Emissivity of the body rl ,T numerically equal to the energy of the body dWl radiated by the body from a unit of body surface, per unit of time at body temperature T, in the wavelength range from l to l +dl, those.

This value is also called the spectral density of the energy luminosity of the body.

Energy luminosity is related to the emissivity by the formula

absorbency body al ,T- a number showing what fraction of the energy of radiation incident on the surface of a body is absorbed by it in the wavelength range from l to l +dl, those.

The body for which al ,T=1 over the entire wavelength range, is called a black body (black body).

The body for which al ,T=const<1 over the entire wavelength range is called gray.

where- spectral density energy luminosity, or emissivity of the body .

Experience shows that the emissivity of a body depends on the temperature of the body (for each temperature, the maximum radiation lies in its own frequency range). Dimension .

Knowing the emissivity, you can calculate the energy luminosity:

called absorption capacity of the body . It also strongly depends on temperature.

By definition, it cannot be greater than one. For a body that completely absorbs radiation of all frequencies, . Such a body is called absolutely black (this is an idealization).

Body for which and is less than unity for all frequencies,called gray body (this is also an idealization).

There is a certain relationship between the emitting and absorbing ability of the body. Let's mentally carry out the following experiment (Fig. 1.1).

Rice. 1.1

Let there be three bodies inside a closed shell. The bodies are in a vacuum, therefore, the exchange of energy can occur only due to radiation. Experience shows that after some time such a system will come to a state of thermal equilibrium (all bodies and the shell will have the same temperature).

In this state, a body with a greater radiative capacity loses more energy per unit time, but, therefore, this body must also have a greater absorbing capacity:

Gustav Kirchhoff in 1856 formulated law and suggested black body model .

The ratio of emissivity to absorptivity does not depend on the nature of the body, it is the same for all bodies.(universal)function of frequency and temperature.

where - universal Kirchhoff function.

This function has a universal, or absolute, character.

The quantities and themselves, taken separately, can change extremely strongly when passing from one body to another, but their ratio constantly for all bodies (at a given frequency and temperature).

For an absolutely black body, therefore, for it, i.e. Kirchhoff's universal function is nothing but the radiance of a completely black body.

Absolutely black bodies do not exist in nature. Soot or platinum black have absorbing power, but only in a limited frequency range. However, a cavity with a small opening is very close in its properties to a completely black body. The beam that got inside, after multiple reflections, is necessarily absorbed, and the beam of any frequency (Fig. 1.2).

Rice. 1.2

The emissivity of such a device (cavity) is very close to f(ν, ,T). Thus, if the walls of the cavity are maintained at a temperature T, then radiation coming out of the hole is very close in spectral composition to the radiation of a completely black body at the same temperature.

Expanding this radiation into a spectrum, we can find the experimental form of the function f(ν, ,T) (Fig. 1.3), at different temperatures T 3 > T 2 > T 1 .

Rice. 1.3

The area covered by the curve gives the energy luminosity of a black body at the appropriate temperature.

These curves are the same for all bodies.

The curves are similar to the velocity distribution function of molecules. But there, the areas covered by the curves are constant, while here, with increasing temperature, the area increases significantly. This suggests that energy compatibility is highly dependent on temperature. Maximum radiation (emissivity) with increasing temperature is shifting towards higher frequencies.

The laws of thermal radiation

Any heated body emits electromagnetic waves. The higher the temperature of a body, the shorter the waves it emits. A body in thermodynamic equilibrium with its radiation is called absolutely black (AChT). The radiation of a black body depends only on its temperature. In 1900, Max Planck derived a formula by which, at a given temperature, a completely black body can calculate the intensity of its radiation.

The Austrian physicists Stefan and Boltzmann established a law expressing the quantitative relationship between the total emissivity and the temperature of a black body:

This law is called Stefan-Boltzmann law . The constant σ \u003d 5.67 ∙ 10 -8 W / (m 2 ∙ K 4) was called Stefan-Boltzmann constant .

All Planck curves have a markedly pronounced maximum attributable to the wavelength

This law is called Wien's law . So, for the Sun T 0 = 5800 K, and the maximum falls on the wavelength λ max ≈ 500 nm, which corresponds to the green color in the optical range.

As the temperature increases, the blackbody radiation maximum shifts to the short-wavelength part of the spectrum. A hotter star radiates most of its energy in the ultraviolet range, a less hot one in the infrared.

Photoelectric effect. Photons

photoelectric effect was discovered in 1887 by the German physicist G. Hertz and experimentally studied by A. G. Stoletov in 1888–1890. The most complete study of the phenomenon of the photoelectric effect was carried out by F. Lenard in 1900. By this time, the electron had already been discovered (1897, J. Thomson), and it became clear that the photoelectric effect (or, more precisely, the external photoelectric effect) consists in pulling electrons out of matter under the influence of light falling on it.

The layout of the experimental setup for studying the photoelectric effect is shown in fig. 5.2.1.

The experiments used a glass vacuum vessel with two metal electrodes, the surface of which was thoroughly cleaned. A voltage was applied to the electrodes U, the polarity of which could be changed using a double key. One of the electrodes (cathode K) was illuminated through a quartz window with monochromatic light of a certain wavelength λ. At a constant luminous flux, the dependence of the photocurrent strength was taken I from the applied voltage. On fig. 5.2.2 shows typical curves of such a dependence, obtained for two values ​​of the intensity of the light flux incident on the cathode.

The curves show that at sufficiently high positive voltages at the anode A, the photocurrent reaches saturation, since all the electrons ejected by light from the cathode reach the anode. Careful measurements have shown that the saturation current I n is directly proportional to the intensity of the incident light. When the voltage across the anode is negative, the electric field between the cathode and anode slows down the electrons. The anode can only reach those electrons whose kinetic energy exceeds | EU|. If the anode voltage is less than - U h, the photocurrent stops. measuring U h, it is possible to determine the maximum kinetic energy of photoelectrons:

Numerous experimenters have established the following basic laws of the photoelectric effect:

1. The maximum kinetic energy of photoelectrons increases linearly with increasing light frequency ν and does not depend on its intensity.
2. For every substance there is a so-called red border photo effect , i.e., the lowest frequency ν min at which an external photoelectric effect is still possible.
3. The number of photoelectrons pulled out by light from the cathode in 1 s is directly proportional to the light intensity.
4. The photoelectric effect is practically inertialess, the photocurrent appears instantly after the start of cathode illumination, provided that the light frequency ν > ν min .

