Volumetric release or absorption of heat in a conductor under the combined action of electric current and temperature gradient

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Description

The Thomson effect refers to thermoelectric effects and consists of the following: when an electric current is passed through a conductor along which there is a temperature gradient, in the conductor (even homogeneous), in addition to Joule heat, depending on the direction of the current, an additional amount of heat will be released or absorbed (Thomson heat ).

Uneven heating of an initially homogeneous conductor changes its properties, making the conductor inhomogeneous. Therefore, the Thomson phenomenon is, in essence, a kind of Peltier phenomenon with the difference that the inhomogeneity is caused not by differences in the chemical composition of the conductor, but by temperature differences.

Experience and theoretical calculations show that the Thomson phenomenon obeys the following law:

,

where is the Thomson heat released (or absorbed) per unit time per unit volume of the conductor (specific thermal power);

j is the current density flowing through the conductor;

Temperature gradient along a conductor;

t is the Thomson coefficient, depending on the nature of the metal and its temperature.

The above formula (the so-called differential form of the law) can be applied to a section of conductor x along which current I flows and there is some temperature difference:

Thomson's law in integral form determines the total amount of Thomson heat Q released (or absorbed) in the entire volume of the conductor under consideration (D V=S D x) during time t:

.

In this case, the Thomson effect is considered positive if the electric current flowing in the direction of the temperature gradient (I dT /d x) causes heating of the conductor (Q t >0), and negative if, in the same direction of the current, cooling of the conductor occurs (Q t<0 ).

Q t = tХD T Х I Х t.

To explain the Thomson effect, it is necessary to consider the influence of two factors. The first factor takes into account the change in the average electron energy along the conductor due to its uneven heating (see Fig. 1a and 1b).

Release of Thomson heat when the current and temperature gradient in the sample are parallel

Rice. 1a

Absorption of Thomson heat with antiparallel current and temperature gradient in the sample

Rice. 1b

Let T 1 >T 2, i.e. the temperature gradient is directed from point 2 to point 1. In the more heated part of the conductor (1), the average electron energy is greater than in the less heated part (2). Therefore, if the direction of the current in the metal (M) corresponds to the movement of electrons from the hot end to the cold (Fig. 1a), then the electrons transfer their excess energy to the crystal lattice, resulting in the release of Thomson heat (Q t >0).

When the current is directed in the opposite direction (Fig. 1b), electrons, moving from the cold end (2) to the heated end (1), will replenish their energy at the expense of the lattice, which will lead to the absorption of the corresponding amount of heat (Q t<0 ).

For a more accurate description of the phenomenon, it is necessary to take into account the second factor, which is associated with the electric field of thermopower that arises under conditions of temperature inhomogeneity (Fig. 2a and 2b).

Cooling of a conductor when electrons are decelerated by the diffusion electric field of a space charge

Rice. 2a

Heating of a conductor during acceleration of electrons by the diffusion electric field of a space charge

Rice. 2b

If the temperature gradient is maintained constant, then there will be a constant flow of heat through the conductor. In metals, heat transfer is carried out mainly by the movement of conduction electrons (e). A diffusion flow of electrons appears, directed against the temperature gradient (from 1 to 2). As a result, the electron concentration at the hot end will decrease and at the cold end it will increase. An electric field E T will appear inside the conductor, directed from 1 to 2, i.e. against a temperature gradient, which prevents further charge separation. If current I is now passed through the conductor from an external source in the direction of the temperature gradient (Fig. 1a and Fig. 2a), then the electric field E T (associated with thermopower) will slow down the electrons, which leads to cooling of section 1-2 (Q t<0 ).

In Fig. Figure 2b shows the opposite situation: the electric field of thermopower E T accelerates conduction electrons, as a result of which Thomson heat is released in section 1-2 of the conductor (Q t >0).

Thus, a comparison of Figures 1a - 2a and 1b - 2b shows that the factors considered act in opposite directions, determining not only the magnitude, but also the sign of t and Q t. The value of the Thomson coefficient for most metals is quite small and does not exceed t » 10-5 V/K.

The Thomson effect, like other thermoelectric phenomena, is phenomenological in nature.

The Thomson coefficient is related to the Peltier coefficients p and thermopower a by the Thomson relation:

.

From measurements of the Thomson coefficient, it is possible to determine the thermopower coefficient of one material, and not the difference between the coefficients of two materials, as in the direct measurement of a and p. This allows by measuring t and determining a from it. in one of the metals, obtain an absolute thermoelectric scale.

The Thomson effect has no technical application, but it must be taken into account in accurate calculations of thermoelectric devices.

The effect was described and discovered in 1854 by William Thomson, who developed the thermodynamic theory of thermoelectricity.

Timing characteristics

Initiation time (log to -3 to 2);

Lifetime (log tc from 15 to 15);

Degradation time (log td from -3 to 2);

Time of optimal development (log tk from -2 to 3).

Diagram:

Technical implementations of the effect

Implementation of the Thomson effect in metals

For a quantitative study of the Thomson phenomenon, an experiment can be used, the diagram of which is shown in Fig. 3.

Scheme of the Thomson phenomenon research experiment

Rice. 3

Two identical rods AB and CD are taken from the test material (M). Ends A and C are connected together and maintained at the same temperature (for example, T A = T C = 1000 ° C). The temperatures of the free ends B and D are also equal (for example, T B = T D = 0 ° C). In the experiment, the temperature difference is measured for two points a and b, selected in such a way that in the absence of current their temperature is the same (T a = T b = T 0). When passing an electric current in one rod, the additional heat flow q passes from left to right (Q t >0), and in the other - from right to left (Q t<0 ). В результате между точками а и b возникает разность температур D Т=Т a -Т b , которая регистрируется термопарами. При изменении направления тока знак разности температур изменяется на противоположный.

The resulting contact potential difference is equal to:

Consider the case when three different conductors are brought into contact at the same temperature.

The potential difference between the ends of an open circuit will be equal to the algebraic sum of the potential jumps in all contacts:

whence using relations (1) and (2) we obtain:

As can be seen, the contact potential difference does not depend on the intermediate conductor.

