It seems that under the influx of heat, some of them will speed up their chaotic rumble. If you heat up a gas, then the molecules that make up yoga simply fly apart one after the other. Heated the heart of the cob sprouts in volume, and then boils. And what will be from hard bodies? Not the skin of them can change their aggregate camp.

Thermal expansion: custom

Thermal expansion - the price of change of expansion and form of heating for temperature change. Mathematically, you can change the volume expansion coefficient, which allows you to predict the behavior of gas and air in the old minds that change. To take the same results for solid body, it is necessary to be safe Physicists have seen a number of studies for such studies and called yoga dilatometry.

Engineers and architects need to know about the behavior of various materials under the influence of high and low temperatures for designing buds, laying roads and pipes.

Gas expansion

Thermal expansion of gas is accompanied by expansion of their space. The philosophers-naturalists commemorated even a long time ago, but only the modern physicists were able to inspire mathematical developments.

For us, in front of the church, the expansion of the wind began to click, the shards were given to them feasible tasks. The stench of the flooring took up to the right, that they tried to achieve superb results. Obviously, such a result of the science of svіvtovaristvo is not satisfied. The accuracy of the world depended on the fact that the thermometer was victorious, on the strength of the richness of other minds. Deyakі fіzikі navіt dіyshli dumіki, scho expansion gazіv deposit vіd zmіni temperature. But staleness is not true ...

Roboty Dalton and Gay-Lussac

The physicists would continue to fight until they were hoarse, or they would throw down vimir, if not Vin, and another physicist, Gay-Lussac, at the same time, one at a time, one could take the same results of the victory.

Lussac tried to find out the reason for such a large number of different results and mentioned that some of the accessories had water at the moment. Naturally, during the process of heating, the won turned into a couple and changed the quantity and storage of additional gases. First of all, having worked out the exercises, - seriously hanging all the instruments, like a victorist for the experiment, and turning on the minimum amount of water from the last gas. After all these manipulations of the first few years, they turned out to be reliable.

Dalton took care of his meals for his colleague and published the results at the very beginning of the 19th century. Vіn vysushuvav povіtrya vapours of sulfuric acid, and heating yoga. Following the series, John Dyishov added that all gas bets are expanded by a factor of 0.376. Lussac had a number of 0.375. Tse became the official result of the follow-up.

Spring of water vapor

Thermal expansion of gases to be deposited in the spring, so that the buildings turn around the outlets. Ziegler became the first chain to reach the middle of the eighteenth century. Ale, the results of yogo doslidіv nadto differed. More reliable numbers high temperatures tatovy cauldron, and for low ones - a barometer.

For example, the French physicist of the 18th century tried to come up with a single formula, as if it would describe the springiness of gases, but it turned out to be rather cumbersome and foldable in vikoristanni. Dalton crossed all the roses with the help of his way, victorious with the help of a siphon barometer. Regardless of those who did not have the same temperature in all cases, the results turned out to be even more accurate. To that, I published them in the tables I looked at with my assistant in physics.

Theory of vaporization

Thermal expansion of gases (as a physical theory) recognized various changes. Vcheni namagalisya dіstatisya sutі protsesіv, yakah go steam. Here, the physicist Dalton was again assigned to us. Vіn vysloviv hypothesis, scho be-any expanse of gas vapors independently, depending on whether there is another gas or steam in this reservoir (imprisonment). Otzhe, it is possible to grow visnovok, so that the homeland does not evaporate, just entering the dotik with atmospheric influences.

The pressure of stepping again on the surface of the countryside is greater expanse between atoms, inspiring them one by one and viparating them, so that they make a bet. But on the molecules of the steam, the force of gravity continues to work, so it was taken into account that the atmospheric pressure does not in any way affect the vaporization of the waters.

RIDIN extension

The thermal expansion of the rivers was carried out in parallel with the expansion of gases. Scientific studies were carried out by your own scientists. For this stench, thermometers, aerometers, obtained judges and other instruments were victorious.

All the while, they uttered the theory of Dalton in the same time in the skin, in that, which uniform rods expand in proportion to the square of the temperature, like they are heated. Naturally, the higher the temperature, the more common the land, but there was no direct fallow between them. That swidkіst expansion in all the rіdins was different.