All these laws of the photoelectric effect fundamentally contradicted the ideas of classical physics about the interaction of light with matter. According to wave concepts, when interacting with an electromagnetic light wave, an electron would have to gradually accumulate energy, and it would take a considerable time, depending on the intensity of light, for the electron to accumulate enough energy to fly out of the cathode. Calculations show that this time should have been calculated in minutes or hours. However, experience shows that photoelectrons appear immediately after the start of illumination of the cathode. In this model, it was also impossible to understand the existence of the red boundary of the photoelectric effect. The wave theory of light could not explain the independence of the energy of photoelectrons from the intensity of the light flux and the proportionality of the maximum kinetic energy to the frequency of light.

Thus, the electromagnetic theory of light proved unable to explain these regularities.

A way out was found by A. Einstein in 1905. A theoretical explanation of the observed laws of the photoelectric effect was given by Einstein on the basis of M. Planck's hypothesis that light is emitted and absorbed in certain portions, and the energy of each such portion is determined by the formula E = h v, where h is Planck's constant. Einstein took the next step in the development of quantum concepts. He came to the conclusion that light has a discontinuous (discrete) structure. An electromagnetic wave consists of separate portions - quanta, subsequently named photons. When interacting with matter, a photon transfers all of its energy h for one electron. Part of this energy can be dissipated by an electron in collisions with atoms of matter. In addition, part of the electron energy is spent on overcoming the potential barrier at the metal–vacuum interface. To do this, the electron must do the work function A depending on the properties of the cathode material. The maximum kinetic energy that a photoelectron emitted from the cathode can have is determined by the energy conservation law:

This formula is called Einstein's equation for the photoelectric effect .

Using the Einstein equation, one can explain all the regularities of the external photoelectric effect. From the Einstein equation, the linear dependence of the maximum kinetic energy on frequency and independence on light intensity, the existence of a red border, and the inertia of the photoelectric effect follow. The total number of photoelectrons leaving the cathode surface in 1 s should be proportional to the number of photons falling on the surface in the same time. It follows from this that the saturation current must be directly proportional to the intensity of the light flux.

As follows from the Einstein equation, the slope of the straight line expressing the dependence of the blocking potential U h from the frequency ν (Fig. 5.2.3), is equal to the ratio of Planck's constant h to the charge of an electron e:

where c is the speed of light, λcr is the wavelength corresponding to the red border of the photoelectric effect. For most metals, the work function A is a few electron volts (1 eV = 1.602 10 -19 J). In quantum physics, the electron volt is often used as a unit of energy. The value of Planck's constant, expressed in electron volts per second, is

Among metals, alkaline elements have the lowest work function. For example, sodium A= 1.9 eV, which corresponds to the red border of the photoelectric effect λcr ≈ 680 nm. Therefore, alkali metal compounds are used to create cathodes in photocells designed to detect visible light.

So, the laws of the photoelectric effect indicate that light, when emitted and absorbed, behaves like a stream of particles called photons or light quanta .

The photon energy is

it follows that the photon has momentum

Thus, the doctrine of light, having completed a revolution lasting two centuries, again returned to the ideas of light particles - corpuscles.

But this was not a mechanical return to Newton's corpuscular theory. At the beginning of the 20th century, it became clear that light has a dual nature. When light propagates, its wave properties appear (interference, diffraction, polarization), and when interacting with matter, corpuscular properties (photoelectric effect). This dual nature of light is called wave-particle duality . Later, the dual nature was discovered in electrons and other elementary particles. Classical physics cannot give a visual model of the combination of wave and corpuscular properties of micro-objects. The motion of micro-objects is controlled not by the laws of classical Newtonian mechanics, but by the laws of quantum mechanics. The black body radiation theory developed by M. Planck and Einstein's quantum theory of the photoelectric effect underlie this modern science.

1. Characteristics of thermal radiation.

2. Kirchhoff's law.

3. Laws of radiation of a black body.

4. Radiation of the Sun.

5. Physical foundations of thermography.

6. Light therapy. Therapeutic uses of ultraviolet light.

7. Basic concepts and formulas.

8. Tasks.

From the whole variety of electromagnetic radiation, visible or invisible to the human eye, one can be distinguished, which is inherent in all bodies - this is thermal radiation.

thermal radiation- electromagnetic radiation emitted by a substance and arising due to its internal energy.

Thermal radiation is caused by the excitation of particles of matter during collisions in the process of thermal motion or by the accelerated motion of charges (oscillations of crystal lattice ions, thermal motion of free electrons, etc.). It occurs at any temperature and is inherent in all bodies. A characteristic feature of thermal radiation is continuous spectrum.

The intensity of radiation and the spectral composition depend on body temperature, therefore, thermal radiation is not always perceived by the eye as a glow. For example, bodies heated to a high temperature emit a significant part of the energy in the visible range, and at room temperature almost all of the energy is emitted in the infrared part of the spectrum.

26.1. Characteristics of thermal radiation

The energy that a body loses due to thermal radiation is characterized by the following values.

radiation flux(F) - energy radiated per unit time from the entire surface of the body.

In fact, this is the power of thermal radiation. The dimension of the radiation flux is [J / s \u003d W].

Energy luminosity(Re) is the energy of thermal radiation emitted per unit time from a unit surface of a heated body:

The dimension of this characteristic is [W / m 2].

Both the radiation flux and the energy luminosity depend on the structure of the substance and its temperature: Ф = Ф(Т), Re = Re(T).

The distribution of energy luminosity over the spectrum of thermal radiation characterizes its spectral density. Let us denote the energy of thermal radiation emitted by a single surface in 1 s in a narrow range of wavelengths from λ before λ +d λ, via dRe.

The spectral density of energy luminosity(r) or emissivity is the ratio of energy luminosity in a narrow part of the spectrum (dRe) to the width of this part (dλ):

An approximate view of the spectral density and energy luminosity (dRe) in the wavelength range from λ before λ +d λ, shown in fig. 26.1.

