When the weather report predicts temperatures around zero, you should not go to the skating rink: the ice will melt. The melting temperature of ice is taken as zero degrees Celsius - the most common temperature scale.
We are well aware of the negative degrees of the Celsius scale - degrees<ниже нуля>, degrees of cold. The lowest temperature on Earth was recorded in Antarctica: -88.3°C. Outside the Earth, even lower temperatures are possible: on the surface of the Moon at lunar midnight it can reach -160°C.
But nowhere can there be arbitrarily low temperatures. Extremely low temperature - absolute zero - on the Celsius scale corresponds to - 273.16 °.
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 limit of cold?
Heat is the chaotic movement of atoms and molecules of matter. When a substance is cooled, thermal energy is taken away from it, and in this case, the random movement of particles weakens. In the end, with strong cooling, thermal<пляска>particles almost completely stops. Atoms and molecules would freeze completely at a temperature that is taken as absolute zero. According to the principles of quantum mechanics, at absolute zero, it is precisely the thermal motion of particles that would stop, but the particles themselves would not freeze, since they cannot be completely at rest. Thus, at absolute zero, the particles must still retain some kind of motion, which is called zero.

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 reaching exact absolute zero is also almost impossible. You can only get closer to him. Because absolutely all of its thermal energy cannot be taken away from a substance by any means. Some of the thermal energy remains during the deepest cooling.
How do they reach ultra-low temperatures?
Freezing a substance is more difficult than heating it. This can be seen at least from a comparison of the design of the stove and refrigerator.
In most domestic 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 refrigerating chamber, 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, making up for the loss of evaporating freon. Energy is used to run the compressor.
In deep-cooling devices, the carrier of cold is a supercold liquid - liquid helium. Colorless, light (8 times lighter than water), it boils under atmospheric pressure at 4.2°K, and in vacuum at 0.7°K. An even lower temperature is given by the light isotope of helium: 0.3°K.
It is quite difficult to arrange a permanent helium refrigerator. Research is carried out simply in liquid helium baths. And to liquefy this gas, physicists use different techniques. For example, pre-cooled and compressed helium is expanded by releasing it through a thin hole into a vacuum chamber. At the same time, the temperature still decreases and some part of the gas turns into a liquid. It is more efficient not only to expand the cooled gas, but also to make it do work - to move the piston.
The resulting liquid helium is stored in special thermoses - Dewar vessels. The cost of this coldest liquid (the only one that does not freeze at absolute zero) is quite high. Nevertheless, liquid helium is now being used more and more widely, 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, such as potassium chromium alum, can rotate along magnetic lines of force. This salt is preliminarily 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 sharply removed, the molecules again turn in different directions, and the spent

