comparison can be carried out by weighing on a spring balance, the error of which does not exceed 1H 10 –8. Standards of multiple and submultiple units for a kilogram are established by combined weighing on scales.
Since the meter is defined in terms of the speed of light, it can be reproduced independently in any well-equipped laboratory. Thus, using the interference method, line and end length measures, which are used in workshops and laboratories, can be checked by comparing directly with the wavelength of light. The error with such methods under optimal conditions does not exceed one billionth (1H 10 –9). With the development of laser technology, such measurements have become very simplified, and their range has expanded significantly.
Likewise, the second, according to its modern definition, can be independently realized in a competent laboratory in an atomic beam facility. The beam's atoms are excited by a high-frequency oscillator tuned to the atomic frequency, and an electronic circuit measures time by counting the periods of oscillation in the oscillator circuit. Such measurements can be carried out with an accuracy of the order of 1H 10 -12 - much higher than was possible with previous definitions of the second, based on the rotation of the Earth and its revolution around the Sun. Time and its reciprocal, frequency, are unique in that their standards can be transmitted by radio. Thanks to this, anyone who has the appropriate radio receiving equipment can receive signals of exact time and reference frequency, almost no different in accuracy from those transmitted over the air.
Mechanics.
Temperature and warmth.
Mechanical units do not allow solving all scientific and technical problems without involving any other relationships. Although the work done when moving a mass against the action of a force, and the kinetic energy of a certain mass are equivalent in nature to the thermal energy of a substance, it is more convenient to consider temperature and heat as separate quantities that do not depend on mechanical ones.
Thermodynamic temperature scale.
The unit of thermodynamic temperature Kelvin (K), called kelvin, is determined by the triple point of water, i.e. the temperature at which water is in equilibrium with ice and steam. This temperature is taken to be 273.16 K, which determines the thermodynamic temperature scale. This scale, proposed by Kelvin, is based on the second law of thermodynamics. If there are two thermal reservoirs with a constant temperature and a reversible heat engine transferring heat from one of them to the other in accordance with the Carnot cycle, then the ratio of the thermodynamic temperatures of the two reservoirs is given by T 2 /T 1 = –Q 2 Q 1 where Q 2 and Q 1 – the amount of heat transferred to each of the reservoirs (the minus sign indicates that heat is taken from one of the reservoirs). Thus, if the temperature of the warmer reservoir is 273.16 K, and the heat taken from it is twice as much as the heat transferred to the other reservoir, then the temperature of the second reservoir is 136.58 K. If the temperature of the second reservoir is 0 K, then it no heat will be transferred at all, since all the gas energy has been converted into mechanical energy in the adiabatic expansion section of the cycle. This temperature is called absolute zero. The thermodynamic temperature commonly used in scientific research coincides with the temperature included in the equation of state of an ideal gas PV = RT, Where P- pressure, V– volume and R– gas constant. The equation shows that for an ideal gas, the product of volume and pressure is proportional to temperature. This law is not exactly satisfied for any of the real gases. But if corrections are made for virial forces, then the expansion of gases allows us to reproduce the thermodynamic temperature scale.
International temperature scale.
In accordance with the definition outlined above, temperature can be measured with very high accuracy (up to approximately 0.003 K near the triple point) by gas thermometry. A platinum resistance thermometer and a gas reservoir are placed in a thermally insulated chamber. When the chamber is heated, the electrical resistance of the thermometer increases and the gas pressure in the reservoir increases (in accordance with the equation of state), and when cooled, the opposite picture is observed. By measuring resistance and pressure simultaneously, you can calibrate the thermometer by gas pressure, which is proportional to temperature. The thermometer is then placed in a thermostat in which the liquid water can be kept in equilibrium with its solid and vapor phases. By measuring its electrical resistance at this temperature, a thermodynamic scale is obtained, since the temperature of the triple point is assigned a value equal to 273.16 K.
There are two international temperature scales - Kelvin (K) and Celsius (C). Temperature on the Celsius scale is obtained from temperature on the Kelvin scale by subtracting 273.15 K from the latter.
Accurate temperature measurements using gas thermometry require a lot of labor and time. Therefore, the International Practical Temperature Scale (IPTS) was introduced in 1968. Using this scale, thermometers of different types can be calibrated in the laboratory. This scale was established using a platinum resistance thermometer, a thermocouple and a radiation pyrometer, used in the temperature intervals between certain pairs of constant reference points (temperature benchmarks). The MPTS was supposed to correspond to the thermodynamic scale with the greatest possible accuracy, but, as it turned out later, its deviations were very significant.