Rice. 26.1. Spectral density of energy luminosity

The dependence of the spectral density of energy luminosity on the wavelength is called body radiation spectrum. Knowing this dependence allows you to calculate the energy luminosity of the body in any wavelength range:

Bodies not only emit, but also absorb thermal radiation. The ability of a body to absorb radiation energy depends on its substance, temperature, and radiation wavelength. The absorption capacity of the body is characterized by monochromatic absorption coefficientα.

Let a stream fall on the surface of the body monochromatic radiation Φ λ with wavelength λ. Part of this flow is reflected and part is absorbed by the body. Let us denote the value of the absorbed flux Φ λ abs.

Monochromatic absorption coefficient α λ is the ratio of the radiation flux absorbed by a given body to the magnitude of the incident monochromatic flux:

The monochromatic absorption coefficient is a dimensionless quantity. Its values ​​lie between zero and one: 0 ≤ α ≤ 1.

The function α = α(λ,Τ), which expresses the dependence of the monochromatic absorption coefficient on the wavelength and temperature, is called absorption capacity body. Her appearance can be quite complex. The simplest types of absorption are considered below.

Completely black body- such a body, the absorption coefficient of which is equal to unity for all wavelengths: α = 1. It absorbs all the radiation incident on it.

According to their absorption properties, soot, black velvet, platinum black are close to an absolutely black body. A very good model of a blackbody is a closed cavity with a small hole (O). The walls of the cavity are blackened in Fig. 26.2.

The beam entering this hole is almost completely absorbed after multiple reflections from the walls. Similar devices

Rice. 26.2. Black body model

used as light standards, used in measuring high temperatures, etc.

The spectral density of the energy luminosity of a completely black body is denoted by ε(λ, Τ). This function plays an important role in the theory of thermal radiation. Its form was first established experimentally, and then obtained theoretically (Planck's formula).

Absolutely white body- such a body, the absorption coefficient of which is equal to zero for all wavelengths: α = 0.

There are no truly white bodies in nature, however, there are bodies that are close to them in properties in a fairly wide range of temperatures and wavelengths. For example, a mirror in the optical part of the spectrum reflects almost all the incident light.

gray body is a body for which the absorption coefficient does not depend on the wavelength: α = const< 1.

Some real bodies have this property in a certain range of wavelengths and temperatures. For example, "gray" (α = 0.9) can be considered human skin in the infrared region.

26.2. Kirchhoff's law

The quantitative relationship between radiation and absorption was established by G. Kirchhoff (1859).

Kirchhoff's law- attitude emissivity body to his absorption capacity the same for all bodies and equal to the spectral density of the energy luminosity of a completely black body:

We note some consequences of this law.

1. If a body at a given temperature does not absorb any radiation, then it does not emit it. Indeed, if for

26.3. Laws of blackbody radiation

The laws of black body radiation were established in the following sequence.

In 1879, J. Stefan experimentally, and in 1884, L. Boltzmann theoretically determined energy luminosity absolutely black body.

Stefan-Boltzmann law - The energy luminosity of a blackbody is proportional to the fourth power of its absolute temperature:

The values ​​of the absorption coefficients for some materials are given in Table. 26.1.

Table 26.1. absorption coefficients

The German physicist W. Wien (1893) established a formula for the wavelength that accounts for the maximum emissivity absolutely black body. The ratio he received was named after him.

As the temperature rises, the maximum emissivity is shifting to the left (Fig. 26.3).

Rice. 26.3. Wien's displacement law illustration

In table. 26.2 shows the colors in the visible part of the spectrum, corresponding to the radiation of bodies at different temperatures.

Table 26.2. Colors of heated bodies

Using the laws of Stefan-Boltzmann and Wien, it is possible to determine the temperatures of bodies by measuring the radiation of these bodies. For example, the temperature of the surface of the Sun (~6000 K), the temperature at the epicenter of the explosion (~10 6 K), etc. are determined in this way. The common name for these methods is pyrometry.

In 1900, M. Planck received a formula for calculating emissivity absolutely black body theoretically. To do this, he had to abandon the classical ideas about continuity the process of radiation of electromagnetic waves. According to Planck, the radiation flux consists of separate portions - quanta, whose energies are proportional to the frequencies of light:

From formula (26.11) one can theoretically obtain the laws of Stefan-Boltzmann and Wien.

26.4. Sun radiation

Within the solar system, the Sun is the most powerful source of thermal radiation that determines life on Earth. Solar radiation has healing properties (heliotherapy), is used as a means of hardening. It can also have a negative effect on the body (burn, thermal

The spectra of solar radiation at the boundary of the earth's atmosphere and at the surface of the earth are different (Fig. 26.4).

Rice. 26.4. Spectrum of solar radiation: 1 - at the boundary of the atmosphere, 2 - at the surface of the Earth

At the boundary of the atmosphere, the spectrum of the Sun is close to the spectrum of a black body. The maximum emissivity is at λ1max= 470 nm (blue).

Near the Earth's surface, the spectrum of solar radiation has a more complex shape, which is associated with absorption in the atmosphere. In particular, it does not contain the high-frequency part of ultraviolet radiation, which is harmful to living organisms. These rays are almost completely absorbed by the ozone layer. The maximum emissivity is at λ2max= 555 nm (green-yellow), which corresponds to the best eye sensitivity.

The flux of solar thermal radiation at the boundary of the earth's atmosphere determines solar constant I.

The flux reaching the earth's surface is much less due to absorption in the atmosphere. Under the most favorable conditions (the sun at its zenith), it does not exceed 1120 W / m 2. In Moscow at the time of the summer solstice (June) - 930 W / m 2.

Both the power of solar radiation near the earth's surface and its spectral composition depend most significantly on the height of the Sun above the horizon. On fig. 26.5 the smoothed curves of distribution of energy of a sunlight are given: I - outside of an atmosphere; II - at the position of the Sun at the zenith; III - at a height of 30 ° above the horizon; IV - under conditions close to sunrise and sunset (10 ° above the horizon).

Rice. 26.5. Energy distribution in the solar spectrum at different heights above the horizon

Different components of the solar spectrum pass through the Earth's atmosphere in different ways. Figure 26.6 shows the transparency of the atmosphere at a high altitude of the Sun.