Fig.1 Connection of three different conductors

If you close the electrical circuit shown in Figure 1, then the applied e. d.s. ε will be equal to the algebraic sum of all potential jumps that occur when bypassing the circuit:

ε = (ϕ 1 − ϕ 2 ) + (ϕ 2 − ϕ 3 ) + (ϕ 3 − ϕ 1 ) , (6)

whence it follows that ε =0.

Thus, when a closed electrical circuit is formed from several metal conductors at the same temperature, e.g. d.s. does not arise due to contact potential difference. For current to occur, the junctions of the conductors must be at different temperatures.

A contact potential difference occurs not only between two metals, but also between two semiconductors, a metal and a semiconductor, or two dielectrics.

1.2 THERMOELECTRIC PHENOMENA

It is known that the work function of electrons from a metal depends on temperature. Therefore, the contact potential difference also depends on temperature. If the temperature of the contacts of a closed circuit consisting of several metals is not the same, then the total e. d.s. circuit will not be equal to zero, and an electric current appears in the circuit. The phenomenon of the occurrence of thermoelectric current (Seebeck effect) and the associated Peltier and Thomson effects are classified as thermoelectric phenomena.

SEEBECK EFFECT

The Seebeck effect is the appearance of an electric current in a closed circuit consisting of dissimilar conductors connected in series, the contacts between which have different temperatures. This effect was discovered by the German physicist T. Seebeck in 1821.

Let's consider a closed circuit consisting of two conductors 1 and 2 with junction temperatures TA (contact A) and TV (contact B), shown in Figure 2.

We consider TA >TV. The electromotive force ε arising in a given circuit is equal to the sum of the potential jumps in both contacts:

Using relation (3), we obtain:

Consequently, e occurs in a closed circuit. d.s., the value of which is directly proportional to the temperature difference across the contacts. This is the thermoelectromotive force

(i.e. d.s.).

Qualitatively, the Seebeck effect can be explained as follows. The external forces that create thermopower are of kinetic origin. Since the electrons inside the metal are free, they can be considered as some kind of gas. The pressure of this gas must be the same along the entire length of the conductor. If different sections of the conductor have different temperatures, then a redistribution of the electron concentration is required to equalize the pressure. This leads to the generation of current.

The direction of current I is indicated in Fig. 2, corresponds to the case TA >TV, n1 >n2. If you change the sign of the contact temperature difference, then the direction of the current will change to the opposite.

PELTIER EFFECT

The Peltier effect is the phenomenon of the release or absorption of additional heat, in addition to Joule heat, in the contact of two different conductors, depending on the direction in which the electric current flows. The Peltier effect is the opposite of the Seebeck effect. If Joule heat is directly proportional to the square of the current strength, then Peltier heat is directly proportional to the current strength to the first power and changes its sign when the direction of the current changes.

Let's consider a closed circuit consisting of two different metal conductors through which current I΄ flows (Fig. 3). Let the direction of the current I΄ coincide with the direction of the current I shown in Fig. 2 for the case of TV >TA. Contact A, which would have a higher temperature in the Seebeck effect, will now cool, and contact B will heat up. The magnitude of Peltier heat is determined by the relation:

Q = П I / t,

where I΄ is the current strength, t is the time it passes, P is the Peltier coefficient, which depends on the nature of the contacting materials and temperature.

Due to the presence of contact potential differences at points A and B, contact electric fields with intensity E r arise. In contact A this field coincides with the direction

movement of electrons, and in contact B electrons move against the field Er. Since electrons are negatively charged, they accelerate in contact B, which leads to an increase in their kinetic energy. When colliding with metal ions, these electrons transfer energy to them. As a result, the internal energy at point B increases and the contact heats up. IN

At point A, the energy of the electrons, on the contrary, decreases, since the field E r slows them down. Accordingly, contact A is cooled, because electrons receive energy from ions at the sites of the crystal lattice.

THOMSON EFFECT

The Thomson effect is that when current passes through an unevenly heated conductor, additional heat is released or absorbed, similar to what occurs in the Peltier effect.

Since different sections of the conductor are heated differently, their physical states also differ. An unevenly heated conductor behaves like a system of physically dissimilar sections in contact. In the hotter part of the conductor, the electron energy is higher than in the less heated part. Therefore, in the process of movement, they give up part of their energy to metal ions at the nodes of the crystal lattice. As a result, heat is released. If electrons move to an area where the temperature is higher, then they increase their energy at the expense of the energy of the ions, and the metal cools.

2. PRACTICAL APPLICATIONS OF THERMOELECTRIC PHENOMENA

The Seebeck effect is widely used in temperature measuring devices and devices for direct conversion of thermal energy into electrical energy. The simplest such device consists of two dissimilar metal conductors M1 and M2 connected in series by soldering or welding. Such a circuit is called a thermoelectric converter (thermocouple), the conductors that make up the thermocouple are called electrodes, and their connections are called junctions. Figure 4 shows typical thermocouple connection circuits.

Fig.4. Typical thermocouple connection circuits

In Fig. 4a, measuring device 1 is connected using connecting wires 2 to the gap of one of the thermoelectrodes M1. This is a typical circuit for switching on a thermocouple with a temperature-controlled contact, where the temperature of one of the junctions is maintained constant (usually at the temperature of melting ice 273K).

In Fig. 4b, the measuring device is connected to the ends of thermoelectrodes M1 and M2; TA and TV are the temperatures of the “hot” and “cold” contacts of the thermocouple, respectively. This is a typical circuit for switching on a thermocouple with a non-thermostated “idle” contact when the temperature of the TV is equal to the ambient temperature.

Thermopower ε of a thermocouple in a small temperature range is proportional to the temperature difference between the junctions:

where αAB - coefficient t.e. d.s.(the value of e.m.f. arising from the difference

junction temperatures in 1K).

α 12 = dT d ε or α 12 = ∆ ∆ T ε .

The thermopower coefficient α 12 depends on the coefficients i.e. d.s. α 1 and α 2 substances of thermoelectrodes:

α 12 = α 1 − α 2 .

Coefficients i.e. d.s. of various substances are determined in relation to lead, for which α Pb = 0. Coefficient i.e. d.s. can have both positive and

negative value and generally depends on temperature.

To obtain the maximum value of i.e. d.s. it is necessary to select materials with the highest coefficients i.e. d.s. opposite sign.

With an increase in the temperature difference between the junctions, i.e. d.s. will not change linearly, so before measuring the temperature using a thermocouple, it is calibrated.

