When heated, it increases as a result of an increase in the speed of movement of atoms in the conductor material with increasing temperature. The specific resistance of electrolytes and coal when heated, on the contrary, decreases, since in these materials, in addition to increasing the speed of movement of atoms and molecules, the number of free electrons and ions per unit volume increases.

Some alloys, which have more than their constituent metals, hardly change resistivity with heating (constantan, manganin, etc.). This is explained by the irregular structure of the alloys and the short mean free path of electrons.

The value showing the relative increase in resistance when the material is heated by 1° (or decreased when cooled by 1°) is called.

If the temperature coefficient is denoted by α, the resistivity at to = 20 o by ρ o, then when the material is heated to a temperature t1, its resistivity p1 = ρ o + αρ o (t1 - to) = ρ o(1 + (α (t1 -to))

and accordingly R1 = Ro (1 + (α (t1 - to))

Temperature coefficient a for copper, aluminum, tungsten is 0.004 1/deg. Therefore, when heated by 100°, their resistance increases by 40%. For iron α = 0.006 1/deg, for brass α = 0.002 1/deg, for fechral α = 0.0001 1/deg, for nichrome α = 0.0002 1/deg, for constantan α = 0.00001 1/deg , for manganin α = 0.00004 1/deg. Coal and electrolytes have a negative temperature coefficient of resistance. The temperature coefficient for most electrolytes is approximately 0.02 1/deg.

The property of conductors to change their resistance depending on temperature is used in resistance thermometers. By measuring the resistance, the ambient temperature is determined by calculation. Constantan, manganin and other alloys with a very small temperature coefficient of resistance are used for the manufacture of shunts and additional resistances to measuring instruments.

Example 1. How will the resistance Ro of an iron wire change when it is heated to 520°? Temperature coefficient a of iron is 0.006 1/deg. According to the formula R1 = Ro + Ro α (t1 - to) = Ro + Ro 0.006 (520 - 20) = 4Ro, that is, the resistance of the iron wire when heated by 520° will increase 4 times.

Example 2. Aluminum wires at a temperature of -20° they have a resistance of 5 ohms. It is necessary to determine their resistance at a temperature of 30°.

R2 = R1 - α R1(t2 - t1) = 5 + 0.004 x 5 (30 - (-20)) = 6 ohms.

The property of materials to change their electrical resistance when heated or cooled is used to measure temperatures. So, thermal resistance, which are wires made of platinum or pure nickel, fused into quartz, are used to measure temperatures from -200 to +600°. Semiconductor thermal resistances with a large negative coefficient are used for precise definition temperatures in narrower ranges.

Semiconductor thermal resistances used to measure temperatures are called thermistors.

Thermistors have a high negative temperature coefficient of resistance, that is, when heated, their resistance decreases. made from oxide (subject to oxidation) semiconductor materials consisting of a mixture of two or three metal oxides. The most common are copper-manganese and cobalt-manganese thermistors. The latter are more sensitive to temperature.

One of the most popular metals in industries is copper. Most widespread she graduated in electrical and electronics. Most often it is used in the manufacture of windings for electric motors and transformers. The main reason for using this particular material is that copper has the lowest electrical resistivity of any material currently available. Until it appears new material with a lower value of this indicator, we can say with confidence that there will be no replacement for copper.

General characteristics of copper

Speaking about copper, it must be said that at the dawn of the electrical era it began to be used in the production of electrical equipment. They began to use it largely due to unique properties, which this alloy possesses. By itself, it is a material characterized by high properties in terms of ductility and good malleability.

Along with the thermal conductivity of copper, one of its most important advantages is its high electrical conductivity. It is due to this property that copper and has become widespread in power plants, in which it acts as a universal conductor. The most valuable material is electrolytic copper, which has a high degree of purity of 99.95%. Thanks to this material, it becomes possible to produce cables.

Pros of using electrolytic copper

The use of electrolytic copper allows you to achieve the following:

• Ensure high electrical conductivity;
• Achieve excellent styling ability;
• Provide a high degree of plasticity.

Areas of application

Cable products made from electrolytic copper are widely used in various industries. Most often it is used in the following areas:

• electrical industry;
• electrical appliances;
• automotive industry;
• production of computer equipment.