26.5. Physical basis of thermography

The thermal radiation of a person makes up a significant proportion of his thermal losses. The radiative loss of a person is equal to the difference emitted flow and absorbed environmental radiation flux. Radiative loss power is calculated by the formula

where S is the surface area; δ - reduced absorption coefficient of the skin (clothing), considered as gray body; T 1 - body surface temperature (clothing); T 0 - ambient temperature.

Consider the following example.

Let us calculate the power of radiative losses of a naked person at an ambient temperature of 18°C ​​(291 K). Let's take: the surface area of ​​the body S = 1.5 m 2; skin temperature T 1 = 306 K (33°C). The reduced absorption coefficient of the skin is found in Table. 26.1 (δ \u003d 5.1 * 10 -8 W / m 2 K 4). Substituting these values ​​into formula (26.11), we obtain

P \u003d 1.5 * 5.1 * 10 -8 * (306 4 - 291 4) ≈122 W.

Rice. 26.6. The transparency of the earth's atmosphere (in percent) for different parts of the spectrum at a high altitude of the Sun.

Human thermal radiation can be used as a diagnostic parameter.

Thermography - a diagnostic method based on the measurement and registration of thermal radiation from the surface of the human body or its individual sections.

The temperature distribution over a small area of ​​the body surface can be determined using special liquid crystal films. Such films are sensitive to small temperature changes (change color). Therefore, a color thermal “portrait” of the body area on which it is superimposed appears on the film.

A more advanced way is to use thermal imagers that convert infrared radiation into visible light. The radiation of the body is projected onto the matrix of the thermal imager using a special lens. After conversion, a detailed thermal portrait is formed on the screen. Areas with different temperatures differ in color or intensity. Modern methods allow fixing the difference in temperatures up to 0.2 degrees.

Thermal portraits are used in functional diagnostics. Various pathologies of the internal organs can form on the surface skin zones with a changed temperature. The detection of such zones indicates the presence of pathology. The thermographic method facilitates the differential diagnosis between benign and malignant tumors. This method is an objective means of monitoring the effectiveness of therapeutic methods of treatment. So, during a thermographic examination of patients with psoriasis, it was found that in the presence of severe infiltration and hyperemia in plaques, an increase in temperature is noted. A decrease in temperature to the level of the surrounding areas in most cases indicates regression process on the skin.

Fever is often an indicator of infection. To determine the temperature of a person, it is enough to look through an infrared device at his face and neck. For healthy people, the ratio of forehead temperature to carotid temperature ranges from 0.98 to 1.03. This ratio can be used in express diagnostics during epidemics for quarantine measures.

26.6. Phototherapy. Therapeutic uses of ultraviolet light

Infrared radiation, visible light and ultraviolet radiation are widely used in medicine. Recall the ranges of their wavelengths:

Phototherapy called the use of infrared and visible radiation for therapeutic purposes.

Penetrating into tissues, infrared rays (as well as visible ones) in the place of their absorption cause the release of heat. The depth of penetration of infrared and visible rays into the skin is shown in Fig. 26.7.

Rice. 26.7. Depth of radiation penetration into the skin

In medical practice, special irradiators are used as sources of infrared radiation (Fig. 26.8).

Minin lamp is an incandescent lamp with a reflector that localizes the radiation in the required direction. The radiation source is a 20-60 W incandescent lamp made of colorless or blue glass.

Light-thermal bath is a semi-cylindrical frame, consisting of two halves connected movably to each other. On the inner surface of the frame, facing the patient, incandescent lamps with a power of 40 W are fixed. In such baths, the biological object is affected by infrared and visible radiation, as well as heated air, the temperature of which can reach 70°C.

Lamp Sollux is a powerful incandescent lamp placed in a special reflector on a tripod. The radiation source is an incandescent lamp with a power of 500 W (tungsten filament temperature 2800°C, radiation maximum falls at a wavelength of 2 μm).

Rice. 26.8. Irradiators: Minin lamp (a), light-thermal bath (b), Sollux lamp (c)

Therapeutic uses of ultraviolet light

Ultraviolet radiation used for medical purposes is divided into three ranges:

When ultraviolet radiation is absorbed in tissues (in the skin), various photochemical and photobiological reactions occur.

used as radiation sources. high pressure lamps(arc, mercury, tubular), fluorescent lamps, gas discharge low pressure lamps one of the varieties of which are bactericidal lamps.

A radiation has an erythemal and tanning effect. It is used in the treatment of many dermatological diseases. Some chemical compounds of the furocoumarin series (for example, psoralen) are able to sensitize the skin of these patients to long-wave ultraviolet radiation and stimulate the formation of melanin pigment in melanocytes. The combined use of these drugs with A-radiation is the basis of a treatment method called photochemotherapy or PUVA therapy(PUVA: P - psoralen; UVA - ultraviolet radiation zone A). Part or all of the body is exposed to radiation.

B radiation has a vitamin-forming, anti-rachitic effect.

C radiation has a bactericidal effect. Irradiation destroys the structure of microorganisms and fungi. C-radiation is created by special bactericidal lamps (Fig. 26.9).

Some medical techniques use C-radiation to irradiate the blood.

Ultraviolet starvation. Ultraviolet radiation is necessary for the normal development and functioning of the body. Its deficiency leads to a number of serious diseases. Residents of the extreme region face ultraviolet starvation

Rice. 26.9. Bactericidal irradiator (a), nasopharyngeal irradiator (b)

North, workers in the mining industry, the subway, residents of large cities. In cities, the lack of ultraviolet radiation is associated with air pollution by dust, smoke, and gases that block the UV part of the solar spectrum. The windows of the premises do not transmit UV rays with a wavelength of λ< 310 нм. Значительно снижают УФ-поток загрязненные стекла и занавеси (тюлевые занавески снижают УФ-излучение на 20 %). Поэтому на многих производствах и в быту наблюдается так называемая «биологическая полутьма». В первую очередь страдают дети (возрастает вероятность заболевания рахитом).