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

Superfluidity

Substance frozen to ultra-low temperatures in liquid helium baths changes markedly. Rubber becomes brittle, lead becomes hard as steel and resilient, 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 without any friction through the narrowest slots.
This phenomenon, discovered in 1937 by the Soviet physicist Academician P. JI. Kapitsa, was then explained by Academician JI. D. Landau.
It turns out that at ultralow temperatures, the quantum laws of the behavior of matter begin to noticeably affect. As one of these laws requires, energy can be transferred from body to body only in quite definite portions-quanta. There are so few heat quanta in liquid helium that there are not enough of them for all atoms. Part of the liquid, devoid of heat quanta, remains at absolute zero temperature, its atoms do not participate in random thermal motion at all and do not interact with the vessel walls in any way. This part (it was called helium-H) possesses superfluidity. With decreasing temperature, helium-II becomes more and more, 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 curious changes occur in the electrical properties of certain materials.
In 1911, the Dutch physicist Kamerling-Onnes made an unexpected discovery: it turned out that at a temperature of 4.12 ° K, electrical resistance completely disappears in mercury. Mercury becomes a superconductor. The electric current induced in the superconducting ring does not decay and can flow almost forever.
Above such a ring, a superconducting ball will float in the air and not fall, as if from a fairy tale.<гроб Магомета>, because its heaviness is compensated by the magnetic repulsion between the ring and the ball. After all, the undamped current in the ring will create a magnetic field, and it, in turn, will induce an electric current in the ball and, along 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 over a hundred different alloys and other chemical compounds.
The temperatures at which superconductivity appears (critical temperatures) are in a fairly wide range, from 0.35°K (hafnium) to 18°K (niobium-tin alloy).
The phenomenon of superconductivity, as well as super-
fluidity, studied in detail. The dependences of critical temperatures on the internal structure of materials and the external magnetic field are 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 connected particles that cannot give energy to the crystal lattice, spend energy quanta to heat it. Pairs of electrons move like<танцуя>, between<прутьями решетки>- ions and bypass them without collisions and energy transfer.
Superconductivity is increasingly being used in technology.
For example, superconducting solenoids are coming into practice - superconductor coils immersed in liquid helium. Once induced current and, consequently, the magnetic field can be stored in them for an arbitrarily long time. It can reach a gigantic value - over 100,000 oersted. In the future, powerful industrial superconducting devices will undoubtedly appear - electric motors, electromagnets, etc.
In radio electronics, supersensitive amplifiers and generators of electromagnetic waves begin to play a significant role, which work especially well in baths with liquid helium - there the internal<шумы>equipment. In electronic computing technology, a bright 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 to higher, more accessible temperatures. Recently, the hope of creating polymer film superconductors has been opened up. 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 bowels of the stars. Where temperatures reach millions of degrees.
The chaotic thermal motion in stars is so intense that whole atoms cannot exist there: they are destroyed in countless collisions.
Therefore, a substance so strongly heated cannot be either solid, liquid, or gaseous. It is in the state of plasma, i.e., a mixture of electrically charged<осколков>atoms - atomic nuclei and electrons.
Plasma is a kind of state of matter. Since its particles are electrically charged, they sensitively obey electric 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. 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 up to 10 million degrees. Under such conditions, close encounters of fast hydrogen nuclei - protons, though rare, do happen. Sometimes approaching protons interact: having overcome electrical repulsion, they fall into the power of giant nuclear forces of attraction, rapidly<падают>each other and merge. Here an instantaneous rearrangement occurs: instead of two protons, a deuteron (the nucleus of a heavy isotope of hydrogen), 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 in 14 billion years. But there are so many protons in the bowels of the luminary that here and there this unlikely event takes place - and our star burns with its even, dazzling flame.
The synthesis of deuterons is only the first step in solar thermonuclear transformations. The newborn deuteron very soon (on average after 5.7 seconds) combines with one more proton. There is a core of light helium and a gamma quantum of electromagnetic radiation. 5.48 MeV of energy is released.
Finally, on average, once every million years, two nuclei of light helium can converge and fuse. Then an ordinary helium nucleus (alpha particle) is formed and two protons are split off. 12.85 MeV of energy is released.
This three-stage<конвейер>thermonuclear reactions is 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 cases, alpha particles are synthesized from hydrogen nuclei. Figuratively speaking, the solar hydrogen plasma<сгорает>, turning into<золу>- helium plasma. And in the process of synthesis of each gram of helium plasma, 175 thousand kWh of energy are released. Great amount!
Every second, the Sun radiates 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, due to the emission of 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 seems to be the main source of energy for all stars. At different temperatures and densities of stellar interiors, different types of reactions take place. In particular, solar<зола>- helium nuclei - at 100 million degrees it becomes thermonuclear itself<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>).

