Calculate absolute zero. Absolute zero temperature

Absolute zero temperature

The limiting temperature at which the volume of an ideal gas becomes equal to zero is taken as absolute zero temperature.

Let's find the value of absolute zero on the Celsius scale.
Equating volume V in formula (3.1) zero and taking into account that

Hence the absolute zero temperature is

t= –273 °C. 2

This is the extreme, lowest temperature in nature, that “greatest or last degree of cold”, the existence of which Lomonosov predicted.

The highest temperatures on Earth—hundreds of millions of degrees—are obtained during explosions of thermonuclear bombs. Even higher temperatures are typical for the inner regions of some stars.

2More accurate value of absolute zero: –273.15 °C.

Kelvin scale

The English scientist W. Kelvin introduced absolute scale temperatures Zero temperature on the Kelvin scale corresponds to absolute zero, and the unit of temperature on this scale is equal to a degree on the Celsius scale, so absolute temperature T is related to temperature on the Celsius scale by the formula

T = t + 273. (3.2)

In Fig. 3.2 shows the absolute scale and the Celsius scale for comparison.

The SI unit of absolute temperature is called kelvin(abbreviated as K). Therefore, one degree on the Celsius scale is equal to one degree on the Kelvin scale:

Thus, absolute temperature, according to the definition given by formula (3.2), is a derived quantity that depends on the Celsius temperature and on the experimentally determined value of a.

Reader: What physical meaning does absolute temperature have?

Let us write expression (3.1) in the form

Considering that temperature on the Kelvin scale is related to temperature on the Celsius scale by the relation T = t + 273, we get

Where T 0 = 273 K, or

Since this relation is valid for arbitrary temperature T, then Gay-Lussac’s law can be formulated as follows:

For a given mass of gas at p = const the following relation holds:

Task 3.1. At a temperature T 1 = 300 K gas volume V 1 = 5.0 l. Determine the volume of gas at the same pressure and temperature T= 400 K.

STOP! Decide for yourself: A1, B6, C2.

Problem 3.2. During isobaric heating, the volume of air increased by 1%. By what percentage did the absolute temperature increase?

= 0,01.

Answer: 1 %.

Let's remember the resulting formula

STOP! Decide for yourself: A2, A3, B1, B5.

Charles's Law

The French scientist Charles experimentally established that if a gas is heated so that its volume remains constant, the pressure of the gas will increase. The dependence of pressure on temperature has the form:

R(t) = p 0 (1 + b t), (3.6)

Where R(t) – pressure at temperature t°C; R 0 – pressure at 0 °C; b is the temperature coefficient of pressure, which is the same for all gases: 1/K.

Reader: Surprisingly, the temperature coefficient of pressure b is exactly equal to the temperature coefficient of volumetric expansion a!

Let us take a certain mass of gas with a volume V 0 at temperature T 0 and pressure R 0 . For the first time, maintaining the gas pressure constant, we heat it to a temperature T 1 . Then the gas will have a volume V 1 = V 0 (1 + a t) and pressure R 0 .

The second time, maintaining the volume of gas constant, we heat it to the same temperature T 1 . Then the gas will have pressure R 1 = R 0 (1 + b t) and volume V 0 .

Since in both cases the gas temperature is the same, the Boyle–Mariotte law is valid:

p 0 V 1 = p 1 V 0 Þ R 0 V 0 (1 + a t) = R 0 (1 + b t)V 0 Þ

Þ 1 + a t = 1 + b tÞ a = b.

So it's not surprising that a = b, no!

Let us rewrite Charles' law in the form

Considering that T = t°С + 273 °С, T 0 = 273 °C, we get

ABSOLUTE ZERO

ABSOLUTE ZERO, the temperature at which all components of the system have the least amount of energy allowed by the laws of QUANTUM MECHANICS; zero on the Kelvin temperature scale, or -273.15°C (-459.67° Fahrenheit). At this temperature, the entropy of the system - the amount of energy available to do useful work - is also zero, although the total amount of energy of the system may be non-zero.

Scientific and technical encyclopedic dictionary.