The thermal expansion of the water, for example, starts from zero degrees Celsius and continues with a decrease in temperature. Previously, such results have shown that it is not the water itself that expands, but the capacity sounds, de won't be known. But a few hours later, the physicist Delyuk still came to the conclusion that the reason for the trace was in the motherland itself. Vіn vyrіshiv know the temperature of the largest thicket. However, youmu did not get away through the lack of details. Rumfort, who was busy with wrapping this image, having established that the maximum thickness of the water is guarded in the range of 4 to 5 degrees Celsius.

Thermal expansion tіl

In solid bodies, the main mechanism of expansion is the change in the amplitude of the crystallization of crystal ridges. Yakscho say in simple words, That atom, which enters the warehouse of the material and zhorstko zcheplenі between itself, mend "tremtіti".

The law of thermal expansion tіl formulations is as follows: be it tilo with a linear expansion L in the process of heating by dT (delta T - difference between the cob temperature and end temperature), expand by the value dL (delta L - the same coefficient of the linear thermal expansion per dozhina ob' єkta and on the temperature difference). This is the simplest version of this law, which is beyond the mind of the guardian, which will expand one by one on all sides. Ale for practical work vikoristovuyut where more cumbersome calculations, shards of true materials lead to negligence, as modeled by physicists and mathematicians.

Thermal expansion rails

For the laying of the curtain wall, engineers-physicists are always employed, the stinks of stink can be accurately counted, as if it were to blame but between the sticks of the rails, so that when heated or cooled, they did not deform.

As it was appointed more, the thermal expansion of the linear expansion of all solid bodies. The 1st rail did not become a vine. Ale, one detail. A linear change is freely seen in that fall, as if the strength of the rubbing does not pour into the body. The slats are zhorstko attached to the sleepers and fastened with slatted slats, this is the law that describes the change of the dozhina, the vrahovu podlannya reshkod at the sight of the running tactic supports.

If the rail cannot change its length, then due to the change in temperature in it, the increase in thermal stress, if you can stretch it, then squeeze it. This phenomenon is described by Hooke's law.

Apparently, when heated, solid bodies increase their contraction. Tse - thermal expansion. Let's look at the reasons why to increase the volume of the body under the hour of heating.

It is obvious that the crystal grows due to the increase in the average size between atoms. Later, the increase in temperature and thrust in itself is an increase in the average distance between the atoms of the crystal. What is the reason for the increase in the number of atoms between atoms during heating?

An increase in the temperature of the crystal means an increase in the energy of the thermal rush, so that the thermal fusion of atoms at the walls (div. page 459), and also, an increase in the amplitude of the fusion.

And to increase the amplitude of the splitting of atoms, it is necessary to bring them up to an increase in the average age of them.

As if the atoms were suvoro Harmonic, then the skin atom of the flooring would approach one of its own susides, moving further away from the other, and the increase in the amplitude of the second coliva would not lead to a change in the middle dstanі, and later, і to thermal expansion.

Indeed, the atoms in the crystal solution are anharmonic (that is not harmonic) colivan. This is determined by the nature of the staleness of the forces of interrelationship between atoms in the middle of them. As it was assigned to the cob of the head of the chapter (div. Fig. 152 and 153), the fallowness is such that, with great distances between atoms, the forces between atoms appear like gravity, and with a change in numbers, the forces change your sign and become the forces of vіdshtovhuvannya, shvidko growing from changes in the country.

It is worth bringing it to the point that with an increase in the "amplitude" of the atoms' cleavage after heating the crystal, the increase in the forces of penetration between atoms outweighs the increase in the forces of gravity. It seems otherwise, it is “easier” for the atom to drink in the presence of a susida, to come closer to another. This, obviously, can lead to an increase in the average age between atoms, so that an increase in the contraction of the body during its heating.

Zvіdsi viplivaє, scho the reason for the thermal expansion of solid bodies is the anharmonicity of the splitting of atoms in the crystal solution.