To the artificial sun

The extraordinary calorie content of thermonuclear<горючего>prompted scientists to seek artificial implementation of nuclear fusion reactions.
<Горючего>There are many isotopes of hydrogen on our planet. For example, superheavy hydrogen tritium can be obtained from lithium metal 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 provide as much energy in a fusion reactor as burning a barrel of premium gasoline now provides.
The difficulty lies in preheating<горючее>to temperatures at which it can ignite with mighty thermonuclear fire.
This problem was first solved in the hydrogen bomb. Hydrogen isotopes there are set on fire by the explosion of an atomic bomb, which is accompanied by heating of the substance to many tens of millions of degrees. In one version of the hydrogen bomb, the thermonuclear fuel is a chemical compound of heavy hydrogen with light lithium - deuteride of light l and t and i. This white powder, similar to table salt,<воспламеняясь>from<спички>, which is the atomic bomb, instantly explodes and creates a temperature of hundreds of millions of degrees.
In order to initiate a peaceful thermonuclear reaction, one must first of all learn how, without the services of an atomic bomb, to heat up small doses of a sufficiently dense plasma of hydrogen isotopes to temperatures of hundreds of millions of degrees. This problem is one of the most difficult in modern applied physics. Scientists from all over the world have been working on it for many years.
We have already said that it is the chaotic motion of particles that creates the heating of bodies, and the average energy of their random motion corresponds to the temperature. To heat up a cold body means to create this disorder in any way.
Imagine that two groups of runners are rapidly rushing towards each other. So they collided, mixed up, a crowd began, confusion. Great mess!
Approximately in the same way, physicists at first tried to obtain a high temperature - by pushing high-pressure gas jets. The gas was heated up to 10 thousand degrees. At one time it was a record: the temperature is higher than on the surface of the Sun.
But with this method, further, rather slow, non-explosive heating of the gas is impossible, since 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 the 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, the hot plasma immediately cools down. On the other hand, one can try to hold and heat up the plasma by creating its accumulation in a vacuum so that it does not touch the walls of the chamber, but hangs in the void, without touching anything. Here one should take advantage of the fact that plasma particles are not neutral, like gas atoms, but electrically charged. Therefore, in motion, they are subject to the action of magnetic forces. The problem arises: to arrange a magnetic field of a special configuration in which the hot plasma would hang like in a bag with invisible walls.
The simplest form of such an electric field is created automatically when strong electric current pulses are passed through the plasma. In this case, magnetic forces are induced around the plasma filament, which tend to compress the filament. The plasma separates from the walls of the discharge tube, and the temperature rises to 2 million degrees near the axis of the filament in a rush of particles.
In our country, such experiments were carried out as early as 1950 under the guidance 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 corktron - a cylindrical vacuum chamber equipped with an external winding, which thickens at the ends of the chamber. The current flowing through the winding creates a magnetic field in the chamber. Its lines of force in the middle part are 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 lines of force and are reflected from the corks. As a result, the plasma is kept 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 motion becomes entangled, becomes disordered - the temperature of hydrogen nuclei rises to tens of millions of degrees.
Additional heating is achieved by electromagnetic<ударами>by plasma, magnetic field compression, 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 a low plasma density.
To excite a self-sustaining reaction, it is necessary to further increase the temperature and density of the plasma. This is difficult to achieve. However, the problem, as scientists are convinced, is undeniably solvable.

G.B. Anfilov

Posting photos and citing articles from our site on other resources is permitted provided that a link to the source and photos is provided.

Have you ever thought about how cold the temperature can be? What is absolute zero? Will humanity ever be able to achieve it and what opportunities will open up after such a discovery? These and other similar questions have long occupied the minds of many physicists and simply inquisitive people.

What is absolute zero

Even if you didn’t like physics since childhood, you probably know the concept of temperature. Thanks to the molecular kinetic theory, we now know that there is a certain static connection between it and the movements of molecules and atoms: the higher the temperature of any physical body, the faster its atoms move, and vice versa. The question arises: "Is there such a lower limit at which elementary particles will freeze in place?". Scientists believe that this is theoretically possible, the thermometer will be at around -273.15 degrees Celsius. This value is called absolute zero. In other words, this is the minimum possible limit to which a physical body can be cooled. There is even an absolute temperature scale (the Kelvin scale), in which absolute zero is the reference point, and the unit division of the scale is equal to one degree. Scientists around the world do not stop working to achieve this value, as this promises great prospects for mankind.

Why is it so important

Extremely low and extremely high temperatures are closely related to the concept of superfluidity and superconductivity. The disappearance of electrical resistance in superconductors will make it possible to achieve unthinkable values ​​of efficiency and eliminate any energy losses. If it were possible to find a way that would allow one to freely reach the value of "absolute zero", many of the problems of mankind would be solved. Trains hovering over the tracks, lighter and smaller engines, transformers and generators, high-precision magnetoencephalography, high-precision clocks are just a few examples of what superconductivity can bring to our lives.