See what "ABSOLUTE ZERO" is in other dictionaries:

Temperature is the minimum limit of temperature that a physical body can have. Absolute zero serves as the starting point for an absolute temperature scale, such as the Kelvin scale. On the Celsius scale, absolute zero corresponds to a temperature of −273 ... Wikipedia

ABSOLUTE ZERO TEMPERATURE- the beginning of the thermodynamic temperature scale; located at 273.16 K (Kelvin) below (see) water, i.e. equal to 273.16°C (Celsius). Absolute zero is the lowest temperature in nature and practically unattainable... Big Polytechnic Encyclopedia

This is the minimum temperature limit that a physical body can have. Absolute zero serves as the starting point for an absolute temperature scale, such as the Kelvin scale. On the Celsius scale, absolute zero corresponds to a temperature of −273.15 °C.... ... Wikipedia

Absolute zero temperature is the minimum temperature limit that a physical body can have. Absolute zero serves as the starting point for an absolute temperature scale, such as the Kelvin scale. On the Celsius scale, absolute zero corresponds to... ... Wikipedia

Razg. Neglected An insignificant, insignificant person. FSRY, 288; BTS, 24; ZS 1996, 33 ...

zero- absolute zero … Dictionary of Russian Idioms

Zero and zero noun, m., used. compare often Morphology: (no) what? zero and zero, why? zero and zero, (see) what? zero and zero, what? zero and zero, what about? about zero, zero; pl. What? zeros and zeros, (no) what? zeros and zeros, why? zeros and zeros, (I see)… … Dmitriev's Explanatory Dictionary

Absolute zero (zero). Razg. Neglected An insignificant, insignificant person. FSRY, 288; BTS, 24; ZS 1996, 33 V zero. 1. Jarg. they say Joking. iron. About severe intoxication. Yuganovs, 471; Vakhitov 2003, 22. 2. Zharg. music Exactly, in full accordance with... ... Large dictionary of Russian sayings

absolute- absolute absurdity, absolute authority, absolute impeccability, absolute disorder, absolute fiction, absolute immunity, absolute leader, absolute minimum, absolute monarch, absolute morality, absolute zero… … Dictionary of Russian Idioms

Books

Absolute zero, Absolute Pavel. The life of all the creations of the mad scientist of the Nes race is very short. But the next experiment has a chance to exist. What awaits him ahead?...

When the weather report predicts temperatures near zero, you shouldn’t go to the skating rink: the ice will melt. The melting temperature of ice is taken to be zero degrees Celsius, the most common temperature scale.
We are very familiar with the negative degrees Celsius scale - degrees<ниже нуля>, degrees of cold. The lowest temperature on Earth was recorded in Antarctica: -88.3°C. Even lower temperatures are possible outside the Earth: on the surface of the Moon at lunar midnight it can reach -160°C.
But arbitrarily low temperatures cannot exist anywhere. The extremely low temperature - absolute zero - corresponds to - 273.16° on the Celsius scale.
The absolute temperature scale, the Kelvin scale, originates from absolute zero. Ice melts at 273.16° Kelvin, and water boils at 373.16° K. Thus, degree K is equal to degree C. But on the Kelvin scale, all temperatures are positive.
Why is 0°K the cold limit?
Heat is the chaotic movement of atoms and molecules of a substance. When a substance is cooled, thermal energy is removed from it, and the random movement of particles is weakened. Eventually, with strong cooling, thermal<пляска>particles almost completely stops. Atoms and molecules would completely freeze at a temperature that is taken to be absolute zero. According to the principles of quantum mechanics, at absolute zero it would be the thermal motion of particles that would cease, but the particles themselves would not freeze, since they cannot be at complete rest. Thus, at absolute zero, particles must still retain some kind of motion, which is called zero motion.

However, to cool a substance to a temperature below absolute zero is an idea as meaningless as, say, the intention<идти медленнее, чем стоять на месте>.