What is the resistivity?

To understand what copper is and its characteristics, it is necessary to understand the main parameter of this metal - resistivity. It should be known and used when performing calculations.

Resistivity is usually understood as a physical quantity, which is characterized as the ability of a metal to conduct electric current.

It is also necessary to know this value in order to make the calculation correctly electrical resistance conductor. When making calculations, they are also guided by its geometric dimensions. When carrying out calculations, use the following formula:

This formula is familiar to many. Using it, you can easily calculate the resistance of a copper cable, focusing only on the characteristics electrical network. It allows you to calculate the power that is inefficiently spent on heating the cable core. Besides this, a similar formula allows you to calculate resistance any cable. It does not matter what material was used to make the cable - copper, aluminum or some other alloy.

A parameter such as electrical resistivity is measured in Ohm*mm2/m. This indicator for copper wiring laid in an apartment is 0.0175 Ohm*mm2/m. If you try to look for an alternative to copper - a material that could be used instead, then only silver can be considered the only suitable one, whose resistivity is 0.016 Ohm*mm2/m. However, when choosing a material, it is necessary to pay attention not only to resistivity, but also to reverse conductivity. This value is measured in Siemens (Cm).

Siemens = 1/ Ohm.

For copper of any weight, this composition parameter is 58,100,000 S/m. As for silver, its reverse conductivity is 62,500,000 S/m.

In our world high technology, when every home has a large number of electrical devices and installations, the importance of a material such as copper is simply invaluable. This material used to make wiring, without which no room can do. If copper did not exist, then man would have to use wires from other available materials, for example, from aluminum. However, in this case one would have to face one problem. The thing is that this material has a much lower conductivity than copper conductors.

Resistivity

The use of materials with low electrical and thermal conductivity of any weight leads to large losses of electricity. A this affects power loss on the equipment used. Most experts call copper as the main material for making insulated wires. It is the main material from which individual elements of equipment powered by electric current are made.

• Boards installed in computers are equipped with etched copper traces.
• Copper is also used to make the most different elements used in electronic devices.
• In transformers and electric motors it is represented by a winding, which is made of this material.

There is no doubt that the expansion of the scope of application of this material will occur with the further development of technological progress. Although, besides copper, there are other materials, but still the designer when creating equipment and various installations use copper. Main reason the demand for this material lies in good electrical and thermal conductivity this metal, which it provides at room temperature.

Temperature coefficient of resistance

All metals with any thermal conductivity have the property of decreasing conductivity with increasing temperature. As the temperature decreases, conductivity increases. Experts call the property of decreasing resistance with decreasing temperature particularly interesting. Indeed, in this case, when the temperature in the room drops to a certain value, the conductor may lose electrical resistance and it will move into the class of superconductors.

In order to determine the resistance value of a particular conductor of a certain weight at room temperature, there is a critical resistance coefficient. It is a value that shows the change in resistance of a section of a circuit when the temperature changes by one Kelvin. To perform electrical resistance calculations copper conductor in a certain time period use the following formula:

ΔR = α*R*ΔT, where α is the temperature coefficient of electrical resistance.

Conclusion

Copper is a material that is widely used in electronics. It is used not only in windings and circuits, but also as a metal for the manufacture of cable products. For machinery and equipment to work effectively, it is necessary correctly calculate the resistivity of the wiring, laid in the apartment. There is a certain formula for this. Knowing it, you can make a calculation that allows you to find out the optimal size of the cable cross-section. In this case, it is possible to avoid loss of equipment power and ensure its efficient use.

Temperature coefficients of resistance of metals

Problem 18.1. To measure temperature, an iron wire was used, which at a temperature t 1 = 10 °C resistance R 1 = 15 ohms. At some temperature t 2 she had resistance R 2 = 18.25 ohms. Find this temperature. The temperature coefficient of resistance of iron is a = 6.0×10 –3 1/°С.

Let's substitute the numerical values:

Answer: .

STOP! Decide for yourself: A5, B7–B9, C3–C4.

Problem 18.2. Find temperature t 2 tungsten filament light bulbs, if connected to a network with voltage U= 220 V current flows through the filament I= 0.68 A. At temperature t 1 = 20 °C thread resistance R 1 = 36 Ohm. Temperature coefficient of resistance of tungsten a = 4.8×10 –3 1/°С.