Fahrenheit temperature scale.
The Fahrenheit temperature scale, which is widely used in combination with the British technical system of units, as well as in non-scientific measurements in many countries, is usually determined by two constant reference points - the melting point of ice (32 ° F) and the boiling point of water (212 ° F) at normal (atmospheric) pressure. Therefore, to get the Celsius temperature from the Fahrenheit temperature, you need to subtract 32 from the latter and multiply the result by 5/9.
Units of heat.
Since heat is a form of energy, it can be measured in joules, and this metric unit has been adopted by international agreement. But since the amount of heat was once determined by the change in temperature of a certain amount of water, a unit called a calorie became widespread and is equal to the amount of heat required to increase the temperature of one gram of water by 1 ° C. Due to the fact that the heat capacity of water depends on temperature , I had to clarify the calorie value. At least two different calories appeared - “thermochemical” (4.1840 J) and “steam” (4.1868 J). The “calorie” used in dietetics is actually a kilocalorie (1000 calories). The calorie is not an SI unit and has fallen into disuse in most fields of science and technology.
Electricity and magnetism.
All commonly accepted electrical and magnetic units of measurement are based on the metric system. In accordance with modern definitions of electrical and magnetic units, they are all derived units, derived by certain physical formulas from the metric units of length, mass and time. Since most electrical and magnetic quantities are not so easy to measure using the standards mentioned, it was found that it is more convenient to establish, through appropriate experiments, derivative standards for some of the indicated quantities, and to measure others using such standards.
SI units.
Below is a list of SI electrical and magnetic units.
The ampere, a unit of electric current, is one of the six SI base units. Ampere is the strength of a constant current, which, when passing through two parallel straight conductors of infinite length with a negligibly small circular cross-sectional area, located in a vacuum at a distance of 1 m from each other, would cause on each section of the conductor 1 m long an interaction force equal to 2H 10 - 7 N.
Volt, a unit of potential difference and electromotive force. Volt is the electrical voltage in a section of an electrical circuit with a direct current of 1 A with a power consumption of 1 W.
Coulomb, a unit of quantity of electricity (electric charge). Coulomb is the amount of electricity passing through the cross-section of a conductor at a constant current of 1 A in 1 s.
Farad, a unit of electrical capacitance. Farad is the capacitance of a capacitor on the plates of which, when charged at 1 C, an electric voltage of 1 V appears.
Henry, unit of inductance. Henry is equal to the inductance of the circuit in which a self-inductive emf of 1 V occurs when the current in this circuit changes uniformly by 1 A in 1 s.
Weber unit of magnetic flux. Weber is a magnetic flux, when it decreases to zero, an electric charge equal to 1 C flows in the circuit connected to it, which has a resistance of 1 Ohm.
Tesla, a unit of magnetic induction. Tesla is the magnetic induction of a uniform magnetic field, in which the magnetic flux through a flat area of 1 m2, perpendicular to the induction lines, is equal to 1 Wb.
Practical standards.
Light and illumination.
Luminous intensity and illuminance units cannot be determined based on mechanical units alone. We can express the energy flux in a light wave in W/m2, and the intensity of the light wave in V/m, as in the case of radio waves. But the perception of illumination is a psychophysical phenomenon in which not only the intensity of the light source is significant, but also the sensitivity of the human eye to the spectral distribution of this intensity.
By international agreement, the unit of luminous intensity is the candela (previously called a candle), equal to the luminous intensity in a given direction of a source emitting monochromatic radiation of frequency 540H 10 12 Hz ( l= 555 nm), the energy force of light radiation of which in this direction is 1/683 W/sr. This roughly corresponds to the luminous intensity of a spermaceti candle, which once served as a standard.
If the luminous intensity of the source is one candela in all directions, then the total luminous flux is 4 p lumens. Thus, if this source is located at the center of a sphere with a radius of 1 m, then the illumination of the inner surface of the sphere is equal to one lumen per square meter, i.e. one suite.
X-ray and gamma radiation, radioactivity.
X-ray (R) is an obsolete unit of exposure dose of x-ray, gamma and photon radiation, equal to the amount of radiation that, taking into account secondary electron radiation, forms ions in 0.001 293 g of air that carry a charge equal to one unit of the CGS charge of each sign. The SI unit of absorbed radiation dose is the gray, equal to 1 J/kg. The standard for absorbed radiation dose is a setup with ionization chambers that measure the ionization produced by radiation.