Moreover, even achieving exact absolute zero is almost impossible. You can only get closer to him. Because by no means can you take away absolutely all of the thermal energy from a substance. Some of the thermal energy remains at the deepest cooling.
How do you achieve ultra-low temperatures?
Freezing a substance is more difficult than heating it. This can be seen even from a comparison of the design of a stove and a refrigerator.
In most household and industrial refrigerators, heat is removed due to the evaporation of a special liquid - freon, which circulates through metal tubes. The secret is that freon can remain in a liquid state only at a sufficiently low temperature. In the refrigerator compartment, due to the heat of the chamber, it heats up and boils, turning into steam. But the steam is compressed by the compressor, liquefied and enters the evaporator, replenishing the loss of evaporated freon. Energy is consumed to operate the compressor.
In deep cooling devices, the cold carrier is an ultra-cold liquid - liquid helium. Colorless, light (8 times lighter than water), it boils under atmospheric pressure at 4.2°K, and in a vacuum at 0.7°K. An even lower temperature is given by the light isotope of helium: 0.3°K.
Setting up a permanent helium refrigerator is quite difficult. Research is carried out simply in baths with liquid helium. And to liquefy this gas, physicists use different techniques. For example, pre-cooled and compressed helium is expanded, released through a thin hole into a vacuum chamber. At the same time, the temperature decreases further and some of the gas turns into liquid. It is more efficient not only to expand the cooled gas, but also to force it to do work - move the piston.
The resulting liquid helium is stored in special thermoses - Dewar flasks. The cost of this very cold liquid (the only one that does not freeze at absolute zero) turns out to be quite high. Nevertheless, liquid helium is used more and more widely these days, not only in science, but also in various technical devices.
The lowest temperatures were achieved in a different way. It turns out that the molecules of some salts, for example potassium chromium alum, can rotate along magnetic force lines. This salt is pre-cooled with liquid helium to 1°K and placed in a strong magnetic field. In this case, the molecules rotate along the lines of force, and the released heat is taken away by liquid helium. Then the magnetic field is abruptly removed, the molecules again turn in different directions, and the expended

This work leads to further cooling of the salt. This is how we obtained a temperature of 0.001° K. Using a similar method in principle, using other substances, we can obtain an even lower temperature.
The lowest temperature obtained so far on Earth is 0.00001° K.

Superfluidity

A substance frozen to ultra-low temperatures in baths of liquid helium changes noticeably. Rubber becomes brittle, lead becomes hard like steel and elastic, many alloys increase strength.

Liquid helium itself behaves in a peculiar way. At temperatures below 2.2° K, it acquires a property unprecedented for ordinary liquids - superfluidity: some of it completely loses viscosity and flows through the narrowest cracks without any friction.
This phenomenon was discovered in 1937 by the Soviet physicist Academician P. JI. Kapitsa, was then explained by Academician JI. D. Landau.
It turns out that at ultra-low temperatures the quantum laws of the behavior of matter begin to have a noticeable effect. As one of these laws requires, energy can be transferred from body to body only in well-defined portions - quanta. There are so few heat quanta in liquid helium that there are not enough of them for all the atoms. The part of the liquid, devoid of heat quanta, remains as if at absolute zero temperature; its atoms do not participate at all in random thermal motion and do not interact in any way with the walls of the vessel. This part (it was called helium-H) has superfluidity. As the temperature decreases, helium-P becomes more and more abundant, and at absolute zero all helium would turn into helium-H.
Superfluidity has now been studied in great detail and has even found a useful practical application: with its help it is possible to separate helium isotopes.

Superconductivity

Near absolute zero, extremely interesting changes occur in the electrical properties of some materials.
In 1911, the Dutch physicist Kamerlingh Onnes made an unexpected discovery: it turned out that at a temperature of 4.12 ° K, electrical resistance in mercury completely disappears. Mercury becomes a superconductor. The electric current induced in a superconducting ring does not die out and can flow almost forever.
Above such a ring, a superconducting ball will float in the air and not fall, like a fairy tale<гроб Магомета>, because its gravity is compensated by the magnetic repulsion between the ring and the ball. After all, a continuous current in the ring will create a magnetic field, and it, in turn, will induce an electric current in the ball and with it an oppositely directed magnetic field.
In addition to mercury, tin, lead, zinc, and aluminum have superconductivity near absolute zero. This property has been found in 23 elements and more than a hundred different alloys and other chemical compounds.
The temperatures at which superconductivity appears (critical temperatures) cover a fairly wide range - from 0.35° K (hafnium) to 18° K (niobium-tin alloy).
The phenomenon of superconductivity, like super-
fluidity has been studied in detail. The dependences of critical temperatures on the internal structure of materials and the external magnetic field were found. A deep theory of superconductivity was developed (an important contribution was made by the Soviet scientist Academician N. N. Bogolyubov).
The essence of this paradoxical phenomenon is again purely quantum. At ultralow temperatures, electrons in