Answer:

STOP! Decide for yourself: B10–B12, C4, C6, C8.

Superconductivity

Rice. 18.3

In 1911, the Dutch scientist Kamerlingh Onnes discovered that at temperatures close to absolute zero, the resistance of some substances abruptly drops to zero (Fig. 18.3). This phenomenon was called superconductivity. The current excited in a ring of superconductor can continue for months and years without dying out after the source is removed.

Approximately half of pure metals can go into a superconducting state, and in total more than a thousand superconductors are currently known. Of the pure metals, niobium has the highest transition temperature (9.3 K), and among alloys the “record holder” is the compound of niobium with germanium (23.2 K).

In a strong magnetic field, superconductivity disappears. The farther the temperature of the superconductor is from the transition point, the stronger the destructive magnetic field should be. Such a destructive magnetic field can also be the field of the current itself in a superconductor. Some alloys manage to maintain superconductivity at currents of several thousand amperes.

It is still unknown whether it is possible to create superconducting materials at temperatures close to room temperature. The creation of such materials would make it possible to transmit electricity over any distance without loss. However, now electromagnets with superconducting windings cooled by liquid helium (boiling point 4.2 K) are often used in particle accelerators, in powerful generators current and in some other devices. Big practical significance would be the creation of materials capable of maintaining a superconducting state at the boiling point of readily available and cheap liquid nitrogen of 77 K.

Free electron concentration n in a metal conductor with increasing temperature remains practically unchanged, but their average speed of thermal movement increases. Vibrations of nodes also intensify crystal lattice. The quantum of elastic vibrations of the medium is usually called phonon. Small thermal vibrations of the crystal lattice can be considered as a collection of phonons. With increasing temperature, the amplitudes of thermal vibrations of atoms increase, i.e. the cross section of the spherical volume occupied by the vibrating atom increases.

Thus, with increasing temperature, more and more obstacles appear in the path of electron drift under the influence of electric field. This leads to the fact that the average free path of an electron λ decreases, the mobility of electrons decreases and, as a consequence, the conductivity of metals decreases and the resistivity increases (Fig. 3.3). The change in the resistivity of a conductor when its temperature changes by 3K, related to the resistivity value of this conductor at a given temperature, is called the temperature coefficient of resistivity TK ρ or . The temperature coefficient of resistivity is measured in K -3. The temperature coefficient of resistivity of metals is positive. As follows from the definition given above, the differential expression for TK ρ has the form:

(3.9)

According to the conclusions of the electronic theory of metals, the values ​​of pure metals in the solid state should be close to the temperature coefficient (TK) of expansion of ideal gases, i.e. 3: 273 = 0.0037. In fact, most metals have ≈ 0.004. Some metals have higher values, including ferromagnetic metals - iron, nickel and cobalt.

Note that for each temperature there is a temperature coefficient TK ρ. In practice, for a certain temperature range, the average value is used TK ρ or :

, (3.10)

Where ρ3 And ρ2- resistivity of conductor material at temperatures T3 And T2 respectively (in this case T2 > T3); there is a so-called average temperature coefficient of resistivity of this material in the temperature range from T3 to T2.

In this case, when the temperature changes in a narrow range from T3 to T2 accept a piecewise linear approximation of the dependence ρ(T):

(3.11)

Reference books on electrical materials usually give values ​​at 20 0 C.

Fig.3.1 Dependence of resistivity ρ metal conductors depending on temperature T. Jump ρ (branch 5) corresponds to the melting point T PL.

Fig.3.2. Dependence of copper resistivity on temperature. The jump corresponds to the melting temperature of copper 1083 0 C.

As follows from formula (3.33), the resistivity of conductors depends linearly on temperature (branch 4 in Fig. 3.3), with the exception of low temperatures and temperatures higher than the melting point T>T PL.

As the temperature approaches 0 0 K, an ideal metal conductor has a resistivity ρ tends to 0 (branch 3). For technically pure conductors (with a very small amount of impurities) over a small area of ​​several kelvins, the value ρ ceases to depend on temperature and becomes constant (branch 2). It is called “residual” resistivity ρ OST. Magnitude ρ OST determined only by impurities. The purer the metal, the less ρ OST .

