How does the resistance of metals change with increasing temperature. Joule-Lenz law in classical electronic theory

Specific resistance, and therefore the resistance of metals, depends on temperature, increasing with temperature. The temperature dependence of conductor resistance is explained by the fact that

1. the intensity of dispersion (number of collisions) of charge carriers increases with increasing temperature;
2. their concentration changes when the conductor is heated.

Experience shows that at temperatures that are not too high and not too low, the dependences of resistivity and conductor resistance on temperature are expressed by the formulas:

\(~\rho_t = \rho_0 (1 + \alpha t) ,\) \(~R_t = R_0 (1 + \alpha t) ,\)

Where ρ 0 , ρ t - resistivity of the conductor substance, respectively, at 0 °C and t°C; R 0 , R t - conductor resistance at 0 °C and t°С, α - temperature coefficient of resistance: measured in SI in Kelvin minus the first power (K ​​-1). For metal conductors, these formulas are applicable starting at temperatures of 140 K and above.

Temperature coefficient The resistance of a substance characterizes the dependence of the change in resistance when heated on the type of substance. It is numerically equal to the relative change in resistance (resistivity) of the conductor when heated by 1 K.

\(~\mathcal h \alpha \mathcal i = \frac(1 \cdot \Delta \rho)(\rho \Delta T) ,\)

where \(~\mathcal h \alpha \mathcal i\) is the average value of the temperature coefficient of resistance in the interval Δ Τ .

For all metal conductors α > 0 and varies slightly with temperature. For pure metals α = 1/273 K -1. In metals, the concentration of free charge carriers (electrons) n= const and increase ρ occurs due to an increase in the intensity of scattering of free electrons on ions of the crystal lattice.

For electrolyte solutions α < 0, например, для 10%-ного раствора поваренной соли α = -0.02 K -1 . The resistance of electrolytes decreases with increasing temperature, since the increase in the number of free ions due to the dissociation of molecules exceeds the increase in the dispersion of ions during collisions with solvent molecules.

Dependency formulas ρ And R on temperature for electrolytes are similar to the above formulas for metal conductors. It should be noted that this linear dependence is preserved only in a small temperature range, in which α = const. At large temperature ranges, the dependence of the electrolyte resistance on temperature becomes nonlinear.

Graphically, the dependences of the resistance of metal conductors and electrolytes on temperature are shown in Figures 1, a, b.

At very low temperatures, close to absolute zero (-273 °C), the resistance of many metals abruptly drops to zero. This phenomenon is called superconductivity. The metal goes into a superconducting state.

The dependence of metal resistance on temperature is used in resistance thermometers. Usually, platinum wire is used as the thermometric body of such a thermometer, the dependence of whose resistance on temperature has been sufficiently studied.

Temperature changes are judged by changes in wire resistance, which can be measured. Such thermometers allow you to measure very low and very high temperatures when conventional liquid thermometers are unsuitable.

Literature

Aksenovich L. A. Physics in secondary school: Theory. Tasks. Tests: Textbook. allowance for institutions providing general education. environment, education / L. A. Aksenovich, N. N. Rakina, K. S. Farino; Ed. K. S. Farino. - Mn.: Adukatsiya i vyakhavanne, 2004. - P. 256-257.

Dependence of metal resistance on temperature. Superconductivity. Wiedemann-Franz law

Specific resistance depends not only on the type of substance, but also on its state, in particular, on temperature. The dependence of resistivity on temperature can be characterized by specifying the temperature coefficient of resistivity of a given substance:

It gives a relative increase in resistance with an increase in temperature by one degree.

ρ=ρ 0 (1+αt) (14.12)

where ρ 0 is the resistivity at 0ºС, ρ is its value at temperature tºС.

The temperature coefficient of resistance can be either positive or negative. For all metals, resistance increases with increasing temperature, and therefore for metals

α >0. For all electrolytes, unlike metals, the resistance always decreases when heated. The resistance of graphite also decreases with increasing temperature. For such substances α<0.

Based on the electronic theory of electrical conductivity of metals, it is possible to explain the dependence of the conductor resistance on temperature. As the temperature rises, its resistivity increases and its electrical conductivity decreases. Analyzing expression (14.7), we see that electrical conductivity is proportional to the concentration of conduction electrons and the mean free path <ℓ> , i.e. the more <ℓ> , the less interference collisions pose to the ordered movement of electrons. Electrical conductivity is inversely proportional to the average thermal velocity <υ τ > . The thermal velocity increases with increasing temperature in proportion to , which leads to a decrease in electrical conductivity and an increase in the resistivity of conductors. By analyzing formula (14.7), it is also possible to explain the dependence of γ and ρ on the type of conductor.