The range of temperatures measured using thermocouples is very large: from the temperature of liquid helium to several thousand degrees. To increase the accuracy of measurements, a thermocouple circuit with a thermostated contact is used (Fig. 4a).

Thermopower is very sensitive to the presence of chemical impurities in the junction. To protect the working junction of the thermocouple from external chemical influences, it can be placed in a protective chemical shell.

To increase thermopower, thermocouples are connected in series into thermopiles. All even-numbered junctions are maintained at one temperature, and odd-numbered junctions at another. The thermoelectromotive force of such a battery is equal to the sum of i.e. d.s. its individual elements

Fig.5 Thermopile

Miniature thermopiles, composed of thin strips of two different materials, are used to detect heated bodies and measure the electromagnetic radiation they emit. When combined with a sensitive galvanometer or electronic amplification device, they can detect, for example, the thermal radiation of a human hand at a distance of several meters. The high sensitivity of thermopiles allows them to be used as sensors for temperature alarm devices.

Thermopiles are also used as electric current generators. They are simple in design and do not contain mechanical moving parts. However, the use of metal thermoelements as generators is ineffective, so semiconductor materials are used to convert thermal energy into electrical energy.

Since the Peltier effect is associated with the processes of heat release and absorption, it is used in cooling devices (refrigerators).

3.CALIBRATION OF THERMOCOUPLE

For calibration, temperature values ​​known in advance with high accuracy are used (for example, the temperature of melting ice, boiling water, melting pure metals). During calibration, the cold junction of the thermocouple is thermostatically controlled in a Dewar vessel with melting ice (i.e., maintained at a temperature of 00 C), and the second junction is alternately immersed in baths with a known temperature. The calibration results are presented in the form of a calibration table or a dependence graph, i.e. d.s. on temperature.

APPLICATION

QUANTUM EXPLANATION OF THE ARISE OF T.E.D.S.

The emergence of thermoelectromotive force is due to three reasons:

1. temperature dependence of the Fermi level, which leads to the appearance of a contact component i.e. d.s.;

2. diffusion of charge carriers from the hot end to the cold, which determines the volumetric part i.e. d.s.;

3. the process of entrainment of electrons by phonons, which gives another component

– phonon.

Let's consider the first reason: Maximum kinetic energy of conduction electrons in a metal at 0K

called the Fermi energy. The Fermi level at absolute zero and the concentration of conduction electrons are related by the relation:

where h is Planck’s constant, m is the electron mass, n is the concentration of conduction electrons.

Dissimilar metals have different concentrations of conduction electrons, so the Fermi levels EF1 and EF2 will also be different. Let the concentration n2 in metal M2 be greater than the concentration n1 in metal M1. Let's consider the energy diagrams of two conductors M1 and M2, located at a short distance from each other (Fig. A1a). Let W0 be the energy of a free electron at rest in a vacuum, where its potential energy is zero. Then, relative to this level, the potential energy of the conduction electron in the metal is determined by its internal potential energy eφ and the effective work function A, and the kinetic energy depends on the temperature and the Fermi level. Let us denote the total energy of an electron in a metal by EF + еφ

If metals M1 and M2 are brought into contact (Fig. A1 b, c), electron diffusion will begin, during which electrons will move from metal 2 to metal 1, since n1

Rice. P1. Energy diagram of two metals:

a) there is no contact; b) in contact, but no balance; c) balance

Indeed, in metal M2 there are filled energy levels located above the Fermi level E F1 of the first metal. Electrons from these levels will move to the underlying free levels of the metal M1, which are located above the level E F1. As a result of diffusion, metal 2 will be charged positively, and metal 1 negatively, and the Fermi level of the first metal rises, and that of the second

falls. Thus, an electric field arises in the contact area, and

therefore and internal contact potential difference , which prevents further movement of electrons. At a certain value of the internal contact potential difference U 12 equilibrium will be established between the metals, and the Fermi levels will become equal. This will happen if the energies are equal

E F 1 + e ϕ 1= E F 2 + e ϕ 2 .

This implies the expression for the internal contact potential difference

If both junctions A and B of the conductors are at the same temperature, then the contact potential differences are equal and have opposite signs, that is, they compensate each other.

During the derivation it was assumed that metals are at low temperatures. However, the result will remain true at other temperatures: you just need to keep in mind that at T≠0K the Fermi level depends not only on the electron concentration, but also on temperature.

Provided that kT<<ЕF эта зависимость имеет следующий вид:

Consequently, if different temperatures are maintained at junctions A and B, then the sum of potential jumps at the junctions will be different from zero and will cause the appearance of an emf. This EMF, caused by contact potential differences, according to expression P2 is equal to:

ε k = U 12 (T A) + U 12 (T B) = 1 e ([ E F 1 (T A)− E F 2 (T A)] + [ E F 1 (T B)− E F 2 (T B) ] ) =

1 e ( [ E F 2 (T B) − E F 2 (T A) ] + [ E F1 (T B) − E F1 (T A) ] )

The last expression can be represented as follows:

The second reason determines the volumetric component i.e. d.s. associated with the non-uniform temperature distribution in the conductor. If the temperature gradient is maintained constant, then there will be a constant flow of heat through the conductor. In a metal, heat transfer is carried out mainly by the movement of conduction electrons. A diffusion flow of electrons appears, directed against the temperature gradient. As a result, the electron concentration at the hot end will decrease, and at the cold end

will increase. An electric field E r T appears inside the conductor, directed against the temperature gradient, which prevents further separation of charges (Fig. A2)

Rice. P2 The emergence of i.e. d.s. in a homogeneous material due to spatial inhomogeneity of temperature.

Thus, in an equilibrium state, the presence of a temperature gradient along the sample creates a constant potential difference at its ends. This is the diffusion (or volumetric) component, i.e. d.s., which is determined by the temperature dependence of the concentration of charge carriers and their mobility. In this case, the electric field arises in the volume of the metal, and not at the contacts themselves.