Latest scientific achievements

In September 2003, researchers from MIT and NASA managed to cool sodium gas to an all-time low. During the experiment, they were only half a billionth of a degree short of the finish line (absolute zero). During the tests, sodium was always in a magnetic field, which kept it from touching the walls of the container. If it were possible to overcome the temperature barrier, the molecular movement in the gas would completely stop, because such cooling would extract all the energy from sodium. The researchers applied a technique whose author (Wolfgang Ketterle) received the Nobel Prize in Physics in 2001. The key point in the tests carried out were the gaseous Bose-Einstein condensation processes. Meanwhile, no one has yet canceled the third law of thermodynamics, according to which absolute zero is not only an insurmountable, but also an unattainable value. In addition, the Heisenberg uncertainty principle applies, and atoms simply cannot stop dead in their tracks. Thus, for the time being, the absolute zero temperature for science remains unattainable, although scientists have been able to approach it at a negligibly small distance.

The term "temperature" appeared at a time when physicists thought that warm bodies consist of a larger amount of a specific substance - caloric - than the same bodies, but cold ones. And the temperature was interpreted as a value corresponding to the amount of caloric in the body. Since then, the temperature of any body is measured in degrees. But in reality it is a measure of the kinetic energy of moving molecules, and, based on this, it should be measured in Joules, in accordance with the SI system of units.

The concept of "absolute zero temperature" comes from the second law of thermodynamics. According to it, the process of transferring heat from a cold body to a hot one is impossible. This concept was introduced by the English physicist W. Thomson. For achievements in physics, he was granted the noble title of "Lord" and the title of "Baron Kelvin". In 1848, W. Thomson (Kelvin) suggested using a temperature scale, in which he took the absolute zero temperature corresponding to the extreme cold as the starting point, and took degrees Celsius as the division price. The unit of Kelvin is 1/27316 of the temperature of the triple point of water (about 0 degrees C), i.e. the temperature at which pure water exists in three forms at once: ice, liquid water, and steam. temperature is the lowest possible low temperature at which the movement of molecules stops, and it is no longer possible to extract thermal energy from the substance. Since then, the absolute temperature scale has been named after him.

Temperature is measured on different scales

The most commonly used temperature scale is called the Celsius scale. It is built on two points: on the temperature of the phase transition of water from liquid to vapor and water to ice. A. Celsius in 1742 proposed to divide the distance between reference points into 100 intervals, and take water as zero, while the freezing point is 100 degrees. But the Swede K. Linnaeus suggested doing the opposite. Since then, water freezes at zero degrees A. Celsius. Although it should boil exactly in Celsius. Absolute zero in Celsius corresponds to minus 273.16 degrees Celsius.

There are several more temperature scales: Fahrenheit, Réaumur, Rankine, Newton, Roemer. They have different and price divisions. For example, the Réaumur scale is also built on the benchmarks of boiling and freezing of water, but it has 80 divisions. The Fahrenheit scale, which appeared in 1724, is used in everyday life only in some countries of the world, including the USA; one is the temperature of the mixture of water ice - ammonia and the other is the temperature of the human body. The scale is divided into one hundred divisions. Zero Celsius corresponds to 32 The conversion of degrees to Fahrenheit can be done using the formula: F \u003d 1.8 C + 32. Reverse translation: C \u003d (F - 32) / 1.8, where: F - degrees Fahrenheit, C - degrees Celsius. If you are too lazy to count, go to the online Celsius to Fahrenheit conversion service. In the box, type the number of degrees Celsius, click "Calculate", select "Fahrenheit" and click "Start". The result will appear immediately.

Named after the English (more precisely Scottish) physicist William J. Rankin, a former contemporary of Kelvin and one of the founders of technical thermodynamics. There are three important points in his scale: the beginning is absolute zero, the freezing point of water is 491.67 degrees Rankine and the boiling point of water is 671.67 degrees. The number of divisions between the freezing of water and its boiling in both Rankine and Fahrenheit is 180.

Most of these scales are used exclusively by physicists. And 40% of American high school students surveyed these days said they don't know what absolute zero temperature is.

The physical concept of "absolute zero temperature" is very important for modern science: such a concept as superconductivity, the discovery of which made a splash in the second half of the 20th century, is closely related to it.