The dangers of ultraviolet radiation

Exposure to excess doses of ultraviolet radiation on the body as a whole and on its individual organs leads to a number of pathologies. First of all, this refers to the consequences of uncontrolled sunbathing: burns, age spots, eye damage - the development of photophthalmia. The effect of ultraviolet radiation on the eye is similar to erythema, since it is associated with the decomposition of proteins in the cells of the cornea and mucous membranes of the eye. Living human skin cells are protected from the destructive action of UV rays "dead-

mi" cells of the stratum corneum of the skin. The eyes are deprived of this protection, therefore, with a significant dose of eye irradiation, inflammation of the horny (keratitis) and mucous membranes (conjunctivitis) of the eye develops after a latent period. This effect is due to rays with a wavelength less than 310 nm. It is necessary to protect the eye from such rays. Special attention should be paid to the blastomogenic effect of UV radiation, leading to the development of skin cancer.

26.7. Basic concepts and formulas

Table continuation

End of table

26.8. Tasks

2. Determine how many times the energy luminosities of areas of the surface of the human body differ, having temperatures of 34 and 33 ° C, respectively?

3. When diagnosing a breast tumor by thermography, the patient is given a glucose solution to drink. After some time, the thermal radiation of the body surface is recorded. Tumor tissue cells intensively absorb glucose, as a result of which their heat production increases. By how many degrees does the temperature of the skin area above the tumor change if the radiation from the surface increases by 1% (1.01 times)? The initial temperature of the body area is 37°C.

6. How much did the human body temperature increase if the radiation flux from the body surface increased by 4%? The initial body temperature is 35°C.

7. There are two identical kettles in a room containing equal masses of water at 90°C. One is nickel plated and the other is black. Which kettle will cool the fastest? Why?

Decision

According to Kirchhoff's law, the ratio of emitting and absorbing abilities is the same for all bodies. Nickel-plated teapot reflects almost all light. Therefore, its absorption capacity is small. Accordingly, the emissivity is also small.

Answer: the dark kettle will cool faster.

8. For the destruction of pest bugs, the grain is exposed to infrared radiation. Why do the bugs die, but the grain does not?

Answer: bugs have black color, therefore intensively absorb infrared radiation and perish.

9. When heating a piece of steel, we will observe a bright cherry-red heat at a temperature of 800 ° C, but a transparent rod of fused quartz does not glow at all at the same temperature. Why?

Decision

See problem 7. A transparent body absorbs a small part of the light. Therefore, its emissivity is small.

Answer: a transparent body practically does not radiate, even when it is strongly heated.

10. Why do many animals sleep curled up in cold weather?

Answer: in this case, the open surface of the body decreases and, accordingly, the radiation losses decrease.

Thermal radiation of bodies is called electromagnetic radiation that occurs due to that part of the internal energy of the body, which is related to the thermal motion of its particles.

The main characteristics of thermal radiation of bodies heated to a temperature T are:

1. Energy luminosityR (T ) -the amount of energy emitted per unit time per unit surface of the body, in the entire range of wavelengths. Depends on the temperature, nature and state of the surface of the radiating body. In the SI system R ( T ) has the dimension [W/m 2 ].

2. Spectral density of energy luminosityr (  ,T) =dW/ d - the amount of energy emitted by a unit of body surface per unit of time in a unit wavelength interval (near the considered wavelength ). Those. this quantity is numerically equal to the energy ratio dW emitted per unit area per unit time in a narrow range of wavelengths from  before  +d , to the width of this interval. It depends on the temperature of the body, the wavelength, and also on the nature and state of the surface of the radiating body. In the SI system r( , T) has the dimension [W/m 3 ].

Energy luminosity R(T) related to the spectral density of energy luminosity r( , T) in the following way:

(1) [W/m2]

3. All bodies not only radiate, but also absorb electromagnetic waves incident on their surface. To determine the absorption capacity of bodies in relation to electromagnetic waves of a certain wavelength, the concept is introduced monochromatic absorption coefficient-the ratio of the energy of a monochromatic wave absorbed by the body surface to the energy of an incident monochromatic wave:

The monochromatic absorption coefficient is a dimensionless quantity that depends on temperature and wavelength. It shows what fraction of the energy of the incident monochromatic wave is absorbed by the surface of the body. Value  ( , T) can take values ​​from 0 to 1.

Radiation in an adiabatically closed system (not exchanging heat with the environment) is called equilibrium. If a small hole is created in the wall of the cavity, the state of equilibrium will change slightly, and the radiation leaving the cavity will correspond to the equilibrium radiation.

If a beam is directed into such a hole, then after repeated reflections and absorption on the walls of the cavity, it will not be able to go back out. This means that for such a hole, the absorption coefficient ( , T) = 1.

The considered closed cavity with a small hole serves as one of the models absolutely black body.

Completely black bodya body is called that absorbs all the radiation incident on it, regardless of the direction of the incident radiation, its spectral composition and polarization (without reflecting or transmitting anything).

For a blackbody, the spectral density of energy luminosity is some universal function of wavelength and temperature f( , T) and does not depend on its nature.

All bodies in nature partially reflect the radiation incident on their surface and therefore do not belong to absolutely black bodies. If the monochromatic absorption coefficient of a body is the same for all wavelengths and lessunits(( , T) = Т = const<1),then such a body is called gray. The coefficient of monochromatic absorption of a gray body depends only on the temperature of the body, its nature and the state of its surface.

Kirchhoff showed that for all bodies, regardless of their nature, the ratio of the spectral density of energy luminosity to the monochromatic absorption coefficient is the same universal function of wavelength and temperature f( , T) , which is the spectral density of the energy luminosity of a black body :

Equation (3) is Kirchhoff's law.

Kirchhoff's law can be formulated like this: for all bodies of the system that are in thermodynamic equilibrium, the ratio of the spectral density of energy luminosity to the coefficient monochromatic absorption does not depend on the nature of the body, is the same function for all bodies, depending on the wavelength and temperature T.