Third source i.e. d.s. – the effect of electron dragging by phonons. In the presence of a temperature gradient along the conductor, a drift of phonons (quanta of energy from elastic vibrations of the lattice) occurs, directed from the hot end to the cold. Colliding with electrons, phonons impart directed motion to them, dragging them along with them. As a result, a negative charge will accumulate near the cold end of the sample (and a positive one at the hot end) until the resulting potential difference balances the entrainment effect. This potential difference represents an additional component i.e. d.s., the contribution of which at low temperatures becomes decisive:

where β 1 = d dT ϕ - volumetric coefficient e.g. d.s. in metal M1.

where β 2 = d dT ϕ - volumetric coefficient i.e. d.s. in metal M2.

The sum of all these emfs forms the thermoelectromotive force

εT = εk + ε A 21 + ε B 12. (P7)

Substituting expressions (A4), (A5) and (A6) into equality (A7), we obtain

The quantity α = β − 1 e dE dT F is called the coefficient i.e. d.s. and is a function

temperature.

The absolute values ​​of all thermoelectric coefficients increase with decreasing carrier concentration. In metals, the concentrations of free electrons are very high and not

depend on temperature; The electron gas is in a degenerate state and therefore the Fermi level, energy and speed of electrons also weakly depend on temperature. Therefore, the thermopower coefficients of “classical” metals are very small (of the order of several μV/K). For semiconductors, α can exceed 1000 µV/K.

Using coefficient α, we present expression (A8) in the form:

where α 12 = α 1 − α 2 - is called differential or specific thermoelectromotive

the strength of a given pair of metals.

If α 12 weakly depends on temperature, then formula (A9) can be approximately represented as:

ε = α 12 (T B − T A ) (A10)

ORDER OF PERFORMANCE OF WORK AND PROCESSING OF MEASUREMENT RESULTS FOR AUD. 317

1. Prepare the digital universal voltmeter V7-23 for operation; to do this, press the “network” button on the front panel of the device, and then the “auto” button. automatic setting of the measurement limit.

2. Connect a standard thermocouple to the B7-23 digital voltmeter. To do this, move the switch “P” of the thermocouple block to the “TP0” position.

3. Set the load current In = 0.6 A at the thermocouple heater source. To turn on the heating of the working junctions of the reference and test thermocouples, set the network toggle switch of the heater power supply to the “on” position.

4. When the temperature of the thermocouple heater reaches, at which the EMF of the reference thermocouple reaches the value ε 0 = 0.5 mV,

It is necessary to connect the thermocouple under study to the input of the digital voltmeter V7-23 instead of the reference thermocouple. To do this, the switch “P” of the thermocouple block should be quickly moved to the “TPn” position and the resulting value of the emf of the thermocouple under study ε n should be entered into the table of measurement results.

Table 1

5. Increase the heater current to 0.8A.

6. Using the “P” switch again, connect the reference thermocouple to the V7-23 digital voltmeter.

and when the EMF of the reference thermocouple reaches the value ε 0 = 1.00 mV

switch “P” to the position corresponding to the measurement of the EMF of the thermocouple under study. The resulting value of the emf of the thermocouple under study ε n should also be entered in Table 1 of the measurement results.

7. Increase heater current by 0.1A

and at the EMF value of the reference thermocouple ε 0 = 1.50 mV

switch “P” to the position corresponding to the measurement of the EMF of the thermocouple under study ε and enter the measurement results in table 1.

8. In a similar way, increasing the heater current according to the recommendations in Table 1, measure the EMF of the thermocouple under study at the EMF values ​​of the reference thermocouple2.00mV; 2.50mV; 3.00mV; 3.50mV; 4.00mV; 4.50mV; 5.00mV; 5.50mV; 6.00mV;

6.50mV; 7.00mV.

9. Based on the results of measurements of the EMF of the reference thermocouple (see Table 1), using the calibration table of the values ​​of the EMF of the reference thermocouple, determine the temperature difference between the heated and cold ends of the thermocouples ∆t and write it in Table 1.

10. Determine the actual values ​​of the heater temperatures as t n = ∆ t + t av and

write down the obtained values ​​of the heater temperature in table 1. Here tav is the temperature of the medium.

11. Using the data from the calibration table and Table 1, construct on graph paper a graph of the dependence of the emf of the reference and test thermocouples on the temperature difference between the ends.

12. Using graphs of the dependence of the emf of the reference and test thermocouples on the temperature difference between the ends along the angle of inclination of the resulting straight lines, determine the values

coefficients t.e.α about 12 d.s. standard and α n 12 thermocouples under study according to the formula: α 12 = ∆ ε / ∆ t

13. Coefficient i.e. d.s.α 12 - a value depending on the coefficients i.e. d.s. substances α 1 and α 2 from which thermocouples are made, and is equal to their difference α 12 = α 1 − α 2.

14. Using the data in Table 2 for coefficients α 1 and α 2 i.e. d.s. materials from which the chromel-copel thermocouple used in this laboratory work as an exemplary thermocouple is made, calculate the value of the coefficient t.e. d.s. α about 12 this

thermocouples. Compare the obtained coefficient value i.e. d.s. α about 12 with the value of the coefficient i.e. d.s. α o 12 obtained when performing step 13 of the task.

15. Using the data in Table 2, determine the material from which thermoelectrode A of the thermocouple under study is made, if it is known that thermoelectrode B of the thermocouple under study is made of alumel, for which α 2 = -17.3 μV/deg

Table 2. Thermal emf coefficients of some materials relative to lead

Piezoelectricity. Piezoelectrics and their applications. Ferroelectrics and electrets, their properties and applications.

Piezoelectricity(from the Greek piézo - pressure and electricity) the phenomenon of the occurrence of dielectric polarization under the influence of mechanical stress (direct piezoelectric effect) and the occurrence of mechanical deformation under the influence of an electric field (inverse piezoelectric effect). Direct and reverse piezoelectric effects are observed in the same crystals - piezoelectrics. Piezoelectrics are crystalline substances in which, when compressed or stretched in certain directions, electrical polarization occurs even in the absence of electricity. fields. The first detailed study of piezoelectric effects was made in 1880 by the brothers J. and P. Curie on a Quartz crystal. Subsequently, piezoelectric properties were discovered in more than 1,500 substances, of which Rochelle salt, barium titanate, etc. are widely used. Piezoelectrics are widely used in technology, acoustics, radiophysics, etc. Their application is based on the conversion of electrical signals into mechanical ones and vice versa. Piezoelectrics are used in resonators that are part of generators, filters, various types of converters and sensors.