superconductor form a system of pairwise bound particles that cannot give energy to the crystal lattice or waste energy quanta on heating it. Pairs of electrons move as if<танцуя>, between<прутьями решетки>- ions and bypass them without collisions and energy transfer.
Superconductivity is increasingly used in technology.
For example, superconducting solenoids are used in practice - coils of superconductor immersed in liquid helium. Once induced current and, consequently, a magnetic field can be stored in them for as long as desired. It can reach a gigantic size - over 100,000 oersted. In the future, powerful industrial superconducting devices will undoubtedly appear - electric motors, electromagnets, etc.
In radio electronics, ultra-sensitive amplifiers and generators of electromagnetic waves, which work especially well in baths with liquid helium, begin to play a significant role - there the internal<шумы>equipment. In electronic computing technology, a brilliant future is promised for low-power superconducting switches - cryotrons (see Art.<Пути электроники>).
It is not difficult to imagine how tempting it would be to advance the operation of such devices into the region of higher, more accessible temperatures. Recently, the hope of creating polymer film superconductors has been discovered. The peculiar nature of electrical conductivity in such materials promises a brilliant opportunity to maintain superconductivity even at room temperatures. Scientists are persistently looking for ways to realize this hope.

In the depths of the stars

And now let's look into the realm of the hottest thing in the world - into the depths of the stars. Where temperatures reach millions of degrees.
The random thermal motion in stars is so intense that entire atoms cannot exist there: they are destroyed in countless collisions.
A substance that is so hot can therefore be neither solid, nor liquid, nor gaseous. It is in the state of plasma, i.e. a mixture of electrically charged<осколков>atoms - atomic nuclei and electrons.
Plasma is a unique state of matter. Since its particles are electrically charged, they are sensitive to electrical and magnetic forces. Therefore, the close proximity of two atomic nuclei (they carry a positive charge) is a rare phenomenon. Only at high densities and enormous temperatures are atomic nuclei colliding with each other able to come close together. Then thermonuclear reactions take place - the source of energy for stars.
The closest star to us, the Sun, consists mainly of hydrogen plasma, which is heated in the bowels of the star to 10 million degrees. Under such conditions, close encounters of fast hydrogen nuclei - protons, although rare, do occur. Sometimes protons that come close interact: having overcome electrical repulsion, they fall into the power of gigantic nuclear forces of attraction, rapidly<падают>on top of each other and merge. Here an instantaneous restructuring occurs: instead of two protons, a deuteron (the nucleus of a heavy hydrogen isotope), a positron and a neutrino appear. The energy released is 0.46 million electron volts (MeV).
Each individual solar proton can enter into such a reaction on average once every 14 billion years. But there are so many protons in the bowels of the light that here and there this unlikely event occurs - and our star burns with its even, dazzling flame.
The synthesis of deuterons is only the first step of solar thermonuclear transformations. The newborn deuteron very soon (on average after 5.7 seconds) combines with another proton. A light helium nucleus and a gamma quantum of electromagnetic radiation appear. 5.48 MeV of energy is released.
Finally, on average once every million years, two light helium nuclei can converge and combine. Then a nucleus of ordinary helium (alpha particle) is formed and two protons are split off. 12.85 MeV of energy is released.
This three-stage<конвейер>thermonuclear reactions are not the only one. There is another chain of nuclear transformations, faster ones. The atomic nuclei of carbon and nitrogen participate in it (without being consumed). But in both options, alpha particles are synthesized from hydrogen nuclei. Figuratively speaking, the hydrogen plasma of the Sun<сгорает>, turning into<золу>- helium plasma. And during the synthesis of each gram of helium plasma, 175 thousand kWh of energy is released. Great amount!
Every second the Sun emits 4,1033 ergs of energy, losing 4,1012 g (4 million tons) of matter in weight. But the total mass of the Sun is 2,1027 tons. This means that in a million years, thanks to radiation, the Sun<худеет>only one ten-millionth of its mass. These figures eloquently illustrate the effectiveness of thermonuclear reactions and the gigantic calorific value of solar energy.<горючего>- hydrogen.
Thermonuclear fusion is apparently the main source of energy for all stars. At different temperatures and densities of stellar interiors, different types of reactions occur. In particular, solar<зола>-helium nuclei - at 100 million degrees it itself becomes thermonuclear<горючим>. Then even heavier atomic nuclei - carbon and even oxygen - can be synthesized from alpha particles.
According to many scientists, our entire Metagalaxy as a whole is also the fruit of thermonuclear fusion, which took place at a temperature of a billion degrees (see Art.<Вселенная вчера, сегодня и завтра>).