At very low temperatures of the order of 1-8ºK, the resistance of some substances sharply drops billions of times and practically becomes zero.

This phenomenon, first discovered by the Dutch physicist G. Kamerlingh-Onnes in 1911, is called superconductivity . Currently, superconductivity has been established in a number of pure elements (lead, tin, zinc, mercury, aluminum, etc.), as well as in a large number of alloys of these elements with each other and with other elements. In Fig. Figure 14.3 schematically shows the dependence of the resistance of superconductors on temperature.

The theory of superconductivity was created in 1958 by N.N. Bogolyubov. According to this theory, superconductivity is the movement of electrons in a crystal lattice without collisions with each other and with lattice atoms. All conduction electrons move as one flow of an inviscid ideal fluid, without interacting with each other or with the lattice, i.e. without experiencing friction. Therefore, the resistance of superconductors is zero. A strong magnetic field, penetrating into a superconductor, deflects electrons, and, disrupting the “laminar flow” of the electron flow, causes electrons to collide with the lattice, i.e. resistance arises.

In the superconducting state, energy quanta are exchanged between electrons, which leads to the creation of attractive forces between electrons that are greater than the Coulomb repulsive forces. In this case, pairs of electrons (Cooper pairs) are formed with mutually compensated magnetic and mechanical moments. Such pairs of electrons move in the crystal lattice without resistance.

One of the most important practical applications of superconductivity is its use in electromagnets with a superconducting winding. If there were no critical magnetic field that destroys superconductivity, then with the help of such electromagnets it would be possible to obtain magnetic fields of tens and hundreds of millions of amperes per centimeter. It is impossible to obtain such large constant fields using conventional electromagnets, since this would require colossal powers, and it would be practically impossible to remove the heat generated when the winding absorbs such large powers. In a superconducting electromagnet, the power consumption of the current source is negligible, and the power consumption for cooling the winding to helium temperature (4.2ºK) is four orders of magnitude lower than in a conventional electromagnet that creates the same fields. Superconductivity is also used to create memory systems for electronic mathematical machines (cryotronic memory elements).

In 1853, Wiedemann and Franz experimentally established that that the ratio of thermal conductivity λ to electrical conductivity γ for all metals at the same temperature is the same and proportional to their thermodynamic temperature.

This suggests that thermal conductivity in metals, like electrical conductivity, is due to the movement of free electrons. We will assume that electrons are similar to a monatomic gas, the thermal conductivity coefficient of which, according to the kinetic theory of gases, is equal to

>>Physics: Dependence of conductor resistance on temperature

Different substances have different resistivities (see § 104). Does resistance depend on the state of the conductor? on its temperature? Experience should give the answer.
If you pass current from the battery through a steel coil and then start heating it in the burner flame, the ammeter will show a decrease in current. This means that as the temperature changes, the resistance of the conductor changes.
If at a temperature equal to 0°C, the resistance of the conductor is equal to R0, and at temperature t it is equal R, then the relative change in resistance, as experience shows, is directly proportional to the change in temperature t:

Proportionality factor α called temperature coefficient of resistance. It characterizes the dependence of the resistance of a substance on temperature. The temperature coefficient of resistance is numerically equal to the relative change in the resistance of the conductor when heated by 1 K. For all metal conductors the coefficient α > 0 and varies slightly with temperature. If the range of temperature changes is small, then the temperature coefficient can be considered constant and equal to its average value over this temperature range. For pure metals α ≈ 1/273 K -1 . U of electrolyte solutions, the resistance does not increase with increasing temperature, but decreases. For them α < 0. Например, для 10%-ного раствора поваренной соли α ≈ -0.02 K -1 .
When a conductor is heated, its geometric dimensions change slightly. The resistance of a conductor changes mainly due to changes in its resistivity. You can find the dependence of this resistivity on temperature if you substitute the values ​​in formula (16.1)
. The calculations lead to the following result:

Because α changes little when the temperature of the conductor changes, then we can assume that the resistivity of the conductor depends linearly on temperature ( Fig.16.2).

