Change the linear dimensions of the body when heated in proportion to the temperature change.

What is important is that the mixture expands as it heats up. This can be easily explained from the position of the mechanical theory of heat, when fragments of heated molecules or atoms begin to crumble rapidly. U solids Ah, the atoms begin to oscillate with greater amplitude around their middle position in the crystal lattice, and they need more space. Through war the body expands. So the very same gases, larger ones, expand with temperature changes through the increased fluidity of the thermal flow of strong molecules ( div. Boyle-Marriott's Law, Charles's Law, Rivalry of an Ideal Gas).

The basic law of thermal expansion shows that a body has a linear dimension L in the mainland world due to an increase in its temperature by Δ T expands by an amount? L, I'm jealous:

Δ L = αLΔ T

de α — so ranks linear thermal expansion coefficient Similar formulas are used for body size changes, body area and volume. In the simplest case, if the coefficient of thermal expansion does not lie either in temperature or directly in expansion, the liquid will expand evenly in all directions in the same type to the most induced formula.

For engineers, thermal expansion is an important reality in life. By designing a steel bridge across a river in a place with a continental climate, it is impossible not to take into account the possible temperature difference between -40°C and +40°C over time. Such differences necessitate a change in the construction of the bridge up to several meters, and so that the place does not collapse and does not suffer from the pressure of breaking the winter, the designers build the bridge from adjacent sections, 'Eating them special. thermal buffer joints, which are part of the sealed, but not tightly connected, rows of teeth, which sit well in the oven and can diverge widely in the cold. There may be many such buffers on any bridge.

However, not all materials, especially those containing solid crystalline bodies, expand evenly in all directions. And not all materials expand at different temperatures, however. The most beautiful butt of the rest is water. When cold, the water initially contracts, like most rivers. However, starting from +4°C to a freezing point of 0°C, water begins to expand when cooled and contract when heated (from the point of view of the formula we can say that in the temperature range from 0°C to +4°C the thermal coefficient water expansion α acquires a negative meaning). Because of this rare effect, the earth’s seas and oceans do not freeze to the bottom in extreme frosts: water that is colder than +4°C becomes less thick, less warm, and drains to the surface, floating to the bottom at temperatures above +4°C.

That the ice has a thickness lower than the thickness of water is yet another (although related to the first) anomalous power of water, which is essential to the life of the planet. If there was no such effect, the cry would sink to the bottom of rivers, lakes and oceans, and the stench, again, would freeze to the bottom, killing everything alive.

It appears that solids, when heated, increase their strength. Tse - thermal expansion. Let's look at the reasons that lead to an increase in body volume during heating.

Obviously, the size of the crystal grows due to the increase in the average distance between the atoms. Therefore, the increase in temperature increases the average distance between the atoms of the crystal. What causes the increase in distance between atoms when heated?

An increase in the temperature of the crystal means an increase in the energy of the thermal flow, that is, the thermal vibrations of atoms in the planets (division 459), and therefore, an increase in the amplitude of these vibrations.

If the increase in the amplitude of the collision of atoms leads to an increase in the average value between them.

If the vibration of the atoms were extremely harmonic, then the skin atom of the table would approach one of its vessels, as much as it would move away from the other, and an increase in the amplitude of this vibration would not lead to a change in the average from the internuclear stage, and therefore to thermal expansion.

In fact, the atoms in the crystal lattice undergo anharmonic (that is, not harmonious) vibrations. This is due to the nature of the strength of interaction between the atoms in the space between them. As it was indicated on the cob of this head (div. Fig. 152 and 153), its depth is such that with great distances between atoms or interactions between atoms appear as gravity forces, and with a change in value stop changing your sign and become the forces of independence, shvidko growing from changes.

This leads to the fact that with an increase in the “amplitude” of the collision of atoms as a result of the heating of the crystal, the increase in the forces of interaction between the atoms outweighs the increase in the forces of gravity. Otherwise, it seems “easier” for an atom to move from one vessel to another. This, of course, can lead to an increase in the average distance between the atoms, so that the body is heated when it is heated.

It appears that the cause of thermal expansion of solids is the anharmonicity of the collision of atoms at the crystal lattice.