Towards the artificial sun

Extraordinary calorific value of thermonuclear<горючего>prompted scientists to achieve artificial implementation of nuclear fusion reactions.
<Горючего>- There are many hydrogen isotopes on our planet. For example, the superheavy hydrogen tritium can be produced from the metal lithium in nuclear reactors. And heavy hydrogen - deuterium is part of heavy water, which can be extracted from ordinary water.
Heavy hydrogen extracted from two glasses of ordinary water would produce as much energy in a thermonuclear reactor as is now produced by burning a barrel of premium gasoline.
The difficulty is to preheat<горючее>to temperatures at which it can ignite with powerful thermonuclear fire.
This problem was first solved in the hydrogen bomb. Hydrogen isotopes there are ignited by the explosion of an atomic bomb, which is accompanied by heating of the substance to many tens of millions of degrees. In one of the versions of the hydrogen bomb, the thermonuclear fuel is a chemical compound of heavy hydrogen with light lithium - light lithium deuteride. This white powder, similar to table salt,<воспламеняясь>from<спички>, which is an atomic bomb, instantly explodes and creates a temperature of hundreds of millions of degrees.
To initiate a peaceful thermonuclear reaction, one must first learn how to heat small doses of a sufficiently dense plasma of hydrogen isotopes to temperatures of hundreds of millions of degrees without the services of an atomic bomb. This problem is one of the most difficult in modern applied physics. Scientists around the world have been working on it for many years.
We have already said that it is the chaotic movement of particles that creates the heating of bodies, and the average energy of their random movement corresponds to the temperature. To heat a cold body means to create this disorder in any way.
Imagine two groups of runners rushing towards each other. So they collided, got mixed up, a crush and confusion began. Great mess!
In much the same way, physicists initially tried to obtain high temperatures - by colliding high-pressure gas jets. The gas heated up to 10 thousand degrees. At one time this was a record: the temperature was higher than on the surface of the Sun.
But with this method, further, rather slow, non-explosive heating of the gas is impossible, since the thermal disorder instantly spreads in all directions, warming the walls of the experimental chamber and the environment. The resulting heat quickly leaves the system, and it is impossible to isolate it.
If gas jets are replaced by plasma flows, the problem of thermal insulation remains very difficult, but there is also hope for its solution.
True, plasma cannot be protected from heat loss by vessels made of even the most refractory substance. In contact with solid walls, hot plasma immediately cools down. But you can try to hold and heat the plasma by creating its accumulation in a vacuum so that it does not touch the walls of the chamber, but hangs in emptiness, not touching anything. Here we should take advantage of the fact that plasma particles are not neutral, like gas atoms, but electrically charged. Therefore, when moving, they are exposed to magnetic forces. The task arises: to create a magnetic field of a special configuration in which hot plasma would hang as if in a bag with invisible walls.
The simplest form of such plasma is created automatically when strong pulses of electric current are passed through the plasma. In this case, magnetic forces are induced around the plasma cord, which tend to compress the cord. The plasma is separated from the walls of the discharge tube, and at the axis of the cord in the crush of particles the temperature rises to 2 million degrees.
In our country, such experiments were performed back in 1950 under the leadership of academicians JI. A. Artsimovich and M. A. Leontovich.
Another direction of experiments is the use of a magnetic bottle, proposed in 1952 by the Soviet physicist G.I. Budker, now an academician. The magnetic bottle is placed in a cork chamber - a cylindrical vacuum chamber equipped with an external winding, which is condensed at the ends of the chamber. The current flowing through the winding creates a magnetic field in the chamber. Its field lines in the middle part are located parallel to the generatrices of the cylinder, and at the ends they are compressed and form magnetic plugs. Plasma particles injected into a magnetic bottle curl around the field lines and are reflected from the plugs. As a result, the plasma is retained inside the bottle for some time. If the energy of the plasma particles introduced into the bottle is high enough and there are enough of them, they enter into complex force interactions, their initially ordered movement becomes confused, becomes disordered - the temperature of the hydrogen nuclei rises to tens of millions of degrees.
Additional heating is achieved by electromagnetic<ударами>by plasma, compression of the magnetic field, etc. Now the plasma of heavy hydrogen nuclei is heated to hundreds of millions of degrees. True, this can be done either for a short time or at low plasma density.
To initiate a self-sustaining reaction, the temperature and density of the plasma must be further increased. This is difficult to achieve. However, the problem, as scientists are convinced, is undoubtedly solvable.