From the foregoing and formula (3) it is clear that at a given temperature, those gray bodies that have a large absorption coefficient radiate more strongly, and absolutely black bodies radiate most strongly. Since for a completely black body(  , T)=1, then formula (3) implies that the universal function f( , T) is the spectral density of the energy luminosity of a black body

THERMAL RADIATION Stefan Boltzmann's law Relation between the energy luminosity Re and the spectral density of the energy luminosity of a completely black body Energy luminosity of a gray body Wien's displacement law (1st law) Dependence of the maximum spectral density of the energy luminosity of a black body on temperature (2nd law) Planck's formula

THERMAL RADIATION 1. The maximum spectral density of the energy luminosity of the Sun falls on the wavelength = 0.48 microns. Assuming that the Sun radiates as a black body, determine: 1) the temperature of its surface; 2) the power radiated by its surface. According to Wien's displacement law Power radiated from the surface of the Sun According to Stefan Boltzmann's law,

THERMAL RADIATION 2. Determine the amount of heat lost by 50 cm 2 from the surface of molten platinum in 1 min, if the absorption capacity of platinum AT = 0.8. The melting point of platinum is 1770 °C. The amount of heat lost by platinum is equal to the energy emitted by its hot surface According to Stefan Boltzmann's law,

THERMAL RADIATION 3. An electric oven consumes power P = 500 W. The temperature of its inner surface with an open small hole with a diameter of d = 5.0 cm is 700 °C. What part of the consumed power is dissipated by the walls? The total power is determined by the sum of the Power dissipated through the hole The power dissipated by the walls According to Stefan Boltzmann's law,

THERMAL RADIATION 4 A tungsten filament is heated in a vacuum with a current of I = 1 A up to a temperature T 1 = 1000 K. At what current strength will the filament heat up to a temperature T 2 = 3000 K? The absorption coefficients of tungsten and its resistivity corresponding to temperatures T 1, T 2 are: a 1 = 0.115 and a 2 = 0.334; 1 = 25, Ohm m, 2 = 96, Ohm m Radiated power is equal to the power consumed from the electrical circuit in steady state Electrical power released in the conductor According to Stefan Boltzmann's law,

THERMAL RADIATION 5. In the spectrum of the Sun, the maximum spectral density of energy luminosity falls on the wavelength 0 = 0.47 µm. Assuming that the Sun radiates as an absolutely black body, find the intensity of solar radiation (i.e., the radiation flux density) near the Earth outside its atmosphere. Luminous intensity (radiant intensity) Luminous flux According to the laws of Stefan Boltzmann and Wien

THERMAL RADIATION 6. Wavelength 0, which accounts for the maximum energy in the radiation spectrum of a black body, is equal to 0.58 microns. Determine the maximum spectral density of energy luminosity (r, T) max, calculated for the wavelength interval = 1 nm, near 0. The maximum spectral density of energy luminosity is proportional to the fifth power of temperature and is expressed by the 2nd Wien's law is given in SI units, in which a single wavelength interval = 1 m. According to the condition of the problem, it is required to calculate the spectral density of energy luminosity calculated for a wavelength interval of 1 nm, so we write out the value of C in SI units and recalculate it for a given wavelength interval:

THERMAL RADIATION 7. A study of the solar radiation spectrum shows that the maximum spectral density of energy luminosity corresponds to a wavelength of =500 nm. Taking the Sun for a black body, determine: 1) the energy luminosity R e of the Sun; 2) the energy flux Ф e radiated by the Sun; 3) the mass of electromagnetic waves (of all lengths) emitted by the Sun in 1 s. 1. According to the laws of Stefan Boltzmann and Wien 2. Luminous flux 3. The mass of electromagnetic waves (of all lengths) emitted by the Sun during the time t = 1 s, we determine by applying the law of proportionality of mass and energy E = ms 2. The energy of electromagnetic waves emitted in time t, is equal to the product of the energy flow Ф e ((radiation power) and time: E \u003d Ф e t. Therefore, Ф e \u003d ms 2, whence m \u003d Ф e / s 2.

Energy luminosity of the body- - a physical quantity that is a function of temperature and numerically equal to the energy emitted by the body per unit time per unit surface area in all directions and over the entire frequency spectrum. J/s m²=W/m²

Spectral density of energy luminosity- a function of frequency and temperature characterizing the distribution of radiation energy over the entire spectrum of frequencies (or wavelengths). , A similar function can also be written in terms of the wavelength

It can be proved that the spectral density of energy luminosity, expressed in terms of frequency and wavelength, are related by the relation:

Completely black body- physical idealization used in thermodynamics, a body that absorbs all electromagnetic radiation falling on it in all ranges and reflects nothing. Despite the name, a black body itself can emit electromagnetic radiation of any frequency and visually have a color. The radiation spectrum of a black body is determined only by its temperature.

The importance of a black body in the question of the spectrum of thermal radiation of any (gray and colored) bodies in general, in addition to being the simplest non-trivial case, is also in the fact that the question of the spectrum of equilibrium thermal radiation of bodies of any color and reflection coefficient is reduced by the methods of classical thermodynamics to the question of radiation from an absolutely black body (and historically this was already done by the end of the 19th century, when the problem of radiation from an absolutely black body came to the fore).

Absolutely black bodies do not exist in nature, therefore, in physics, a model is used for experiments. It is a closed cavity with a small opening. Light entering through this hole will be completely absorbed after repeated reflections, and the hole will look completely black from the outside. But when this cavity is heated, it will have its own visible radiation. Since the radiation emitted by the inner walls of the cavity, before it exits (after all, the hole is very small), in the vast majority of cases, it will undergo a huge number of new absorptions and radiations, it can be said with certainty that the radiation inside the cavity is in thermodynamic equilibrium with the walls. (In fact, the hole for this model is not important at all, it is only needed to emphasize the fundamental observability of the radiation inside; the hole can, for example, be completely closed, and quickly opened only when the balance has already been established and the measurement is being made).

2. Kirchhoff's radiation law is a physical law established by the German physicist Kirchhoff in 1859. In the modern formulation, the law reads as follows: The ratio of the emissivity of any body to its absorption capacity is the same for all bodies at a given temperature for a given frequency and does not depend on their shape, chemical composition, etc.

It is known that when electromagnetic radiation falls on a certain body, part of it is reflected, part is absorbed, and part can be transmitted. The fraction of absorbed radiation at a given frequency is called absorption capacity body . On the other hand, each heated body radiates energy according to a certain law, called emissivity of the body.