To understand what absolute zero is, one should refer to the works of such famous physicists as G. Fahrenheit, A. Celsius, J. Gay-Lussac and W. Thomson. It was they who played a key role in the creation of the main temperature scales still used today.

The first to offer his own temperature scale in 1714 was the German physicist G. Fahrenheit. At the same time, the temperature of the mixture, which included snow and ammonia, was taken as absolute zero, that is, the lowest point on this scale. The next important indicator was which began to equal 1000. Accordingly, each division of this scale was called the “degree Fahrenheit”, and the scale itself was called the “Fahrenheit scale”.

After 30 years, the Swedish astronomer A. Celsius proposed his own temperature scale, where the main points were the melting temperature of ice and water. This scale was called the "Celsius scale", it is still popular in most countries of the world, including Russia.

In 1802, while conducting his famous experiments, the French scientist J. Gay-Lussac discovered that the volume of a mass of gas at constant pressure is directly dependent on temperature. But the most curious thing was that when the temperature changed by 10 Celsius, the volume of the gas increased or decreased by the same amount. Having made the necessary calculations, Gay-Lussac found that this value was equal to 1/273 of the volume of gas at a temperature equal to 0C.

The obvious conclusion followed from this law: the temperature equal to -2730C is the lowest temperature, even approaching which it is impossible to reach it. This temperature is called "absolute zero temperature".

Moreover, absolute zero became the starting point for creating the absolute temperature scale, in which the English physicist W. Thomson, also known as Lord Kelvin, took an active part.

His main research concerned the proof that no body in nature can be cooled below absolute zero. At the same time, he actively used the second one, therefore, the absolute temperature scale introduced by him in 1848 became known as the thermodynamic or "Kelvin scale".

In subsequent years and decades, only a numerical refinement of the concept of "absolute zero" took place, which, after numerous agreements, began to be considered equal to -273.150C.

It is also worth noting that absolute zero plays a very important role in the whole fact that in 1960 at the next General Conference on Weights and Measures, the unit of thermodynamic temperature - kelvin - became one of the six basic units of measurement. At the same time, it was specifically stipulated that one degree Kelvin is numerically equal to one, only here the reference point “according to Kelvin” is considered to be absolute zero, that is, -273.150С.

The main physical meaning of absolute zero is that, according to the basic physical laws, at such a temperature, the energy of motion of elementary particles, such as atoms and molecules, is equal to zero, and in this case, any chaotic motion of these same particles should stop. At a temperature equal to absolute zero, atoms and molecules should take a clear position in the main points of the crystal lattice, forming an ordered system.

Currently, using special equipment, scientists have been able to obtain a temperature only a few millionths higher than absolute zero. It is physically impossible to achieve this value itself because of the second law of thermodynamics described above.

Absolute zero temperature

The limiting temperature at which the volume of an ideal gas becomes 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) to zero and taking into account that

.

Hence the absolute zero temperature is

t= -273 °С. 2

This is the limiting, 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 - were obtained during the explosions of thermonuclear bombs. Even higher temperatures are characteristic of the inner regions of some stars.

2A more accurate value for 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 degrees Celsius, so the absolute temperature T is related to temperature on the Celsius scale by the formula

T = t + 273. (3.2)

On 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 Celsius equals one degree Kelvin:

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

Reader: What is the physical meaning of absolute temperature?

We write expression (3.1) in the form

.

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

where T 0 = 273 K, or

Since this relation is valid for an arbitrary temperature T, then the Gay-Lussac law can be formulated as follows:

For a given mass of gas at p = const, the relation

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.

Task 3.2. With isobaric heating, the volume of air increased by 1%. By what percent did the absolute temperature increase?

= 0,01.

Answer: 1 %.

Remember the resulting formula

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

Charles' law

The French scientist Charles experimentally found that if you heat a gas so that its volume remains constant, then 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) is pressure at temperature t°C; R 0 – pressure at 0 °С; 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, keeping the pressure of the gas constant, we heat it to a temperature T one . Then the gas will have volume V 1 = V 0 (1 + a t) and pressure R 0 .

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

Since the gas temperature is the same in both cases, 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 there is nothing surprising in the fact that a = b, no!

Let us rewrite Charles's law in the form

.

Given that T = t°С + 273 °С, T 0 \u003d 273 ° С, we get