G.B. Anfilov

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Any physical body, including all objects in the Universe, has a minimum temperature or its limit. The starting point of any temperature scale is considered to be the value of absolute zero temperature. But this is only in theory. The chaotic movement of atoms and molecules, which give up their energy at this time, has not yet been stopped in practice.

This is the main reason why absolute zero temperatures cannot be reached. There are still debates about the consequences of this process. From the point of view of thermodynamics, this limit is unattainable, since the thermal movement of atoms and molecules stops completely, and a crystal lattice is formed.

Representatives of quantum physics envision the presence of minimum zero oscillations at absolute zero temperatures.

What is the value of absolute zero temperature and why it cannot be achieved

At the General Conference on Weights and Measures, a reference or reference point was established for the first time for measuring instruments that determine temperature indicators.

Currently, in the International System of Units, the reference point for the Celsius scale is 0°C for freezing and 100°C for boiling, the value of absolute zero temperatures is equal to −273.15°C.

Using temperature values on the Kelvin scale according to the same International System of Units, boiling of water will occur at the reference value of 99.975 ° C, absolute zero is equal to 0. On the Fahrenheit scale the indicator corresponds to -459.67 degrees.

But, if these data are obtained, why then is it impossible to achieve absolute zero temperatures in practice? For comparison, we can take the well-known speed of light, which is equal to the constant physical value of 1,079,252,848.8 km/h.

However, this value cannot be achieved in practice. It depends on the transmission wavelength, the conditions, and the required absorption of a large amount of energy by the particles. To obtain the value of absolute zero temperatures, a large output of energy is required and the absence of its sources to prevent it from entering atoms and molecules.

But even in conditions of complete vacuum, scientists were unable to obtain either the speed of light or absolute zero temperatures.

Why is it possible to reach approximately zero temperatures, but not absolute zero?

What will happen when science can come close to achieving the extremely low temperature of absolute zero remains only in the theory of thermodynamics and quantum physics. What is the reason why absolute zero temperatures cannot be achieved in practice.

All known attempts to cool a substance to the lowest limit due to maximum energy loss led to the fact that the heat capacity of the substance also reached a minimum value. The molecules were simply no longer able to give up the remaining energy. As a result, the cooling process stopped without reaching absolute zero.

When studying the behavior of metals under conditions close to absolute zero temperatures, scientists found that a maximum decrease in temperature should provoke a loss of resistance.

But the cessation of the movement of atoms and molecules only led to the formation of a crystal lattice, through which passing electrons transferred part of their energy to stationary atoms. Again, it was not possible to reach absolute zero.

In 2003, the temperature was only half a billionth of 1°C short of absolute zero. NASA researchers used a Na molecule to conduct experiments, which was always in a magnetic field and gave up its energy.

The closest achievement was achieved by scientists at Yale University, who in 2014 achieved a figure of 0.0025 Kelvin. The resulting compound, strontium monofluoride (SrF), lasted only 2.5 seconds. And in the end it still disintegrated into atoms.

Absolute zero corresponds to a temperature of −273.15 °C.

It is believed that absolute zero is unattainable in practice. Its existence and position on the temperature scale follows from extrapolation of observed physical phenomena, and such extrapolation shows that at absolute zero the energy of thermal motion of molecules and atoms of a substance should be equal to zero, that is, the chaotic movement of particles stops, and they form an ordered structure, occupying clear position in the nodes of the crystal lattice. However, in fact, even at absolute zero temperature, the regular movements of the particles that make up matter will remain. The remaining oscillations, such as zero-point oscillations, are due to the quantum properties of the particles and the physical vacuum that surrounds them.

At present, in physical laboratories it has been possible to obtain temperatures exceeding absolute zero by only a few millionths of a degree; to achieve it itself, according to the laws of thermodynamics, is impossible.

Notes

Literature

G. Burmin. Assault on absolute zero. - M.: “Children’s Literature”, 1983.