The quantity of thermal expansion is characterized by the coefficients of linear and volumetric expansion, which are assigned in such a way. Give your body a longevity I when changing the temperature by degrees, change your longevity by a linear expansion coefficient

so that the coefficient of linear expansion is more effective when the temperature changes by one degree. So the very coefficient of the volume expansion is determined by the formula

so the coefficient of the cost of the change is up to one degree. then the coefficient of volumetric expansion of the crystal

For crystals with cubic symmetry, like for isotropic solids,

The spool, made from such bodies, is filled with a sack and after heating (it seems to be of a larger diameter).

For some crystals (for example, hexagonal)

The coefficients of linear and volumetric expansion are practically littered with constant ones, as the temperature intervals, in which stinks are vitiated, are small, and the temperatures themselves are high. The coefficients of thermal expansion have increased depending on the temperature and, moreover, it is the same as the heat capacity, so that at low temperatures the coefficient changes with the decrease in temperature in proportion to the cube of the temperature, pragnuchi, like the heat capacity,

to zero for absolute zero. It’s not surprising, because it’s the heat capacity, and the thermal expansion of the coating with the grate’s cracks: the heat capacity gives the amount of heat necessary for increasing the average energy of the thermal colivans of atoms, which should be deposited in the amplitude of the coliving, coffe cent of thermal expansion without intermediary overlaps from the middle distances between atoms, yakі tezh lie in the amplitude of atomic coliving

There is an important law, according to Gruneisen: the change of the coefficient of thermal expansion to the atomic heat capacity of a solid body for this speech is a constant value (so that it does not lie in the temperature).

The coefficients of thermal expansion of solid bodies sound even smaller, as can be seen from the table. 22. Indicated in this table the value of the coefficient a can be seen up to the temperature interval between and

Table 22 (div. scan) Coefficient of thermal expansion of solid bodies

Deyakі speechovina may have a particularly low coefficient of thermal expansion. Such power, for example, quartz The colors of the speech took a wide zastosuvannya in the exact application.

If you heat the body, then the number of atoms (molecules) will be intense. The stench of rozshtovhuvatimut one of one and take more space. This fact is well explained: when solids are heated, rіdkі and gas-like bodies expand.

About the thermal expansion of gases for a long time not to be brought up: even the proportionality of temperature to gas was taken as the basis of our temperature scale.

Z formula V \u003d V 0 / 273 * T bachimo, scho gas at a constant pressure growth when heated at 1 0 C by 1 / 273 part (tobto by 0.0037) yogo volume at 0 ° C (these positions can be called Gay-Lussac law).

In savvy minds, then at room temperature and normal atmospheric pressure, the expansion of the greater number of gases is two or three less than the expansion of gases.

We already repeatedly spoke about the originality of the expansion of the water. When heated from 0 to 4 ° C, the volume of water changes with heating. This special feature of the expanded water plays a colossal role of life on Earth. In the autumn in the world of cooling, the upper balls, which are chilled, become thinner and sink to the bottom. There is warm water on their bottom. Ale, such a shift is less likely to be quiet until the temperature of the water drops to 4 ° C. With a further drop in temperature, the upper balls no longer squash, therefore, they do not become important and do not sink to the bottom. Starting with the temperature, the upper ball, gradually cooling down, reaches zero degrees and freezes.

Only the peculiarity of the water and the freezing of the river to the bottom. Yakby water raptom has lost its miraculous peculiarity, to inspire for modest fantasies it is easy to reveal one's own grave traces of it.

Thermal expansion of solid bodies is less, lower thermal expansion is equal. It is hundreds and thousands of times less than the expansion of gases.

In bagatioh vipadkah thermal expansion є I will cover with a shroud. So, changing the roaming parts of the annual mechanism with a change in temperature would have led to a change in the course of the year, yakby for these fine details did not stagnate a special alloy-invar (invariant in the translation means immutable, stars and the name "invar"). Іnvar - steel with a large amount of nickel - is widely stagnated in the priladobduvanni. Shearing from January will be more than a millionth part of its life for a change in temperature by 1 ° C.

Insignificantly, it would seem, thermal expansion of solid bodies can lead to serious consequences. On the right, in that it is not easy to cause the thermal expansion of solid bodies through their small stiffness.