The values ​​and can vary greatly when moving from one body to another, however, according to the Kirchhoff radiation law, the ratio of the emitting and absorbing abilities does not depend on the nature of the body and is a universal function of frequency (wavelength) and temperature:

By definition, a completely black body absorbs all radiation falling on it, that is, for it. Therefore, the function coincides with the emissivity of an absolutely black body, described by the Stefan-Boltzmann law, as a result of which the emissivity of any body can be found based only on its absorption capacity.

Stefan-Boltzmann law- the law of radiation of a completely black body. Determines the dependence of the radiation power of an absolutely black body on its temperature. The wording of the law: The radiation power of an absolutely black body is directly proportional to the surface area and the fourth power of body temperature: P = Sεσ T 4 , where ε is the degree of emissivity (for all substances ε< 1, для абсолютно черного тела ε = 1).

Using Planck's law for radiation, the constant σ can be defined as where is Planck's constant, k is the Boltzmann constant, c is the speed of light.

Numerical value J s −1 m −2 K −4 .

The German physicist W. Wien (1864-1928), relying on the laws of thermo- and electrodynamics, established the dependence of the wavelength l max corresponding to the maximum of the function r l , T , temperature T. According to Wien's displacement law,l max \u003d b / T

i.e. the wavelength l max corresponding to the maximum value of the spectral density of energy luminosity r l , T blackbody is inversely proportional to its thermodynamic temperature, b- Wien's constant: its experimental value is 2.9 10 -3 m K. The expression (199.2) is therefore called the law bias The fault is that it shows the displacement of the position of the maximum of the function r l , T as the temperature increases to the region of short wavelengths. Wien's law explains why, as the temperature of heated bodies decreases, long-wave radiation predominates in their spectrum (for example, the transition of white heat to red when the metal cools).

Despite the fact that the Stefan-Boltzmann and Wien laws play an important role in the theory of thermal radiation, they are particular laws, since they do not give a general picture of the distribution of energy over frequencies at different temperatures.

3. Let the walls of this cavity completely reflect the light falling on them. Let's place in the cavity some body that will emit light energy. An electromagnetic field will arise inside the cavity and, in the end, it will be filled with radiation that is in a state of thermal equilibrium with the body. Equilibrium will also come in the case when, in any way, the exchange of heat of the investigated body with its environment is completely eliminated (for example, we will conduct this mental experiment in a vacuum, when there are no phenomena of heat conduction and convection). Only due to the processes of emission and absorption of light, equilibrium will necessarily come: the radiating body will have a temperature equal to the temperature of electromagnetic radiation isotropically filling the space inside the cavity, and each selected part of the body surface will emit as much energy per unit time as it absorbs. In this case, equilibrium must occur regardless of the properties of the body placed inside the closed cavity, which, however, affect the time it takes to establish equilibrium. The energy density of the electromagnetic field in the cavity, as will be shown below, in the state of equilibrium is determined only by the temperature.

To characterize equilibrium thermal radiation, not only the volume energy density is important, but also the distribution of this energy over the spectrum. Therefore, we will characterize the equilibrium radiation isotropically filling the space inside the cavity using the function u ω - spectral density of radiation, i.e., the average energy of a unit volume of the electromagnetic field, distributed in the frequency range from ω to ω + δω and related to the value of this interval. Obviously the value uω should depend significantly on temperature, so we denote it u(ω, T). Total energy density U(T) connected with u(ω, T) formula .

Strictly speaking, the concept of temperature is applicable only to equilibrium thermal radiation. At equilibrium, the temperature must remain constant. However, often the concept of temperature is also used to characterize incandescent bodies that are not in equilibrium with radiation. Moreover, with a slow change in the parameters of the system, it is possible in each given period of time to characterize its temperature, which will slowly change. So, for example, if there is no influx of heat and radiation is due to a decrease in the energy of a luminous body, then its temperature will also decrease.

Let us establish a connection between the emissivity of a black body and the spectral density of equilibrium radiation. To do this, we calculate the energy flux incident on a unit area located inside a closed cavity filled with medium-density electromagnetic energy U ω . Let the radiation fall on a unit area in the direction determined by the angles θ and ϕ (Fig. 6a) within the solid angle dΩ:

Since equilibrium radiation is isotropic, a fraction equal to the total energy filling the cavity propagates in a given solid angle. The flow of electromagnetic energy passing through a unit area per unit time

Replacing dΩ expression and integrating over ϕ within (0, 2π) and over θ within (0, π/2), we obtain the total energy flux incident on a unit area:

It is obvious that under equilibrium conditions it is necessary to equate the expression (13) of the emissivity of a completely black body rω , which characterizes the energy flux emitted by the site in a unit frequency interval near ω:

Thus, it is shown that the emissivity of an absolutely black body, up to a factor c/4, coincides with the spectral density of equilibrium radiation. Equality (14) must be satisfied for each spectral component of the radiation, therefore it follows from this that f(ω, T)= u(ω, T) (15)

In conclusion, we point out that the radiation of an absolute black body (for example, the light emitted by a small hole in the cavity) will no longer be in equilibrium. In particular, this radiation is not isotropic, since it does not propagate in all directions. But the distribution of energy over the spectrum for such radiation will coincide with the spectral density of equilibrium radiation isotropically filling the space inside the cavity. This makes it possible to use relation (14), which is valid at any temperature. No other light source has a similar energy distribution across the spectrum. So, for example, an electric discharge in gases or a glow under the action of chemical reactions has spectra that differ significantly from the glow of an absolutely black body. The distribution of energy over the spectrum of incandescent bodies also differs markedly from the glow of a blackbody, which was higher by comparing the spectra of a common light source (an incandescent lamp with a tungsten filament) and a blackbody.

4. Based on the law of equipartition of energy over degrees of freedom: for each electromagnetic oscillation, there is an average energy that is added from two parts kT. One half is introduced by the electrical component of the wave, and the other half by the magnetic component. By itself, the equilibrium radiation in the cavity can be represented as a system of standing waves. The number of standing waves in three-dimensional space is given by:

In our case, the speed v should be equal to c, moreover, two electromagnetic waves with the same frequency, but with mutually perpendicular polarizations, can move in the same direction, then (1) in addition should be multiplied by two:

So, Rayleigh and Jeans, energy was assigned to each oscillation. Multiplying (2) by , we obtain the energy density that falls on the frequency interval dω:

Knowing the relationship of the emissivity of a completely black body f(ω, T) with an equilibrium energy density of thermal radiation, for f(ω, T) we find: Expressions (3) and (4), are called Rayleigh-Jeans formula.