The increase in resistance can be explained by the fact that with increasing temperature, the amplitude of vibrations of ions at the nodes of the crystal lattice increases, so free electrons collide with them more often, thereby losing the direction of movement. Although the coefficient α is quite small, taking into account the dependence of resistance on temperature when calculating heating devices is absolutely necessary. Thus, the resistance of the tungsten filament of an incandescent lamp increases by more than 10 times when current passes through it.
Some alloys, such as a copper-nickel alloy (constantan), have a very small temperature coefficient of resistance: α ≈ 10 -5 K -1 ; The resistivity of constantan is high: ρ ≈ 10 -6 Ohm m. Such alloys are used for the manufacture of standard resistances and additional resistances to measuring instruments, i.e. in cases where it is required that the resistance does not change noticeably with temperature fluctuations.
The dependence of metal resistance on temperature is used in resistance thermometers. Typically, the main working element of such a thermometer is platinum wire, the dependence of whose resistance on temperature is well known. Temperature changes are judged by changes in wire resistance, which can be measured.
Such thermometers allow you to measure very low and very high temperatures when conventional liquid thermometers are unsuitable.
The resistivity of metals increases linearly with increasing temperature. For electrolyte solutions it decreases with increasing temperature.

???
1. When does a light bulb consume more power: immediately after turning it on or after a few minutes?
2. If the resistance of the electric stove spiral did not change with temperature, then its length at rated power should be greater or less?

G.Ya.Myakishev, B.B.Bukhovtsev, N.N.Sotsky, Physics 10th grade

If you have corrections or suggestions for this lesson,

The resistance of metals is due to the fact that electrons moving in a conductor interact with ions of the crystal lattice and thereby lose part of the energy that they acquire in an electric field.

Experience shows that the resistance of metals depends on temperature. Each substance can be characterized by a constant value for it, called temperature coefficient of resistance α. This coefficient is equal to the relative change in the resistivity of the conductor when it is heated by 1 K: α =

where ρ 0 is the resistivity at temperature T 0 = 273 K (0°C), ρ is the resistivity at a given temperature T. Hence, the dependence of the resistivity of a metal conductor on temperature is expressed by a linear function: ρ = ρ 0 (1+ αT).

The dependence of resistance on temperature is expressed by the same function:

R = R 0 (1+ αT).

The temperature coefficients of resistance of pure metals differ relatively little from each other and are approximately equal to 0.004 K -1. A change in the resistance of conductors with a change in temperature leads to the fact that their current-voltage characteristic is not linear. This is especially noticeable in cases where the temperature of the conductors changes significantly, for example when operating an incandescent lamp. The figure shows its volt-ampere characteristic. As can be seen from the figure, the current strength in this case is not directly proportional to the voltage. However, one should not think that this conclusion contradicts Ohm's law. The dependence formulated in Ohm's law is valid only with constant resistance. The dependence of the resistance of metal conductors on temperature is used in various measuring and automatic devices. The most important of them is resistance thermometer. The main part of the resistance thermometer is a platinum wire wound on a ceramic frame. The wire is placed in a medium whose temperature needs to be determined. By measuring the resistance of this wire and knowing its resistance at t 0 = 0 °C (i.e. R 0), calculate the temperature of the medium using the last formula.

Superconductivity. However, until the end of the 19th century. it was impossible to check how the resistance of conductors depends on temperature in the region of very low temperatures. Only at the beginning of the 20th century. The Dutch scientist G. Kamerlingh Onnes managed to transform the most difficult to condense gas - helium - into a liquid state. The boiling point of liquid helium is 4.2 K. This made it possible to measure the resistance of some pure metals when they are cooled to a very low temperature.

In 1911, the work of Kamerlingh Onnes culminated in a major discovery. Studying the resistance of mercury as it was constantly cooled, he discovered that at a temperature of 4.12 K the resistance of mercury dropped abruptly to zero. Subsequently, he was able to observe the same phenomenon in a number of other metals when they were cooled to temperatures close to absolute zero. The phenomenon of complete loss of electrical resistance by a metal at a certain temperature is called superconductivity.

Not all materials can become superconductors, but their number is quite large. However, many of them were found to have a property that significantly hampered their use. It turned out that for most pure metals, superconductivity disappears when they are in a strong magnetic field. Therefore, when a significant current flows through a superconductor, it creates a magnetic field around itself and superconductivity disappears in it. Nevertheless, this obstacle turned out to be surmountable: it was found that some alloys, for example, niobium and zirconium, niobium and titanium, etc., have the property of maintaining their superconductivity at high current values. This allowed for more widespread use of superconductivity.

2. How does the resistivity of a conductor depend on its temperature? In what units is the temperature coefficient of resistance measured?

3. How can we explain the linear dependence of the resistivity of a conductor on temperature?

4. Why does the resistivity of semiconductors decrease with increasing temperature?

5. Describe the process of intrinsic conduction in semiconductors.