Thermal expansion is highly characterized by the coefficients of linear and volumetric expansion, which are calculated in this way. Let the body live I when the temperature changes by degrees, changes its contribution to the linear expansion coefficient is determined from the relationship

Then the linear expansion coefficient is the same as when changing the temperature by one degree. So the coefficient of volumetric expansion itself is determined by the formula

Then the coefficient of the traditional water change is adjusted to one degree. then the coefficient of volumetric expansion of the crystal

For crystals with cubic symmetry, as well as for isotropic solids,

The core, turned from such bodies, loses its core even after heating (obviously, a larger diameter).

In large crystals (for example, hexagonal)

The coefficients of linear and volumetric expansion are practically not constant, since the temperature intervals in which smells are observed are small, and the temperatures themselves are high. The coefficients of thermal expansion must depend on the temperature and, moreover, just like the heat capacity, so at low temperatures the coefficients change with lower temperatures in proportion to the cube of the temperature, just like the heat capacity,

to zero for absolute zero. This is not surprising, since both heat capacity and thermal expansion are associated with lattice vibrations: heat capacity provides a quantity of heat necessary to increase the average energy of thermal vibrations of atoms, which is stored in the amplifier Here is the kolivan, the coefficient of thermal expansion between the middle connections atoms that may lie within the amplitude of atomic colivans

This shows an important law discovered by Grüneisen: the ratio of the coefficient of thermal expansion to the atomic heat capacity of a solid for a given expression is a constant value (so it does not depend on temperature).

The coefficients of thermal expansion of solids are very small, as can be seen from the table. 22. Enter the coefficient values ​​in this table and bring them to the temperature range between and

Table 22 (div. scan) Thermal expansion coefficients of solids

These types of products have a particularly low thermal expansion coefficient. Such power is used, for example, in quartz. Another example can be an alloy of nickel and iron (36% Ni), known as invar. These words were widely used in precise adjustment.

[Physics 24] Forces of intermolecular interactions. Aggregate mill of the Republic. The nature of the thermal collapse of molecules in solid, rare, gas-like bodies and its change with temperature increases. Thermal expansion of tel. Linear expansion of solids during heating. The volume of thermal expansion of solids and radius. Move between aggregate mills. Heat of phase transition. Rivnavaga phases. Compensation of heat balance.

Forces of intermolecular interactions.

Intermolecular interactions may occur electric nature. Between themthere is a lot of difficulty and weight, which will quickly change with increasingstand between the molecules.Silly vidshtovhuvannyaonly in even the smallest places.Practical speech behavioryogo aggregation millis indicated by what it isdominant: gravitychi chaotic thermal roc.Forces dominate in solid bodiesmutual relations, that stinksretains its shape.

Aggregate mill of the Republic.

• to preserve volume and shape,
• the presence of both distant (solid body) and nearby order (ridina), and other authorities.

Thermal disturbance in solids is especially important. At high
temperatures, an intense thermal movement causes molecules to be brought closer together.
stan, movement of molecules progressive and obertal. . Gases have less than 1% obscurity
affects the molecules themselves. At intermediate temperatures
molecules constantly move in space, exchanging places, prote
Standing between them does not move much, d – homeland. Character of the molecules
in the country it has a collateral and progressive character (in that moment, if there is a stench
jump at the new position of the river).

Thermal expansion of tel.

The thermal collapse of molecules explains the phenomenon of thermal expansion of bodies. At
When heated, the amplitude of the collateral flow of molecules increases, which leads to
increased size of bodies.

Linear expansion of solids during heating.

The linear expansion of a solid is described by the formula: L=L0(1+at), where a is the linear expansion coefficient ~10^-5 K^-1.

The volume of thermal expansion of solids and radius.

The volume of expansion of the body is described by a similar formula: V = V0(1+Bt), B-volume expansion coefficient, with B = 3a.
Move between aggregate mills.

Rechovina can be found in solid, rare, and gas-like states. qi
become called aggregate camps of speech. Rechovina can move from
I will become one before another. The characteristic feature of the transformation of speech is
the possibility of establishing stable heterogeneous systems, if speech can
found immediately in several aggregate mills. When describing such systems
to understand the broader concepts of the phase of speech. For example, coal on a solid
The aggregate plant can have two different phases – diamond and graphite. Phase
is called the totality of all parts of the system, which includes the external
seamlessly and physically homogeneous. How many phases of speech are given?
temperature and pressure begin to collide one after another, and at this point the mass is the same
The phases do not amount to the same amount of changes, so we can talk about phase equality.