When a steel shear is heated at 1°C, the length of the dozhina grows by more than a hundred hundred thousand, that is, by an unfathomable amount. However, in order to expand the expansion and squeeze the haircut by one hundred thousandth, a force of 20 kgf per 1 cm 2 is required. І t_lki in order to reduce the temperature increase by more than 1 0 С!

Spiral forces, which are caused by thermal expansion, can lead to breakdowns and catastrophes, even if they are not called. So, in order to overcome these forces, the slats of the slats are laid out of the gaps. About qі forces to be brought to mind when prompted by glassy dishes, which easily crack when heated unevenly. In laboratory practice, this is cured with a small amount of dishes from a quartz warehouse (melting quartz - silicon oxide, which is found in an amorphous steel). With the same heating, the copper bar will move down by a millimeter, and such a bar of quartz rock will change its depth by an incomprehensible value of 30-40 microns. The expansion of quartz flooring is scanty, so a quartz vessel can be heated to hundreds of degrees, and then, without fear, throw Yogo into cold water.

Tsya dominion is characteristic of all speeches. If the speech is heated, the particles begin to collapse intensively, which will lead to an increase in the average age between them.

The greater the tіl zbіlshhuyut svіy vіy єm at the result of the increase in temperature, prote vіdomo sprouts of vinyatkіv. The most common butts of the rule are water, yak in the range of 0? C to 4? C changes its contact at elevated temperatures or pure silicon at temperatures between -255? C i -153? C.

The division of metrology, which increases its power, is called a dilatometer, and the device for determining the parameters of thermal expansion is called a dilatometer.

The stage of expansion of the speech is brought to the change in temperature is called the coefficient of thermal expansion, which in general lies in the temperature.

1. Coefficient of volumetric thermal expansion (hot drop)

In the case of a hot gas, or a solid body, the coefficient of volumetric thermal expansion may look

Index p means that the press is overstayed by the current expansion hour, and the index V blatantly, what about the (not linear) expansion. In times of gas, the fact of becoming a vice is important, shards of gas can be deposited in a vice, as well as temperature. For gases of small size, the deposit is described as equal to the ideal gas.

2. Thermal expansion of solid bodies

2.1. Linear thermal expansion

p align="justify"> The coefficient of linear thermal expansion is set as a change in the linear expansion of the material to a change in temperature. Otzhe, tse vіdnosna zmіna dovzhini gradusіv zmіni temperature. Nehtuyuchy vise, you can write:

de - Linear expansion (for example, dovzhina) and - Change of linear expansion by one temperature change.

visible change in the linear dimension, which can be seen as a visible deformation, can be written:

Tse equal good practice doti, docks vvazhatimuyusya coefficient of linear expansion constant in the temperature range. As a result, the coefficient of linear expansion is changed, equal to the next integration.

2.2. Thermal expansion volume

For solids, you can press the pressure on the material, and the volume coefficient of thermal expansion can be recorded

de - About the material, that intensity of change in the volume of change in temperature.

Tse means that the increase is bound to be a certain fixed proportion. For example, a steel block with a volume of 1 m? can expand up to 1.02 m?, with a temperature increase of 50 K. Ce expansion 2%, or 0.04% per skin K. Since we know the coefficient of thermal expansion, we can expand the value of the volume of the body for changing temperature.

In the examined case, it is important that the coefficient of temperature expansion lie in temperature. For small changes in temperature, it is necessary for close proximity, although it is not always correct. Since the coefficient of volume expansion is constantly changing with temperature, then the same is due to the integration:

here - Pochatkova temperature and the coefficient of volumetric thermal expansion as a function of temperature T.

2.3. Variation of isotropic materials

For isotropic materials, the linear thermal expansion factor should be approximately one third of the volumetric thermal expansion factor.

2.4. Variation of anisotropic materials

Materials with an anisotropic structure, such as crystals or composites, as a rule, may have different coefficients of linear expansion in different straight lines. As a result, the significant expansion of the volume is divided unevenly between the three axes. In such cases, for expansion of thermal expansion, introduce a tensor of the coefficient of thermal expansion, which can contain up to six independent components.