Near absolute zero, another dependence is possible ρ on temperature, namely, at a certain temperature T S resistivity ρ drops abruptly to almost zero (branch 3). This state is called superconductivity, and conductors with this property are called superconductors. The phenomenon of superconductivity will be discussed below in 3.3.

Example 3. 6. The temperature coefficient of resistivity of copper at room temperature is 4.3 30-3 -3 K. Determine how many times the electron free path will change when the copper conductor is heated from 300 to 3000 K.

Solution. The electron mean free path is inversely proportional to the resistivity. Therefore, by how many times the resistivity of copper increases when heated, by how many times the electron free path will decrease. The resistivity of copper will increase several times. Consequently, the electron free path will decrease by 3 times.

Change in the resistivity of metals during melting.

When metals transition from solid to liquid, most of them experience an increase in resistivity ρ , as shown in Fig. 3.3 (branch 5). Table 3.2 shows the values ​​​​showing the relative change in resistivity various metals when melting. The resistivity increases during melting for those metals (Hg, Au, Zn, Sn, Na) that increase in volume during melting, i.e. reduce density. However, some metals, such as gallium (Ga) and bismuth (Bi), reduce ρ 0.58 and 0.43 times, respectively. For most metals in the molten state, the resistivity increases with increasing temperature (branch 6 in Fig. 3.3), which is associated with an increase in their volume and a decrease in density.

Table 3.2. Relative change in resistivity of various metals during melting.

Change in resistivity of metals during deformation.

Change ρ during elastic deformations of metal conductors is explained by a change in the amplitude of vibrations of the nodes of the metal crystal lattice. When stretched, these amplitudes increase, and when compressed, they decrease. An increase in the amplitude of oscillations of nodes leads to a decrease in the mobility of charge carriers and, as a consequence, to an increase in ρ.

A decrease in the oscillation amplitude, on the contrary, leads to a decrease in ρ. However, even significant plastic deformation, as a rule, increases the resistivity of metals due to distortion of the crystal lattice by no more than 4-6%. The exception is tungsten (W), ρ which increases by tens of percent with significant compression. In connection with the above, it is possible to use plastic deformation and the resulting hardening to increase the strength of conductor materials without compromising their electrical properties. During recrystallization, the resistivity can be reduced again to its original value.

Specific resistance of alloys.

As already indicated, impurities disrupt the correct structure of metals, which leads to an increase in their resistivity. Figure 3.3 shows the dependence of resistivity ρ and conductivity γ copper concentration N various impurities in fractions of a percent. We emphasize that any alloying leads to an increase in the electrical resistivity of the alloyed metal compared to the alloyed one. This also applies to cases when a metal with a lower ρ. For example, when alloying copper with silver ρ there will be more copper-silver alloy than ρ copper, despite the fact that ρ less silver than ρ copper, as can be seen from Fig. 3.3.

Fig.3.3. Resistivity Dependence ρ and conductivity γ copper from the content of impurities.

Significant increase ρ observed when two metals are fused if they form with each other solid solution, in which atoms of one metal enter the crystal lattice of another. Curve ρ has a maximum corresponding to a certain specific ratio between the content of components in the alloy. Such a change ρ from the content of alloy components can be explained by the fact that due to its more complex structure compared to pure metals, the alloy can no longer be likened to a classical metal.

The change in the specific conductivity of the γ alloy in this case is caused not only by a change in the mobility of carriers, but in some cases also by a partial increase in the concentration of carriers with increasing temperature. An alloy in which the decrease in mobility with increasing temperature is compensated by an increase in carrier concentration will have a zero temperature coefficient of resistivity. As an example, Fig. 3.4 shows the dependence of the resistivity of a copper-nickel alloy on the composition of the alloy.

Heat capacity, thermal conductivity and heat of fusion of conductors.

Heat capacity characterizes the ability of a substance to absorb heat Q when heated. Heat capacity WITH of any physical body is a value equal to the amount of thermal energy absorbed by this body when it is heated by 3K without changing its phase state. Heat capacity is measured in J/K. Heat capacity metal materials increases with increasing temperature. Therefore, the heat capacity WITH determined with an infinitesimal change in its state:

Fig.3.4. Dependence of resistivity of copper-nickel alloys on composition (in percent by weight).