Apparently, under the influx of heat, parts are speeding up their chaotic collapse. As soon as a gas is heated, the molecules that form it simply fly apart. The heated liquid will initially increase in volume, and then evaporate. What will happen to solid bodies? Not every one of them can change their aggregation station.

Thermal expansion: advanced

Thermal expansion is a change in the size and shape of a body due to a change in temperature. Mathematically, it is possible to calculate the volumetric expansion coefficient, which allows us to predict the behavior of gases and gases in current minds that are changing. To obtain the same results for solids, it is necessary to use the following methods: Physicists have created a whole section for such studies and called it dilatometry.

Engineers and architects need knowledge of the behavior of various materials under the influence of high and low temperatures for the design of structures, laid roads and pipes.

Gas expansion

Thermal expansion of gases is accompanied by expansion of their space. This was noted by natural philosophers long ago, but only modern physicists have come up with mathematical developments.

We have been busy with the expansion of the field for a long time, but they were faced with strong tasks. The stench of the table was inveterately taken up to the point that they were trying to achieve superb results. Of course, the scientific community is not satisfied with this result. The accuracy of the world lay in the hands of other rich minds. Some physicists have come up with ideas that the expansion of gases occurs due to temperature changes. But this staleness is not completely...

Robot Dalton and Gay-Lussac

Physicists would have fought until they were hoarse, or they would have given up extinction, as if not Vine and another physicist, Gay-Lussac, had simultaneously been able to reverse the results of extinction.

Lussac tried to find out the reason for such a number of different results and noted that in some devices there was water at the time of discovery. Naturally, during the heating process it turned into steam and changed the quantity and storage of trace gases. The first thing to do, after completing the exercises, is to carefully dry all the instruments used for carrying out the experiment, and turn on the minimum amount of moisture from the traced gas. After all these manipulations, the first few traces turned out to be reliable.

Dalton took up these studies before his colleague and published the results at the very beginning of the 19th century. The wine was dried in the steam of sulfuric acid and then heated. After a series of studies, John discovered that all gases and vapors expand by a coefficient of 0.376. Lussac's number was 0.375. This became the official result of the investigation.

Resiliency of water vapor

Thermal expansion of gases is stored under their pressure, so that it can turn around at the outlet. The first chain of thought was traced to Ziegler in the mid-eighteenth century. But the results of this investigation must have varied. More reliable figures have been removed and used for high temperatures tat cauldron, and for short ones - a barometer.

For example, at the end of the 18th century, the French physicist Prony tried to derive a single formula that would describe the springiness of gases, but it turned out to be too bulky and complicated for the vicorist. Dalton, having decided to verify all the rules associated with the siphon barometer. Despite the fact that not all subjects had the same temperature, the results turned out to be even more accurate. Therefore, he published them in the form of a table with his assistant in physics.

The theory of vaporization

The thermal expansion of gases (as a physical theory) has seen various changes. For a long time now, the essence of the processes that produce steam has been discussed. Here the physicist Dalton, already familiar to us, appears again. We have formulated a hypothesis that any space is saturated with gas vapors regardless of what type of gas or vapor is in the tank (accommodated). So, you can earn money so that the country does not vaporize, just by entering the dot with atmospheric air.

The pressure of the air on the surface of the middle increases the space between the atoms, driving them one at a time and vaporizing, so that the steam is created. Although the force of gravity continues to act on the vapor molecules, it has always been taken into account that atmospheric pressure does not affect the vaporization process.

Expansion of the district

Thermal expansion was monitored in parallel with the expansion of gases. They themselves have been engaged in scientific research for centuries. For this stench, thermometers, aerometers, scientific instruments and other instruments were used.

All of them have closely followed Dalton's theory that similar units expand in proportion to the square of the temperature at which they are heated. Naturally, the higher the temperature, there was more pressure on them, otherwise there was no direct storage between them. This fluidity of expansion was different for all countries.

Thermal expansion of water, for example, begins at zero degrees Celsius and continues at lower temperatures. Previously, such research results were associated with the fact that it is not the water itself that expands, but the sound of the water being present. And after about an hour, the physicist DeLuca finally came to the idea that the reason for the trace should be found in the country itself. You want to know the temperature of the thickest liquid. However, this was not explained through the lack of detailed details. Rumfort, who took up the study of this phenomenon, established that the maximum thickness of water should be kept between 4 and 5 degrees Celsius.