3. Thermal expansion of gases

4. Thermal expansion rіdin

The shards of the countryside do not have good overall dimensions, so the temperature expansion for the countryside is considered in the overall plan:

as a manuscript

Ministry of Education and Science of the Russian Federation

Volgograd State University of Architecture and Life

Department of Physics

THERMAL EXPANSION OF SOLID TIL

Methodical instructions for laboratory work No. 10

Volgograd2013

UDC 537(076.5)

Thermal expansion of solids: Method. vkaz_vka to laboratory work / order. , ; VolgDASA, Volgograd, 20s.

Helpful method laboratory workє vimir coefficient of linear thermal expansion of a solid body. Given the designation of the coefficients of linear and volumetric expansion. The phenomenon of thermal expansion is explained. A description of the vimir method was given. The order of vikonannya roboti is described. The rules of safety engineering have been introduced and control power has been established.

For students of all specialties from the discipline "Physics"

Il. 5. Tab. 2. Bibliogr. 2 titles

© Volgograd State Academy of Architecture and Life, 2002

© Warehouse, 2002

Meta roboti ─ vimir coefficient of linear thermal expansion of a solid body.

Fit That Fit . 1. Metal tube. 2. Electric heating system. 3. Down sensor. 4. Thermocouple. 5. Milivoltmeter (or miliammeter). 6. Laboratory autotransformer (LATR).

1. THEORETICAL ENTRY

All bodies expand during heating, and when cooled, they shrink. For solid bodies, it is not possible to talk about linear expansion. The deposition of a certain temperature is protected during heating of wires on power lines, installed steam pipelines, coupled bridges, laying rails thinly.

To characterize such an extension, we introduce the following designation: - the length of the same body at a temperature of K. Change the length of the body when heated in the same way http://pandia.ru/text/80/058/images/image007_40.gif" width="97" height ="52 src=">

The change in the water temperature rises to a change in temperature, which is called, is called the coefficient of linear thermal expansion:

(1)

With large changes in temperature or high accuracy, it is impossible to keep the coefficient a constant. Vіn zrostaє zі zbіlshennyam temperature i zmenshuєtsya z її zmenshennyam, pragnuch to zero near absolute zero. The value of the coefficients of linear thermal expansion is shown in Table. 1.

Table 1

From the formula (1) we see that the body’s body is at any temperature

(2)

To characterize the volume expansion of the body, the following signs are introduced: i - the volume of the body according to the temperature http://pandia.ru/text/80/058/images/image012_33.gif" when heated on

http://pandia.ru/text/80/058/images/image015_29.gif" width="168" height="52"> (3)

Body volume at a certain temperature

(4)

For solid bodies, Table. 1 introduced only the coefficients of the linear expansion, the fragments between the coefficients of the linear expansion and the volumetric expansion are the same song.

If you take a cube from a given speech with a rib at a temperature (Fig. 1), its volume will increase to a volume when it is heated to a rib, so that the formulas in (2) and (4) can be represented

http://pandia.ru/text/80/058/images/image024_17.gif" width="299 height=28" height="28">

p align="justify"> Coefficient of linear expansion for hard speeches Again, in this case, you can correct the members, which will avenge a2 and a3, as innumerably small higher orders of any number, which will avenge a in the first step. Viide stars

Yakshcho masa tila m when the temperature changes, it is overstayed, then the thickness of the speech is due to the fall in temperature, the shards of volume change with the temperature. T formula http://pandia.ru/text/80/058/images/image030_10.gif" width="239" height="52"> (6)

When rozrahunkah sled vrakhovuvat, scho tables indicate the thickness of speech at 273 K. The thickness for lower temperatures is calculated for such a formula (6).

In certain crystals, when heated, they grow differently in certain lines, in certain lines they do not only grow, but change. Such a phenomenon is called anisotropy.

In solid tіlі atoms zdіysnyuyut teplovі kolivanya schodo vozlіv crystalline ґrat. On fig. 2 shows the two closest atoms, apart r.gif" width="76" height="25 src="> The amplitude of thermal cracking of atoms in solid bodies does not exceed 10% of the equally important difference between atoms (tobto. X- Minimum value). Yakshcho atoms moved from the cob position to X, then the potential energy of their interdependence is healthy

(7)

de Aі b- Positive positive coefficients;

- Minimum value of potential energy.