Heat capacity ratio WITH to body weight m called specific heat capacity With:

Specific heat capacity is measured in J/(kg? K). The values ​​of the specific heat capacity of metals are given in table. 3.3. As can be seen from Table 3.3, refractory materials are characterized by low specific heat capacity values. So, for example, for tungsten (W) With=238, and for molybdenum (Mo) With=264J/(kg?K). Low-melting materials, on the contrary, are characterized high value specific heat capacity. For example, aluminum (Al) With=922, and for magnesium (Mg) With=3040J/(kg? K). Copper has a specific heat capacity c = 385 J/(kg? K). For metal alloys, the specific heat capacity is in the range of 300-2000 J/(kg? K). C is important characteristic metal

Thermal conductivity called the transfer of thermal energy Q in an unevenly heated medium as a result of thermal movement and interaction of its constituent particles. The transfer of heat in any environment or any body occurs from hotter parts to cold ones. As a result of heat transfer, the temperature of the environment or body is equalized. In metals, thermal energy is transferred by conduction electrons. The number of free electrons per unit volume of metal is very large. Therefore, as a rule, the thermal conductivity of metals is much greater than the thermal conductivity of dielectrics. The fewer impurities metals contain, the higher their thermal conductivity. As impurities increase, their thermal conductivity decreases.

As is known, the process of heat transfer is described by Fourier's law:

. (3.14)

Here is the heat flux density, i.e. the amount of heat passing along the coordinate x through a unit of cross-sectional area per unit of time, J/m 2?s,

Temperature gradient along the coordinate x, K/m,

The proportionality coefficient, called the thermal conductivity coefficient (previously designated), W/K?m.

Thus, the term thermal conductivity corresponds to two concepts: this is the process of heat transfer and the proportionality coefficient that characterizes this process.

So, free electrons in a metal determine both its electrical and thermal conductivity. The higher the electrical conductivity γ of a metal, the greater its thermal conductivity should be. With increasing temperature, when the mobility of electrons in the metal and, accordingly, its specific conductivity γ decrease, the ratio /γ of the thermal conductivity of the metal to its specific conductivity should increase. Mathematically this is expressed Wiedemann-Franz-Lorenz law

/γ = L 0 T, (3.15)

Where T- thermodynamic temperature, K,

L 0 - Lorentz number, equal

L 0 = . (3.16)

Substituting the values ​​of the Boltzmann constant into this expression k= J/K and electron charge e= 3.602?30 -39 Cl we get L 0 = /

The Wiedemann-Franz-Lorentz law is satisfied in the temperature range close to normal or slightly elevated for most metals (with the exception of manganese and beryllium). According to this law, metals that have high electrical conductivity also have high thermal conductivity.

Temperature and heat of fusion. The heat absorbed by a solid crystalline body during its transition from one phase to another is called the heat of phase transition. In particular, the heat absorbed by a solid crystalline body during its transition from solid to liquid is called heat of fusion and the temperature at which melting occurs (at constant pressure) is called melting point and denote T PL.. The amount of heat that must be supplied per unit mass of a solid crystalline body at temperature T PL to convert it into a liquid state is called specific heat of fusion r PL and is measured in MJ/kg or kJ/kg. The values ​​of the specific heat of fusion for a number of metals are given in Table 3.3.

Table.3. 3. Specific heat of fusion of some metals.

Depending on the melting point, refractory metals are distinguished, having a melting point higher than that of iron, i.e. higher than 3539 0 C and low-melting with a melting point less than 500 0 C. The temperature range from 500 0 C to 3539 0 C refers to the average melting point values.

The work function of an electron leaving a metal.

Experience shows that free electrons practically do not leave the metal at ordinary temperatures. This is due to the fact that a retaining material is created in the surface layer of the metal. electric field. This electric field can be thought of as a potential barrier that prevents electrons from escaping from the metal into the surrounding vacuum.

A holding potential barrier is created for two reasons. Firstly, due to the attractive forces from the excess positive charge that arose in the metal as a result of electrons escaping from it, and, secondly, due to the repulsive forces from the previously emitted electrons, which formed an electron cloud near the surface of the metal. This electron cloud, together with the outer layer of positive lattice ions, forms an electric double layer, the electric field of which is similar to that of a parallel-plate capacitor. The thickness of this layer is equal to several interatomic distances (30 -30 -30 -9 m).