Ferroelectrics– dielectrics that have spontaneous polarization in a certain temperature range, i.e. polarization in the absence of an external electric field. These include the well-studied Rochelle salt (from which they get the name ferroelectrics) NaKC4H4O6ˑ4H2O and barium titanate BaTiO3. Ferroelectrics are widely used in many areas of modern technology: radio engineering, electroacoustics, quantum electronics and measurement technology.

Electrets– dielectrics that maintain a polarized state for a long time after removing the external electric field. There are several traditional applications for electrets. They are used as elements: converters of mechanical, thermal, acoustic (microphones), optical, radiation and other signals into electrical (current pulses), storage devices, electric motors, generators; filters and membranes; anti-corrosion structures; friction units; sealing systems; medical applicators, antithrombogenic implants

Thermoelectric phenomena are a set of physical phenomena caused by the relationship between thermal and electrical processes in metals and semiconductors. Thermoelectric phenomena include: Seebeck effect, Peltier effect, Thomson effect. To some extent, all these effects are the same, since the cause of all thermoelectric phenomena is a violation of thermal equilibrium in the flow of carriers (that is, the difference between the average energy of electrons in the flow and the Fermi energy).

Seebeck effect- the phenomenon of the occurrence of EMF in a closed electrical circuit consisting of series-connected dissimilar conductors, the contacts between which are at different temperatures. The Seebeck effect is that in a closed circuit consisting of dissimilar conductors, a thermo-EMF arises if the contact points are maintained at different temperatures. A circuit that consists of only two different conductors is called a thermoelement or thermocouple. The magnitude of the resulting thermo-EMF, to a first approximation, depends only on the material of the conductors and the temperatures of the hot (T1) and cold (T2) contacts. In a small temperature range, the thermo-EMF can be considered proportional temperature difference: where is the thermoelectric ability of the pair (or thermo-EMF coefficient). In the simplest case, the thermo-emf coefficient is determined only by the materials of the conductors, however, strictly speaking, it also depends on temperature, and in some cases changes sign with a change in temperature. A more correct expression for thermal emf: The magnitude of thermo-emf is millivolts at a temperature difference of 100 K and a cold junction temperature of 0 °C (for example, a copper-constantan pair gives 4.25 mV, platinum-platinum-rhodium - 0.643 mV, nichrome-nickel - 4.1 mV.

The Peltier effect is a thermoelectric phenomenon in which heat is released or absorbed when an electric current passes at the point of contact (junction) of two dissimilar conductors. The amount of heat generated and its sign depend on the type of contacting substances, the direction and strength of the flowing electric current:

Q = P A B It = (P B -P A)It, where Q is the amount of heat released or absorbed; I is the current strength; t is the time the current flows; P is the Peltier coefficient, which is related to the thermo-EMF coefficient α second Thomson's relation P = αT, where T is the absolute temperature in K.

The Thomson effect is one of the thermoelectric phenomena, which consists in the fact that in a homogeneous unevenly heated conductor with a direct current, in addition to the heat released in accordance with the Joule-Lenz law, additional Thomson heat will be released or absorbed in the volume of the conductor depending on the direction of the current .The amount of Thomson heat is proportional to the current strength, time and temperature difference, depending on the direction of the current. In general, the amount of heat released in the volume dV is determined by the relation: where

Thomson coefficient.

The resulting contact potential difference is equal to:

Consider the case when three different conductors are brought into contact at the same temperature.

The potential difference between the ends of an open circuit will be equal to the algebraic sum of the potential jumps in all contacts:

whence using relations (1) and (2) we obtain:

As can be seen, the contact potential difference does not depend on the intermediate conductor.

Fig.1 Connection of three different conductors

If you close the electrical circuit shown in Figure 1, then the applied e. d.s. ε will be equal to the algebraic sum of all potential jumps that occur when bypassing the circuit:

ε = (ϕ 1 − ϕ 2 ) + (ϕ 2 − ϕ 3 ) + (ϕ 3 − ϕ 1 ) , (6)

whence it follows that ε =0.

Thus, when a closed electrical circuit is formed from several metal conductors at the same temperature, e.g. d.s. does not arise due to contact potential difference. For current to occur, the junctions of the conductors must be at different temperatures.

A contact potential difference occurs not only between two metals, but also between two semiconductors, a metal and a semiconductor, or two dielectrics.

1.2 THERMOELECTRIC PHENOMENA

It is known that the work function of electrons from a metal depends on temperature. Therefore, the contact potential difference also depends on temperature. If the temperature of the contacts of a closed circuit consisting of several metals is not the same, then the total e. d.s. circuit will not be equal to zero, and an electric current appears in the circuit. The phenomenon of the occurrence of thermoelectric current (Seebeck effect) and the associated Peltier and Thomson effects are classified as thermoelectric phenomena.

SEEBECK EFFECT

The Seebeck effect is the appearance of an electric current in a closed circuit consisting of dissimilar conductors connected in series, the contacts between which have different temperatures. This effect was discovered by the German physicist T. Seebeck in 1821.

Let's consider a closed circuit consisting of two conductors 1 and 2 with junction temperatures TA (contact A) and TV (contact B), shown in Figure 2.

We consider TA >TV. The electromotive force ε arising in a given circuit is equal to the sum of the potential jumps in both contacts:

Using relation (3), we obtain:

Consequently, e occurs in a closed circuit. d.s., the value of which is directly proportional to the temperature difference across the contacts. This is the thermoelectromotive force

(i.e. d.s.).

Qualitatively, the Seebeck effect can be explained as follows. The external forces that create thermopower are of kinetic origin. Since the electrons inside the metal are free, they can be considered as some kind of gas. The pressure of this gas must be the same along the entire length of the conductor. If different sections of the conductor have different temperatures, then a redistribution of the electron concentration is required to equalize the pressure. This leads to the generation of current.

The direction of current I is indicated in Fig. 2, corresponds to the case TA >TV, n1 >n2. If you change the sign of the contact temperature difference, then the direction of the current will change to the opposite.

PELTIER EFFECT

The Peltier effect is the phenomenon of the release or absorption of additional heat, in addition to Joule heat, in the contact of two different conductors, depending on the direction in which the electric current flows. The Peltier effect is the opposite of the Seebeck effect. If Joule heat is directly proportional to the square of the current strength, then Peltier heat is directly proportional to the current strength to the first power and changes its sign when the direction of the current changes.