In fig.

(8)

When the atoms are close together, the force and interaction may change the nature of the explosion. Navpaki, when you are far away, that is, the force that attracts you..gif" width="51" height="23"> r 0 yak equally important vіdstanі. Yakby coefficient b having reached zero, then the potential energy and the force of mutual modality would be seen

(9)

which would give harmony to the atoms. Graph of potential energy in times is a symmetrical curve (Fig. 3, dotted curve). due to the symmetry of the potential curve of the temperature increase, even though it would have led to an increase in the amplitude of the splitting of atoms, but the middle distance between the atoms would have lost its constant. width="59" height="24 src="> to produce thermal expansion of solid bodies.

The thermal expansion of solid bodies in a scatter drop reveals anisotropy. So, for example, a crystal of calcite (CaCO3) expands in one direction when heated (O X) and squeeze into others (Pro At, Pro Z). If you grow from such a crystal, then when you heat it up, it transforms into an ellipsoid.

2. WIMIRYUWAN METHOD

On fig. 5 shows a laboratory setup. The voltage from the LATR is supplied to the electric heating coil, built into the tube, thermal expansion is carried out. One of the ends of the tube is rigidly fastened, the other one is larger and rests against the down sensor. The temperature of the tube is controlled by an additional thermocouple, one of the junctions as reinforcements on the tube. For vimiryuvannya thermoEPS vikoristovuetsya milivoltmeter (or miliammeter).

3. ORDER OF VICONANNY ROBOTI

1. Reverse the connection of the millivoltmeter (or milliammeter) to the “thermocouple” terminal and the autotransformer to the “to LATR” terminal.

2. Calculate the price of a millivoltmeter (or a milliamperemeter) for the distance between the measurements indicated on the floor version of the instruction.

3. Reverse the installed sensor down to zero, sort out in the yogo scale, determine the price down.

4. Take away the call, increase the LATR at the border. Turn the handle of the LATR behind the year arrow until it stops, set the voltage of the electric heating.

5. The heating of the metal tube should be under the pressure, as if it were being controlled by the sensor. The heating temperature of the tube, ventilated according to the room temperature, is controlled by a thermocouple with an additional millivoltmeter and a graduation graph. At the moment, if the increase is more than 0.1 mm, write it down in the table. 2 millivoltmeter readings..gif" width="65" height="23"> mm, turn the LATR handle against the year arrow until it stops and turn the LATR out of the fence.

7. Carry out a measurement of the millivoltmeter reading for the same mm values; 0.5 mm; 0.4mm; 0.3 mm; 0.2 mm, 0.1 mm for cooling mode.

8. Vznachte for the help of the graduation schedule, which is added to the laboratory installation, the value of the heating temperature. for skin value D l like when heated, so when cooled. find the value of the coefficient of linear thermal expansion and enter it in table 2.

10. Stay on the millimeter paper graph of the fallow D l according to temperature DТ.

· Be careful about the hour of work. Unique to the contact in the areas of strumming or blasting.

· Do not overheat the unit.

· In case of inaccuracies, turn to the dismissal or the dismissal of the clerk's laboratory assistant.

· Do not deprive after the robot installation included in the merging.

POWER CONTROLS

1. Give the designation of the coefficient of linear thermal expansion. What is the order of magnitude of which coefficient?

2. Physical change of the coefficient of volumetric thermal expansion. What is the order of magnitude?

3. How is the coefficient of thermal linear expansion and volume expansion related to each other? Enter formula (5).

4. Explain the thermal expansion behind the additional curve of the potential energy of the interaction of atoms.

5. How to deposit the coefficient of thermal expansion of temperature?

6. How to deposit thick solid body during heating?

7. What is called thermal expansion anisotropy?

8. How is the coefficient of linear thermal expansion in this laboratory robot?

bibliographic list

1. Physics course M: Vishcha. school, 1999

2. Physics course / , . M: Vishcha. school, 1999