It does not create an electric field in external space, but creates a potential barrier that prevents free electrons from escaping from the metal. The work function of an electron leaving a metal is the work done to overcome the potential barrier at the metal-vacuum interface. In order for an electron to fly out of a metal, it must have a certain energy sufficient to overcome the attractive forces of positive charges in the metal and the repulsive forces of electrons previously emitted from the metal. This energy is denoted by the letter A and is called the work function of an electron leaving the metal. The work function is determined by the formula:

Where e- electron charge, K;

Output potential, V.

Based on the foregoing, we can assume that the entire volume of the metal for conduction electrons represents a potential well with a flat bottom, the depth of which is equal to the work function A. The work function is expressed in electron volts (eV). The electron work function values ​​for metals are given in Table 3.3.

If you impart energy to the electrons in the metal sufficient to overcome the work function, then some of the electrons may leave the metal. This phenomenon of metal emitting electrons is called electronic emissions. To obtain free electrons in electronic devices there is a special metal electrode - cathode.

Depending on the method of transmitting energy to the electrons of the cathode, the following types of electron emission are distinguished:

- thermionic, in which additional energy is imparted to electrons as a result of heating the cathode;

- photoelectronic, in which the cathode surface is exposed to electromagnetic radiation;

- secondary electronic, which is the result of bombardment of the cathode by a stream of electrons or ions moving at high speed;

- electrostatic, in which a strong electric field at the surface of the cathode creates forces that promote the escape of electrons beyond its limits.

Thermionic emission phenomenon is used in vacuum tubes, X-ray tubes, electron microscopes etc.

Thermoelectromotive force (thermo-emf).

When two different metal conductors A and B (or semiconductors) come into contact (Fig. 3.5), a contact potential difference, which is due to the difference in the work function of electrons from different metals. In addition, the electron concentrations of different metals and alloys may also be different.

In this case, electrons from metal A, where their concentration is higher, will move to metal B, where their concentration is lower. As a result, metal A will have a positive charge, and metal B will have a negative charge. In accordance with the electronic theory of metals, the contact potential difference or EMF between conductors A and B is equal to (Fig. 3.5):

(3.17)

Where U A And U B— potentials of contacting metals; n A And n B- electron concentrations in metals A and B; k- Boltzmann constant, e- electron charge, T- thermodynamic temperature. If the electron concentration is greater in metal B, then the potential difference will change sign, since the logarithm of a number less than one will be negative. The contact potential difference can be measured experimentally. The first such measurements were carried out in 3797 by the Italian physicist A. Volta, who discovered this phenomenon.

Fig.3.5. The formation of a contact potential difference or EMF between two different conductors A and B.

It goes without saying that if two conductors A and B form a closed circuit (Fig. 3.6) and the temperatures of both contacts are the same, then the sum of the potential differences or the resulting emf is zero.

(3.18)

If one of the contacts or, as they are called, “junctions” of two metals has a temperature T3, and the other - temperature T2. In this case, a thermo-EMF arises between the junctions equal to

(3.19)

Where - constant thermo-EMF coefficient for a given pair of conductors, measured in μV/K. It depends on the absolute value of the temperatures of the “hot” and “cold” contacts, as well as on the nature of the contacting materials. As can be seen from formula (3.39), the thermo-EMF should be proportional to the temperature difference between the junctions.

Fig3.6. Thermocouple diagram.

The dependence of thermo-EMF on the junction temperature difference may not always be strictly linear. Therefore the coefficient with T must be adjusted according to temperature values T 3 And T 2.

A system of two wires isolated from each other, made of different metals or alloys, soldered in two places is called thermocouple. It is used to measure temperatures. The temperature of one junction (cold) is usually known, and the second junction is placed in the place whose temperature they want to measure. A measuring instrument, for example a millivoltmeter, is connected to the thermocouple mV, graduated in degrees Celsius or degrees Kelvin (Fig. 3.6).