Let's consider a closed circuit consisting of two different metal conductors through which current I΄ flows (Fig. 3). Let the direction of the current I΄ coincide with the direction of the current I shown in Fig. 2 for the case of TV >TA. Contact A, which would have a higher temperature in the Seebeck effect, will now cool, and contact B will heat up. The magnitude of Peltier heat is determined by the relation:

Q = П I / t,

where I΄ is the current strength, t is the time it passes, P is the Peltier coefficient, which depends on the nature of the contacting materials and temperature.

Due to the presence of contact potential differences at points A and B, contact electric fields with intensity E r arise. In contact A this field coincides with the direction

movement of electrons, and in contact B electrons move against the field Er. Since electrons are negatively charged, they accelerate in contact B, which leads to an increase in their kinetic energy. When colliding with metal ions, these electrons transfer energy to them. As a result, the internal energy at point B increases and the contact heats up. IN

At point A, the energy of the electrons, on the contrary, decreases, since the field E r slows them down. Accordingly, contact A is cooled, because electrons receive energy from ions at the sites of the crystal lattice.

THOMSON EFFECT

The Thomson effect is that when current passes through an unevenly heated conductor, additional heat is released or absorbed, similar to what occurs in the Peltier effect.

Since different sections of the conductor are heated differently, their physical states also differ. An unevenly heated conductor behaves like a system of physically dissimilar sections in contact. In the hotter part of the conductor, the electron energy is higher than in the less heated part. Therefore, in the process of movement, they give up part of their energy to metal ions at the nodes of the crystal lattice. As a result, heat is released. If electrons move to an area where the temperature is higher, then they increase their energy at the expense of the energy of the ions, and the metal cools.

2. PRACTICAL APPLICATIONS OF THERMOELECTRIC PHENOMENA

The Seebeck effect is widely used in temperature measuring devices and devices for direct conversion of thermal energy into electrical energy. The simplest such device consists of two dissimilar metal conductors M1 and M2 connected in series by soldering or welding. Such a circuit is called a thermoelectric converter (thermocouple), the conductors that make up the thermocouple are called electrodes, and their connections are called junctions. Figure 4 shows typical thermocouple connection circuits.

Fig.4. Typical thermocouple connection circuits

In Fig. 4a, measuring device 1 is connected using connecting wires 2 to the gap of one of the thermoelectrodes M1. This is a typical circuit for switching on a thermocouple with a temperature-controlled contact, where the temperature of one of the junctions is maintained constant (usually at the temperature of melting ice 273K).

In Fig. 4b, the measuring device is connected to the ends of thermoelectrodes M1 and M2; TA and TV are the temperatures of the “hot” and “cold” contacts of the thermocouple, respectively. This is a typical circuit for switching on a thermocouple with a non-thermostated “idle” contact when the temperature of the TV is equal to the ambient temperature.

Thermopower ε of a thermocouple in a small temperature range is proportional to the temperature difference between the junctions:

where αAB - coefficient t.e. d.s.(the value of e.m.f. arising from the difference

junction temperatures in 1K).

α 12 = dT d ε or α 12 = ∆ ∆ T ε .

The thermopower coefficient α 12 depends on the coefficients i.e. d.s. α 1 and α 2 substances of thermoelectrodes:

α 12 = α 1 − α 2 .

Coefficients i.e. d.s. of various substances are determined in relation to lead, for which α Pb = 0. Coefficient i.e. d.s. can have both positive and

negative value and generally depends on temperature.

To obtain the maximum value of i.e. d.s. it is necessary to select materials with the highest coefficients i.e. d.s. opposite sign.

With an increase in the temperature difference between the junctions, i.e. d.s. will not change linearly, so before measuring the temperature using a thermocouple, it is calibrated.

The range of temperatures measured using thermocouples is very large: from the temperature of liquid helium to several thousand degrees. To increase the accuracy of measurements, a thermocouple circuit with a thermostated contact is used (Fig. 4a).

Thermopower is very sensitive to the presence of chemical impurities in the junction. To protect the working junction of the thermocouple from external chemical influences, it can be placed in a protective chemical shell.

To increase thermopower, thermocouples are connected in series into thermopiles. All even-numbered junctions are maintained at one temperature, and odd-numbered junctions at another. The thermoelectromotive force of such a battery is equal to the sum of i.e. d.s. its individual elements

Fig.5 Thermopile

Miniature thermopiles, composed of thin strips of two different materials, are used to detect heated bodies and measure the electromagnetic radiation they emit. When combined with a sensitive galvanometer or electronic amplification device, they can detect, for example, the thermal radiation of a human hand at a distance of several meters. The high sensitivity of thermopiles allows them to be used as sensors for temperature alarm devices.

Thermopiles are also used as electric current generators. They are simple in design and do not contain mechanical moving parts. However, the use of metal thermoelements as generators is ineffective, so semiconductor materials are used to convert thermal energy into electrical energy.

Since the Peltier effect is associated with the processes of heat release and absorption, it is used in cooling devices (refrigerators).

3.CALIBRATION OF THERMOCOUPLE

For calibration, temperature values ​​known in advance with high accuracy are used (for example, the temperature of melting ice, boiling water, melting pure metals). During calibration, the cold junction of the thermocouple is thermostatically controlled in a Dewar vessel with melting ice (i.e., maintained at a temperature of 00 C), and the second junction is alternately immersed in baths with a known temperature. The calibration results are presented in the form of a calibration table or a dependence graph, i.e. d.s. on temperature.

APPLICATION

QUANTUM EXPLANATION OF THE ARISE OF T.E.D.S.

The emergence of thermoelectromotive force is due to three reasons:

1. temperature dependence of the Fermi level, which leads to the appearance of a contact component i.e. d.s.;

2. diffusion of charge carriers from the hot end to the cold, which determines the volumetric part i.e. d.s.;

3. the process of entrainment of electrons by phonons, which gives another component

– phonon.

Let's consider the first reason: Maximum kinetic energy of conduction electrons in a metal at 0K

called the Fermi energy. The Fermi level at absolute zero and the concentration of conduction electrons are related by the relation:

where h is Planck’s constant, m is the electron mass, n is the concentration of conduction electrons.