Thermal expansion

In solid bodies, the head mechanism expands and changes the amplitude of the crystalline horns. Yakshcho kazati in simple words, The atoms that enter the material warehouse and are tightly coupled with each other begin to “tremble.”

The law of thermal expansion of bodies is formulated as follows: if a body with a linear dimension L is heated by dT (delta T is the difference between the core and end temperatures), it expands by the value dL (delta L is the coefficient linear thermal expansion for dovzhin ob' This is due to the difference in temperature). This is the simplest version of this law, which states that the body expands on all sides. Ale for practical robots Instead of using much more cumbersome calculations, the actual materials are not very complex, as modeled by physicists and mathematicians.

Thermal expansion of the slats

To lay the slick sheet, physical engineers are now called upon to accurately calculate the debris that must be placed between the rails so that when heated or cooled, the parts do not deform.

As it was indicated above, thermal linear expansion stagnates in all solids. The first rail was not a culprit. Ale is one detail. Linear change is easily observed in cases where the force of rubbing does not flow into the body. The slats are rigidly attached to the sleepers and welded from the slat slats, according to the law that describes the change of life, there is a heel transition in the form of running and stick supports.

Since the rack cannot change its tension, then with a change in temperature the thermal stress in it increases, which can either be stretched or compressed. This phenomenon is described by Hooke's law.

as a manuscript

Ministry of Education and Science of the Russian Federation

Volgograd State University of Architecture and Civil Engineering

Department of Physics

THERMAL EXPANSION OF SOLID TILES

Methodical introductions to laboratory work No. 10

Volgograd2013

UDC 537(076.5)

Thermal expansion of solids: Method. inserts before laboratory work / Order. , ; VolgDASA, Volgograd, 20с.

By reference laboratory robots This is the coefficient of linear thermal expansion of a solid. The identification of coefficients for linear and volumetric expansion is given. The phenomenon of thermal expansion is explained. A description of the vimiru method has been provided. The order of the Vikonanny robots is described. Safety rules have been established and food control has been established.

For students of all specialties in the discipline “Physics”

Il. 5. Table. 2. Bibliogr. 2 titles

© Volgograd State Academy of Architecture and Construction, 2002

© Skladannya, 2002

Meta robots ─ expression of the coefficient of linear thermal expansion of a solid.

Adjust it and adjust it . 1. Metal tube. 2. Electric heating system. 3. Downlight sensor. 4. Thermocouple. 5. Millivoltmeter (or milliampermeter). 6. Laboratory autotransformer (LATR).

1. THEORETICALLY INTRODUCTION

All bodies expand when heated, and contract when cold. For solids, it makes sense to talk about linear expansion. Dependency of temperature is ensured when heating wires on power lines, steam lines, damaged bridges, laying slats, etc.

To characterize such an expansion, the following values ​​are introduced: - dovzhin of the same body at a temperature K. Change of dovzhin of the body when heated at the same temperature http://pandia.ru/text/80/058/images/image007_40.gif" width="97" height ="52 src=">

The ratio of the water change until the temperature change that occurs is called the linear thermal expansion coefficient:

(1)

With large temperature changes or high precision, the adjustment and expansion coefficient cannot be kept constant. It rises with higher temperatures and changes with these changes, falling to zero near absolute zero. The values ​​of linear thermal expansion coefficients are shown in table. 1.

Table 1

From formula (1) it is clear that the body’s doubling for any temperature

(2)

To characterize the volumetric expansion of the body, the following values ​​are entered: i – corresponding to the volume of the body at 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 higher temperatures

(4)

For solids, see table. 1 is added to the coefficient of linear expansion, the remainder between the coefficients of linear expansion and volumetric expansion is the basis of the song connection.

If we take a cube of a given ribs at a temperature (Fig. 1), its volume, when heated, increases to the volume of the ribs, so we can substitute the formulas in (2) and (4)

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

p align="justify"> Linear expansion coefficient for solid speeches Also, in this expression it is possible to obtain members that place a2 and a3, as infinitely small greater orders of magnitude than the number that place a in the first step. Viide stars

Yakshcho masa tila m when the temperature changes, it becomes constant, then the thickness of the liquid must lie with the temperature, since the volume changes with the temperature. T formula http://pandia.ru/text/80/058/images/image030_10.gif" width="239" height="52"> (6)

When dissolving the traces, ensure that the tables indicate the strength of the resin at 273 K. The strength at other temperatures is calculated using the following formula (6).