In some cases, a control relay or solenoid coil is connected to the ends of the thermocouple (Fig. 3.7). When a certain temperature difference is reached, under the influence of thermoEMF, a current begins to flow through the relay coil P, causing the relay to operate or the valve to open using a solenoid. Examples of the most common thermocouples, their temperature ranges and applications are given below on pages 325-330.

	Fig.4

Fig.3.7. Connection diagram of a thermocouple to a relay in an automatic control circuit

Thermo-EMF can be useful in some cases, but harmful in others. For example, when measuring temperature with thermocouples, it is useful. IN measuring instruments and reference resistors, it is harmful. Here they strive to use materials and alloys with the lowest possible thermo-EMF coefficient relative to copper.

Example 3.7. The thermocouple was calibrated at the cold junction temperature T 0 =0 o C. Calibration data is given in table 3.4

Table 3.4

Thermocouple calibration data

T, o C
Thermo-EMF, mV	0,0	0,33	0,65	3,44	2,33	3,25	4.23	5,24	6,27	7,34	8,47	9,63

This thermocouple was used to measure the temperature in the furnace. The temperature of the cold junction of the thermocouple during the measurement was 300 o C. The voltmeter during the measurement showed a voltage of 7.82 mV. Using the calibration table, determine the temperature in the oven.

Solution. If the temperature of the cold junction during measurement does not correspond to the calibration conditions, then the law of intermediate temperatures must be applied, which is written as follows:

The junction temperatures are indicated in parentheses. The found thermo-EMF corresponds, in accordance with the calibration table, to the temperature in the furnace T= 900 o C.

Temperature coefficient of linear expansion of conductors(TCLR). This coefficient, designated shows the relative change in the linear dimensions of the conductor, and in particular its length, depending on temperature:

It is measured in K-3. Figure 3.8 shows the extensions of rods 3 m long, made of various materials, with increasing temperature,

Fig.3.8. Dependence of the elongation of a rod 1 m long on the temperature of the material.

It should be borne in mind that if the resistor is made of wire, then when it is heated, the length of the wire and its radius increase in proportion to its temperature. The cross-section increases in proportion to the square of the linear dimensions, i.e. proportional to the square of the radius. This means that as the linear dimensions of the wire increase when heated, the resistance of this wire decreases. Thus, when a wire is heated, the value of its resistance is influenced by two factors acting in opposite directions: an increase in resistivity ρ and an increase in the cross-section of the wire.

Due to the above, the temperature coefficient of the electrical resistance of the wire will be equal to:

Load expansion joints will not be able to compensate for such an extension. In this case, the adjustment of the contact network will be disrupted, the sag will increase, and the conditions for normal current collection will not be met. Under these conditions it is impossible to ensure high speed train movement and there will be a real threat of breakdown of current collectors.

In order to prevent such a development of events, the heating temperature of the wires should be limited to the value permissible under the conditions for ensuring normal operating conditions for this contact network design. If the temperature rises above this permissible value, the traction load must be limited.

In addition, the length of the anchor sections should be limited so that the length of the wire does not exceed 800 m. In this case, when the temperature of the contact wire increases by 300 0 C, the elongation will not exceed 3.4 m, which is quite acceptable under the conditions of compensation for the elongation of the traction suspension. If we take the minimum temperature as -40 0 C, then the maximum temperature of the contact wire should not exceed 60 0 C (in some designs 50 0 C).

When creating electric vacuum devices, it is necessary to select metal conductors in such a way that their TCLE is approximately the same as that of vacuum glass or vacuum ceramics. Otherwise, thermal shocks may occur, leading to the destruction of vacuum devices.

Mechanical properties of conductors characterized by tensile strength and elongation at break Δ l/l as well as fragility and hardness. These properties depend on the mechanical and heat treatment, as well as the presence of alloying and impurities in conductors. In addition, the tensile strength depends on the temperature of the metal and the duration of the tensile force.

As noted above, to compensate for the linear expansion of contact wires, their tension is carried out by temperature compensators with weights creating a tension of 30 kN (3 t). This tension ensures normal current collection conditions. The greater the tension, the more elastic the suspension will be and better conditions current collection However, the permissible tension depends on the tensile strength, which decreases with increasing temperature.