Dissimilar metals have different concentrations of conduction electrons, so the Fermi levels EF1 and EF2 will also be different. Let the concentration n2 in metal M2 be greater than the concentration n1 in metal M1. Let's consider the energy diagrams of two conductors M1 and M2, located at a short distance from each other (Fig. A1a). Let W0 be the energy of a free electron at rest in a vacuum, where its potential energy is zero. Then, relative to this level, the potential energy of the conduction electron in the metal is determined by its internal potential energy eφ and the effective work function A, and the kinetic energy depends on the temperature and the Fermi level. Let us denote the total energy of an electron in a metal by EF + еφ

If metals M1 and M2 are brought into contact (Fig. A1 b, c), electron diffusion will begin, during which electrons will move from metal 2 to metal 1, since n1

Rice. P1. Energy diagram of two metals:

a) there is no contact; b) in contact, but no balance; c) balance

Indeed, in metal M2 there are filled energy levels located above the Fermi level E F1 of the first metal. Electrons from these levels will move to the underlying free levels of the metal M1, which are located above the level E F1. As a result of diffusion, metal 2 will be charged positively, and metal 1 negatively, and the Fermi level of the first metal rises, and that of the second

falls. Thus, an electric field arises in the contact area, and

therefore and internal contact potential difference , which prevents further movement of electrons. At a certain value of the internal contact potential difference U 12 equilibrium will be established between the metals, and the Fermi levels will become equal. This will happen if the energies are equal

E F 1 + e ϕ 1= E F 2 + e ϕ 2 .

This implies the expression for the internal contact potential difference

If both junctions A and B of the conductors are at the same temperature, then the contact potential differences are equal and have opposite signs, that is, they compensate each other.

During the derivation it was assumed that metals are at low temperatures. However, the result will remain true at other temperatures: you just need to keep in mind that at T≠0K the Fermi level depends not only on the electron concentration, but also on temperature.

Provided that kT<<ЕF эта зависимость имеет следующий вид:

Consequently, if different temperatures are maintained at junctions A and B, then the sum of potential jumps at the junctions will be different from zero and will cause the appearance of an emf. This EMF, caused by contact potential differences, according to expression P2 is equal to:

ε k = U 12 (T A) + U 12 (T B) = 1 e ([ E F 1 (T A)− E F 2 (T A)] + [ E F 1 (T B)− E F 2 (T B) ] ) =

1 e ( [ E F 2 (T B) − E F 2 (T A) ] + [ E F1 (T B) − E F1 (T A) ] )

The last expression can be represented as follows:

The second reason determines the volumetric component i.e. d.s. associated with the non-uniform temperature distribution in the conductor. If the temperature gradient is maintained constant, then there will be a constant flow of heat through the conductor. In a metal, heat transfer is carried out mainly by the movement of conduction electrons. A diffusion flow of electrons appears, directed against the temperature gradient. As a result, the electron concentration at the hot end will decrease, and at the cold end

will increase. An electric field E r T appears inside the conductor, directed against the temperature gradient, which prevents further separation of charges (Fig. A2)

Rice. P2 The emergence of i.e. d.s. in a homogeneous material due to spatial inhomogeneity of temperature.

Thus, in an equilibrium state, the presence of a temperature gradient along the sample creates a constant potential difference at its ends. This is the diffusion (or volumetric) component, i.e. d.s., which is determined by the temperature dependence of the concentration of charge carriers and their mobility. In this case, the electric field arises in the volume of the metal, and not at the contacts themselves.

Third source i.e. d.s. – the effect of electron dragging by phonons. In the presence of a temperature gradient along the conductor, a drift of phonons (quanta of energy from elastic vibrations of the lattice) occurs, directed from the hot end to the cold. Colliding with electrons, phonons impart directed motion to them, dragging them along with them. As a result, a negative charge will accumulate near the cold end of the sample (and a positive one at the hot end) until the resulting potential difference balances the entrainment effect. This potential difference represents an additional component i.e. d.s., the contribution of which at low temperatures becomes decisive:

where β 1 = d dT ϕ - volumetric coefficient e.g. d.s. in metal M1.

where β 2 = d dT ϕ - volumetric coefficient i.e. d.s. in metal M2.

The sum of all these emfs forms the thermoelectromotive force

εT = εk + ε A 21 + ε B 12. (P7)

Substituting expressions (A4), (A5) and (A6) into equality (A7), we obtain

The quantity α = β − 1 e dE dT F is called the coefficient i.e. d.s. and is a function

temperature.

The absolute values ​​of all thermoelectric coefficients increase with decreasing carrier concentration. In metals, the concentrations of free electrons are very high and not

depend on temperature; The electron gas is in a degenerate state and therefore the Fermi level, energy and speed of electrons also weakly depend on temperature. Therefore, the thermopower coefficients of “classical” metals are very small (of the order of several μV/K). For semiconductors, α can exceed 1000 µV/K.

Using coefficient α, we present expression (A8) in the form:

where α 12 = α 1 − α 2 - is called differential or specific thermoelectromotive

the strength of a given pair of metals.

If α 12 weakly depends on temperature, then formula (A9) can be approximately represented as:

ε = α 12 (T B − T A ) (A10)

ORDER OF PERFORMANCE OF WORK AND PROCESSING OF MEASUREMENT RESULTS FOR AUD. 317

1. Prepare the digital universal voltmeter V7-23 for operation; to do this, press the “network” button on the front panel of the device, and then the “auto” button. automatic setting of the measurement limit.

2. Connect a standard thermocouple to the B7-23 digital voltmeter. To do this, move the switch “P” of the thermocouple block to the “TP0” position.

3. Set the load current In = 0.6 A at the thermocouple heater source. To turn on the heating of the working junctions of the reference and test thermocouples, set the network toggle switch of the heater power supply to the “on” position.

4. When the temperature of the thermocouple heater reaches, at which the EMF of the reference thermocouple reaches the value ε 0 = 0.5 mV,

It is necessary to connect the thermocouple under study to the input of the digital voltmeter V7-23 instead of the reference thermocouple. To do this, the switch “P” of the thermocouple block should be quickly moved to the “TPn” position and the resulting value of the emf of the thermocouple under study ε n should be entered into the table of measurement results.

