1. Characteristics of thermal radiation.
2. Kirchhoff's law.
3. Laws of black body radiation.
4. Radiation from the Sun.
5. Physical foundations of thermography.
6. Phototherapy. Therapeutic use of ultraviolet light.
7. Basic concepts and formulas.
8. Tasks.
Of the variety of electromagnetic radiation, visible or invisible to the human eye, one can single out one that 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 during thermal motion or the accelerated movement 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 spectral composition depend on body temperature, so 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 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 quantities.
Radiation flux(F) - energy emitted per unit of 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 = W].
Energetic 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/m2].
Both the radiation flux and the energetic luminosity depend on the structure of the substance and its temperature: Ф = Ф(Т), Re = Re(T).
The distribution of energetic luminosity over the spectrum of thermal radiation characterizes it 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.
Spectral density of energetic luminosity(r) or emissivity is called the ratio of energetic luminosity in a narrow part of the spectrum (dRe) to the width of this part (dλ):
Approximate form of spectral density and energetic luminosity (dRe) in the wavelength range from λ before λ + d λ, shown in Fig. 26.1.
Rice. 26.1. Spectral density of energetic luminosity
The dependence of the spectral density of energetic luminosity on wavelength is called radiation spectrum of the body. Knowledge of this dependence allows one to calculate the energetic luminosity of a 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 wavelength of the radiation. 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 magnitude 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:
Monochromatic absorption coefficient is a dimensionless quantity. Its values lie between zero and one: 0 ≤ α ≤ 1.
The function α = α(λ,T), expressing the dependence of the monochromatic absorption coefficient on wavelength and temperature, is called absorption capacity bodies. Its appearance can be quite complex. The simplest types of absorption are discussed below.
Pure black body- a body whose absorption coefficient is equal to unity for all wavelengths: α = 1. It absorbs all radiation incident on it.
In terms of their absorption properties, soot, black velvet, and platinum black are close to the absolutely black body. A very good model of a black body is a closed cavity with a small hole (O). The walls of the cavity are blackened (Fig. 26.2.
The beam entering this hole is almost completely absorbed after repeated 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 an absolutely black body is denoted by ε(λ,Τ). This function plays a vital role in the theory of thermal radiation. Its form was first established experimentally and then obtained theoretically (Planck's formula).
Absolutely white body- a body whose absorption coefficient is zero for all wavelengths: α = 0.
There are no truly white bodies in nature, but 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 of 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, human skin in the infrared region can be considered “gray” (α = 0.9).
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 is the same for all bodies and is equal to the spectral density of the energy luminosity of an absolutely black body:
Let us 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 black body radiation
The laws of blackbody radiation were established in the following sequence.
In 1879 J. Stefan experimentally, and in 1884 L. Boltzmann theoretically determined energetic luminosity absolutely black body.
Stefan-Boltzmann law - The energetic luminosity of a completely black body is proportional to the fourth power of its absolute temperature:
The values of 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 at which the maximum occurs emissivity absolutely black body. The ratio he obtained was named after him.
As the temperature increases, the maximum emissivity shifts to the left (Fig. 26.3).
Rice. 26.3. Illustration of Wien's displacement law
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 Stefan-Boltzmann and Wien laws, it is possible to determine the temperatures of bodies by measuring the radiation of these bodies. For example, this is how the temperature of the solar surface (~6000 K), the temperature at the epicenter of an explosion (~10 6 K), etc. are determined. The general name of 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 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 Stefan-Boltzmann and Wien laws.
26.4. Radiation from the Sun
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) and is used as a means of hardening. It can also have a negative effect on the body (burn, heat
The spectra of solar radiation at the boundary of the Earth's atmosphere and at the Earth's surface are different (Fig. 26.4).
Rice. 26.4. Solar radiation spectrum: 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 completely black body. The maximum emissivity occurs at λ 1max= 470 nm (blue color).
At 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 occurs at λ 2max= 555 nm (green-yellow), which corresponds to the best eye sensitivity.
The flux of thermal radiation from the Sun at the boundary of the Earth's atmosphere determines solar constant I.
The flux reaching the earth's surface is significantly less due to absorption in the atmosphere. Under the most favorable conditions (the sun at its zenith) it does not exceed 1120 W/m2. In Moscow at the time of the summer solstice (June) - 930 W/m2.
Both the power of solar radiation at the earth's surface and its spectral composition most significantly depend on the height of the Sun above the horizon. In Fig. Figure 26.5 shows smoothed distribution curves of solar energy: I - outside the atmosphere; II - when the Sun is at its 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 differently. Figure 26.6 shows the transparency of the atmosphere at a high altitude of the Sun.
26.5. Physical foundations of thermography
Human thermal radiation makes up a significant proportion of his heat losses. Radiative losses of a person are equal to the difference emitted flow and absorbed environmental radiation flux. The radiative loss power is calculated using the formula
where S is the surface area; δ - reduced absorption coefficient of skin (clothing), considered as gray body; T 1 - body surface temperature (clothing); T 0 - ambient temperature.