Formulas (3) and (4) agree satisfactorily with experimental data only for long wavelengths; at shorter wavelengths, agreement with experiment diverges sharply. Moreover, integration (3) over ω in the range from 0 to for the equilibrium energy density u(T) gives an infinitely large value. This result, called ultraviolet catastrophe, obviously, is in conflict with the experiment: the equilibrium between the radiation and the radiating body must be established at finite values u(T).

ultraviolet catastrophe- a physical term describing the paradox of classical physics, which consists in the fact that the total power of thermal radiation of any heated body must be infinite. The name of the paradox was due to the fact that the spectral power density of the radiation had to grow indefinitely as the wavelength shortened. In essence, this paradox showed, if not the internal inconsistency of classical physics, then at least an extremely sharp (absurd) discrepancy with elementary observations and experiment.

5. Planck's hypothesis- a hypothesis put forward on December 14, 1900 by Max Planck and consisting in the fact that during thermal radiation, energy is emitted and absorbed not continuously, but in separate quanta (portions). Each such portion-quantum has energy , proportional to the frequency ν radiation:

where h or - the coefficient of proportionality, later called Planck's constant. Based on this hypothesis, he proposed a theoretical derivation of the relationship between the temperature of a body and the radiation emitted by this body - Planck's formula.

Planck formula- an expression for the spectral power density of radiation from a black body, which was obtained by Max Planck. For the radiation energy density u(ω, T):

The Planck formula was obtained after it became clear that the Rayleigh-Jeans formula satisfactorily describes radiation only in the region of long waves. To derive the formula, Planck in 1900 made the assumption that electromagnetic radiation is emitted in the form of separate portions of energy (quanta), the magnitude of which is related to the radiation frequency by the expression:

The coefficient of proportionality was subsequently called Planck's constant, = 1.054 10 −27 erg s.

To explain the properties of thermal radiation, it was necessary to introduce the concept of the emission of electromagnetic radiation in portions (quanta). The quantum nature of radiation is also confirmed by the existence of a short-wavelength boundary of the bremsstrahlung spectrum.

X-ray radiation occurs when solid targets are bombarded with fast electrons. Here, the anode is made of W, Mo, Cu, Pt - heavy refractory or high thermal conductivity metals. Only 1–3% of the electron energy goes to radiation, the rest is released at the anode in the form of heat, so the anodes are cooled with water. Once in the anode material, the electrons experience strong deceleration and become a source of electromagnetic waves (X-rays).

The initial speed of an electron when it hits the anode is determined by the formula:

where U is the accelerating voltage.

> Noticeable radiation is observed only during a sharp deceleration of fast electrons, starting from U~ 50 kV, while ( with is the speed of light). In induction electron accelerators - betatrons, electrons acquire energy up to 50 MeV, = 0.99995 with. By directing such electrons to a solid target, we obtain X-ray radiation with a small wavelength. This radiation has a high penetrating power. According to classical electrodynamics, when an electron decelerates, radiation of all wavelengths from zero to infinity should appear. The wavelength at which the maximum radiation power falls should decrease as the electron speed increases. However, there is a fundamental difference from the classical theory: zero power distributions do not go to the origin, but break off at finite values ​​- this is short-wavelength edge of the X-ray spectrum.

It has been experimentally established that

The existence of a short-wavelength boundary follows directly from the quantum nature of radiation. Indeed, if radiation arises due to the energy lost by the electron during deceleration, then the energy of the quantum cannot exceed the energy of the electron EU, i.e. , from here or .

In this experiment, you can determine the Planck constant h. Of all the methods for determining Planck's constant, the method based on measuring the short-wavelength edge of the bremsstrahlung spectrum is the most accurate.

7. Photo effect- this is the emission of electrons of a substance under the influence of light (and, generally speaking, any electromagnetic radiation). In condensed substances (solid and liquid), external and internal photoelectric effects are distinguished.

Laws of the photoelectric effect:

Wording 1st law of photoelectric effect: the number of electrons ejected by light from the surface of a metal per unit time at a given frequency is directly proportional to the light flux illuminating the metal.

According to 2nd law of photoelectric effect, the maximum kinetic energy of electrons ejected by light increases linearly with the frequency of light and does not depend on its intensity.

3rd law of photoelectric effect: for each substance there is a red border of the photoelectric effect, that is, the minimum frequency of light ν 0 (or the maximum wavelength λ 0), at which the photoelectric effect is still possible, and if ν 0, then the photoelectric effect no longer occurs.

The theoretical explanation of these laws was given in 1905 by Einstein. According to him, electromagnetic radiation is a stream of individual quanta (photons) with energy hν each, where h is Planck's constant. With the photoelectric effect, part of the incident electromagnetic radiation is reflected from the metal surface, and part penetrates into the surface layer of the metal and is absorbed there. Having absorbed a photon, the electron receives energy from it and, doing the work function, leaves the metal: hν = A out + We, where We- the maximum kinetic energy that an electron can have when flying out of the metal.

From the law of conservation of energy, when light is represented in the form of particles (photons), Einstein's formula for the photoelectric effect follows: hν = A out + Ek

where A out- so-called. work function (the minimum energy required to remove an electron from a substance), Ek is the kinetic energy of an emitted electron (depending on the velocity, either the kinetic energy of a relativistic particle can be calculated or not), ν is the frequency of an incident photon with energy hν, h is Planck's constant.

Work function- the difference between the minimum energy (usually measured in electron volts), which must be imparted to an electron for its "direct" removal from the volume of a solid, and the Fermi energy.

"Red" border of the photoelectric effect- minimum frequency or maximum wavelength λ max light, at which the external photoelectric effect is still possible, that is, the initial kinetic energy of photoelectrons is greater than zero. The frequency depends only on the work function of the output. A out electron: , where A out is the work function for a specific photocathode, h is Planck's constant, and with is the speed of light. Work function A out depends on the material of the photocathode and the state of its surface. The emission of photoelectrons begins immediately, as soon as light falls on the photocathode with a frequency or wavelength .