Table 1

5. Increase the heater current to 0.8A.

6. Using the “P” switch again, connect the reference thermocouple to the V7-23 digital voltmeter.

and when the EMF of the reference thermocouple reaches the value ε 0 = 1.00 mV

switch “P” to the position corresponding to the measurement of the EMF of the thermocouple under study. The resulting value of the emf of the thermocouple under study ε n should also be entered in Table 1 of the measurement results.

7. Increase heater current by 0.1A

and at the EMF value of the reference thermocouple ε 0 = 1.50 mV

switch “P” to the position corresponding to the measurement of the EMF of the thermocouple under study ε and enter the measurement results in table 1.

8. In a similar way, increasing the heater current according to the recommendations in Table 1, measure the EMF of the thermocouple under study at the EMF values ​​of the reference thermocouple2.00mV; 2.50mV; 3.00mV; 3.50mV; 4.00mV; 4.50mV; 5.00mV; 5.50mV; 6.00mV;

6.50mV; 7.00mV.

9. Based on the results of measurements of the EMF of the reference thermocouple (see Table 1), using the calibration table of the values ​​of the EMF of the reference thermocouple, determine the temperature difference between the heated and cold ends of the thermocouples ∆t and write it in Table 1.

10. Determine the actual values ​​of the heater temperatures as t n = ∆ t + t av and

write down the obtained values ​​of the heater temperature in table 1. Here tav is the temperature of the medium.

11. Using the data from the calibration table and Table 1, construct on graph paper a graph of the dependence of the emf of the reference and test thermocouples on the temperature difference between the ends.

12. Using graphs of the dependence of the emf of the reference and test thermocouples on the temperature difference between the ends along the angle of inclination of the resulting straight lines, determine the values

coefficients t.e.α about 12 d.s. standard and α n 12 thermocouples under study according to the formula: α 12 = ∆ ε / ∆ t

13. Coefficient i.e. d.s.α 12 - a value depending on the coefficients i.e. d.s. substances α 1 and α 2 from which thermocouples are made, and is equal to their difference α 12 = α 1 − α 2.

14. Using the data in Table 2 for coefficients α 1 and α 2 i.e. d.s. materials from which the chromel-copel thermocouple used in this laboratory work as an exemplary thermocouple is made, calculate the value of the coefficient t.e. d.s. α about 12 this

thermocouples. Compare the obtained coefficient value i.e. d.s. α about 12 with the value of the coefficient i.e. d.s. α o 12 obtained when performing step 13 of the task.

15. Using the data in Table 2, determine the material from which thermoelectrode A of the thermocouple under study is made, if it is known that thermoelectrode B of the thermocouple under study is made of alumel, for which α 2 = -17.3 μV/deg

Table 2. Thermal emf coefficients of some materials relative to lead

One of the simplest and most important applications of the theory of irreversible processes is the establishment of the relationship between the Peltier effect and Thomson's heat. These phenomena are always associated with a temperature difference inside the material, i.e., with irreversible heat transfer by thermal conductivity. In addition, any attempt to measure Peltier and Thomson heat inevitably produces proportional and therefore always irreversible Joule heat.

The first application of thermodynamics to consider these effects was made by Thomson, who simply ignored the irreversible processes associated with thermal conductivity and the formation of Joule heat. Thomson considered thermoelectric effects using the methods we discussed above for reversible processes. For example, the formula for Carnot efficiency, or the law of conservation of entropy in an isolated system, was used. The objection that an increase in entropy is necessarily associated with Joule heat and thermal conductivity was refuted by Thomson by the fact that Joule heat is proportional and therefore, with a sufficiently low current strength, it can become arbitrarily small compared to the Peltier and Thomson heats, which are proportional. However, neglecting thermal conductivity cannot be justified in this way. This, in particular, was shown by Boltzmann during a thorough analysis. Therefore, the justification that Thomson gave for the effects he discovered is not rigorous. Only taking into account irreversible effects, using Onsager's theory, we will give a more reasonable conclusion.

Rice. 123. To calculate the work obtained according to Fig. 122 during a continuous process.

Rice. 124. Scheme for determining the Peltier and Thomson coefficient.

Below we first present Thomson's theoretically flawless derivation, and then a more rigorous derivation.

Thomson's conclusion. For clarity, consider the diagram shown in Fig. 124.

Two wires made of dissimilar materials are soldered together at the ends. Let the temperatures of both junctions. To intermediately connect the voltage source V, wire B is cut. represents the voltage at which there is no current. With an infinitesimal change in V, a current of one direction or another can be passed through the wires. If we take a battery as a voltage source, it will be somewhat discharged when V increases, and, conversely, charged when it decreases. We use a system of thermostats that maintain a constant temperature at individual points in the circuit; First we will do this for the junctions, bringing them to temperatures. Then, by adjusting the voltage source V, we will achieve the absence of current. Let's call it thermo-e. d.s. thermoelement A temperature difference will be established along the wires. Let us now place each point of the wires in thermostats with the corresponding temperature. Thus, for all subsequent experiments, the temperature at each point turns out to be given. Now let's increase the voltage a little, obtaining a current that flows in the wire from a in wire B - from. In this case, you can notice that the thermostat supplies a certain amount of heat to the wires, proportional to

Let us introduce the definition of the Peltier coefficient. If current flows through the junctions between metals in the direction from A to B, then an amount of heat is taken per second from the thermostat surrounding the junction and supplied to the junction. Due to linearity, it inevitably follows

Thomson's coefficient. If there is a temperature difference in the wire (homogeneous) through which current flows, then heat is released in it, proportional to the temperature difference and the magnitude of the current. If the coordinate measured along the wire and a function is given, then in order to maintain the temperature of a section of the wire constant over time, heat must be supplied to it. Therefore, if the temperature increases on a certain section of the wire, then this section takes away heat from the thermostat per second

Let us denote by Thomson coefficients for metals Both that and are still unknown functions of temperature. Let us now apply both basic laws of thermodynamics to analyze the circuit shown in Fig. 124, neglecting thermal conductivity and Joule heat. Let us assume that V is slightly below the equilibrium value. In this case, the current flows in the direction in which work is being done on the voltage source (the battery is charging). Work is done per second. According to the first law, this work is equal to the heat removed from the thermostat. Hence we have.