In some crystals, when heated, their linear dimensions in some directions grow differently, in some directions they not only grow, but rather change. This phenomenon is called anisotropy.

In a solid body, atoms undergo thermal vibrations due to the assemblies of crystalline rocks. In Fig. 2 shows the two closest atoms, stand up r between which changes occur during the collocation process..gif" width="76" height="25 src="> The amplitude of thermal collocation of atoms of solids does not exceed 10% of the equal distance between atoms (together. X- Minimum value). As the atoms have moved from the cob position to X, then the potential energy of their interaction is equal to

(7)

de Aі b- Positive positive coefficients;

- Minimum value of potential energy.

In Fig..gif (width="13" height="15"> (suction line). The obvious asymmetrical nature of the value of the curve. We know the force of interaction between atoms

(8)

When atoms are brought close together, the force and interaction takes on the nature of a change. However, when seen, i.e., the force that confirms the attraction..gif" width="51" height="23"> what is used with the values r 0 as an equally important issue. Yakbi coefficient b having reached zero, then the potential energy and the force of interaction would appear

(9)

which would indicate the harmonious vibrations of atoms. The graph of potential energy is a symmetrical curve (Fig. 3, dotted curve). Due to the symmetry of the potential curve, the temperature shift would lead to an increase in the amplitude of the collision of atoms, otherwise the average distance between the atoms would become unchanged. width="59" height="24 src="> bring to thermal expansion of solids.

Thermal expansion of solids at the glacial fall exhibits anisotropy. So, for example, a calcite crystal (CaCO3) expands in one direction when heated (O X) and squeezes in others (About U, Pro Z). Once a crystal is formed from such a crystal, when heated it turns into an epoxy.

2. VIMIRYUVAN METHOD

In Fig. 5 shows a laboratory setup. The voltage from the LATR is supplied to an electric heating coil mounted in the tube, the thermal expansion of which is monitored. One end of the tube is firmly secured, the other is loose and rests against the pressure sensor. The temperature of the tube is measured using a thermocouple, one of the junctions of some reinforcements on the tube. To adjust the thermo-EPS, a millivoltmeter (or a milliampermeter) is used.

3. ORDER OF WYCONANNA ROBOTI

1. Turn over the connections of the millivoltmeter (or milliammeter) to the “thermocouple” terminal and the autotransformer to the “to LATR” terminal.

2. Calculate the price per millivoltmeter (or milliampermeter) for the intervals indicated in the desktop version of the instructions.

3. Turn the sensor setting to zero, look at its scale, and calculate the price.

4. Remove the allowance from the deposit, close the LATR at the edge. Turn the LATR handle behind the year arrow until it stops, install the electric heating voltage.

5. Heating of the metal tube is accompanied by heating, as the sensor is vibrating. The heating temperature of the tube, kept at room temperature, is measured by a thermocouple using a millivoltmeter and a calibration graph. At the moment, if the pressure is less than 0.1 mm, write down in the table. 2 millivoltmeter readings..gif" width="65" height="23"> mm, turn the LATR knob against the year arrow until it stops and screw the LATR in from the edge.

7. Calibrate the millivoltmeter reading for the same values ​​in mm; 0.5 mm; 0.4 mm; 0.3 mm; 0.2 mm, 0.1 mm in cooling mode.

8. With the help of the calibration chart, which is supplied to the laboratory installation, indicate the heating temperature. for skin value D l both when heated and when cooled. find the values ​​of the linear thermal expansion coefficient and enter them into table 2.

10. Stay on the millimeter paper for the duration schedule D l type of temperature DT.

· Be careful when working. Contact us in the localities using torkan strums or darts.

· Do not allow the unit to overheat.

· In case of malfunction, please contact the drawing laboratory assistant.

· Do not delete the installation included in the measure after installation.

CONTROL FOOD

1. Give the value of the linear thermal expansion coefficient. What is the order of magnitude of this coefficient?

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

3. How are the coefficients of thermal linear and volumetric expansion related to each other? Write formula (5).

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

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

6. How to preserve the thickness of a solid when heated?

7. What is called anisotropy of thermal expansion?

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

bibliographic list

1. Physics course M: Vischa. school, 1999 r.

2. Physics course / , . M: Vischa. school, 1999 r.