For hard-drawn copper, from which contact wires are made, a sharp decrease in tensile strength occurs at temperatures above 200 0 C. Temporary tensile strength also decreases with increasing duration of exposure high temperature. Time until metal fracture depending on its absolute temperature T(K) and design features and manufacturing technology are determined by the formula:

. (3.22)

Here: C 3 and C 2 are thermal resistance coefficients, depending on the design and properties of the metals. Figure 3.9 shows the dependence of the time to destruction on temperature, expressed in degrees Celsius, for wires made of different metals.

Thus, when increasing the tension of the contact wire in order to increase the elasticity of the suspension, the strength of the contact wire should also be taken into account in accordance with Fig. 3.9.

Fig.3. 9. Dependence of time before metal rupture on temperature and type of wire. 1 - aluminum and stranded steel-aluminum; 2 - copper contact; 3 - stranded steel-copper bimetallic; 4 - bronze heat-resistant contact.

The main characteristics of conductor materials are:

1. Thermal conductivity;
2. Contact potential difference and thermoelectromotive force;
3. Tensile strength and tensile elongation.

ρ - a value characterizing the ability of a material to provide resistance electric current. Specific resistance is expressed by the formula:

For long conductors (wires, cords, cable cores, busbars), the length of the conductor l usually expressed in meters, cross-sectional area S- in mm², conductor resistance r- in Ohm, then the dimension of resistivity

Data on the resistivities of various metal conductors are given in the article "Electrical resistance and conductivity".

α is a value characterizing the change in conductor resistance depending on temperature.
The average value of the temperature coefficient of resistance in the temperature range t 2° - t 1° can be found by the formula:

Data on temperature coefficients of resistance of various conductor materials are given in the table below.

The value of temperature coefficients of resistance of metals

Thermal conductivity

λ is a quantity characterizing the amount of heat passing per unit time through a layer of matter. Thermal conductivity dimension

Thermal conductivity has great value for thermal calculations of machines, apparatus, cables and other electrical devices.

Thermal conductivity value λ for some materials

Silver Copper Aluminum Brass Iron, steel Bronze Concrete Brick Glass Asbestos Tree Cork

350 - 360 340 180 - 200 90 - 100 40 - 50 30 - 40 0,7 - 1,2 0,5 - 1,2 0,6 - 0,9 0,13 - 0,18 0,1 - 0,15 0,04 - 0,08

From the data presented it is clear that metals have the greatest thermal conductivity. Non-metallic materials have significantly lower thermal conductivity. It reaches especially low values ​​for porous materials, which I use specifically for thermal insulation. According to electron theory high thermal conductivity metals is due to the same conduction electrons as electrical conductivity.

Contact potential difference and thermoelectromotive force

As stated in the article “Metal Conductors,” positive metal ions are located at the nodes of the crystal lattice, forming, as it were, its frame. Free electrons fill the lattice like a gas, sometimes called "electron gas." The pressure of the electron gas in a metal is proportional to the absolute temperature and the number of free electrons per unit volume, which depends on the properties of the metal. When two dissimilar metals come into contact at the point of contact, the pressure of the electron gas equalizes. As a result of electron diffusion, a metal whose number of electrons decreases is charged positively, and a metal whose number of electrons increases is charged negatively. A potential difference occurs at the point of contact. This difference is proportional to the temperature difference between the metals and depends on their type. A thermoelectric current arises in a closed circuit. The electromotive force (EMF) that creates this current is called thermoelectromotive force(thermo-EMF).

The phenomenon of contact potential difference is used in technology to measure temperature using thermocouples. When measuring small currents and voltages in a circuit at the junction of different metals, a large potential difference may arise, which will distort the measurement results. In this case, it is necessary to select materials so that the measurement accuracy is high.

Tensile strength and tensile elongation

When choosing wires, in addition to the cross-section, wire material, and insulation, it is necessary to take into account their mechanical strength. This is especially true for wires air lines power transmission The wires are stretched. Under the influence of force applied to the material, the latter elongates. If we designate the original length l 1 and the final length l 2, then the difference l 1 - l 2 = Δ l will absolute elongation.

Attitude

called relative elongation.

The force that produces material rupture is called breaking load, and the ratio of this load to the cross-sectional area of ​​the material at the moment of destruction is called temporary tensile strength and is designated

Data on tensile strengths for various materials are given below.

Tensile strength value for various metals