Consider the following example.
Let's calculate the power of radiative losses of an undressed person at an ambient temperature of 18°C (291 K). Let us assume: body surface area S = 1.5 m2; skin temperature T 1 = 306 K (33°C). The given skin absorption coefficient can be found from the table. 26.1 (δ = 5.1*10 -8 W/m 2 K 4). Substituting these values into formula (26.11), we obtain
P = 1.5*5.1*10 -8 * (306 4 - 291 4) ≈122 W.
Rice. 26.6. Transparency of the earth's atmosphere (in percent) for different parts of the spectrum at high altitudes of the Sun.
Human thermal radiation can be used as a diagnostic parameter.
Thermography - a diagnostic method based on measuring and recording thermal radiation from the surface of the human body or its individual parts.
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 changes in temperature (change color). Therefore, a color thermal “portrait” of the area of the body on which it is applied appears on the film.
A more advanced method is to use thermal imagers that convert infrared radiation into visible light. The body radiation is projected onto the thermal imager matrix using a special lens. After conversion, a detailed thermal portrait is formed on the screen. Areas of different temperatures differ in color or intensity. Modern methods make it possible to record differences in temperatures of up to 0.2 degrees.
Thermal portraits are used in functional diagnostics. Various pathologies of internal organs can form skin zones with altered temperatures on the surface. 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 treatments. Thus, during a thermographic examination of patients with psoriasis, it was found that in the presence of pronounced infiltration and hyperemia in the plaques, an increase in temperature is noted. A decrease in temperature to the level of surrounding areas in most cases indicates regression process on the skin.
An elevated temperature is often an indicator of infection. To determine a person's temperature, just look through an infrared device at his face and neck. For healthy people, the ratio of forehead temperature to carotid artery temperature ranges from 0.98 to 1.03. This ratio can be used for express diagnostics during epidemics for carrying out quarantine measures.
26.6. Phototherapy. Therapeutic uses of ultraviolet light
Infrared radiation, visible light and ultraviolet radiation are widely used in medicine. Let us recall their wavelength ranges:
Phototherapy called the use of infrared and visible radiation for medicinal purposes.
Penetrating into tissues, infrared rays (like visible ones) at the point of 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's lamp It is an incandescent lamp with a reflector that localizes the radiation in the required direction. The source of radiation is a 20-60 W incandescent lamp made of colorless or blue glass.
Light-thermal bath It is a semi-cylindrical frame consisting of two halves, movably connected to each other. On the inner surface of the frame, facing the patient, incandescent lamps with a power of 40 W are mounted. In such baths, the biological object is exposed to infrared and visible radiation, as well as heated air, the temperature of which can reach 70°C.
Sollux lamp It is a powerful incandescent lamp placed in a special reflector on a tripod. The radiation source is a 500 W incandescent lamp (tungsten filament temperature 2,800°C, maximum radiation occurs at a wavelength of 2 μm).
Rice. 26.8. Irradiators: Minin lamp (a), light-heat 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 (skin), various photochemical and photobiological reactions occur.
The radiation sources used are high pressure lamps(arc, mercury, tubular), luminescent lamps, gas discharge low pressure lamps, One of the varieties of which is 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) can 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 of zone A). Part or the entire body is exposed to radiation.
B-radiation has a vatimin-forming, anti-rickets effect.
C-radiation has a bactericidal effect. When irradiated, the structure of microorganisms and fungi is destroyed. C-radiation is created by special bactericidal lamps (Fig. 26.9).
Some treatment techniques use C-radiation to irradiate the blood.
Ultraviolet fasting. Ultraviolet radiation is necessary for the normal development and functioning of the body. Its deficiency leads to a number of serious diseases. Residents of extreme conditions face ultraviolet starvation
Rice. 26.9. Bactericidal irradiator (a), irradiator for the nasopharynx (b)
North, workers of the mining industry, metro, residents of large cities. In cities, the lack of ultraviolet radiation is associated with atmospheric air pollution with dust, smoke, and gases that retain the UV part of the solar spectrum. Room windows do not transmit UV rays with wavelength 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 the emergence of a number of pathologies. First of all, this applies to the consequences of uncontrolled sunbathing: burns, age spots, eye damage - the development of photoophthalmia. 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 effects 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 radiation to the eyes, after a latent period, inflammation of the cornea (keratitis) and mucous membranes (conjunctivitis) develops. This effect is caused by rays with a wavelength less than 310 nm. It is necessary to protect the eye from such rays. Particular 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 the table
26.8. Tasks
2.
Determine how many times the energy luminosities of areas of the human body surface that have temperatures of 34 and 33°C, respectively, differ?
3.
When diagnosing a breast tumor using 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 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 the room, containing equal masses of water at 90°C. One of them is nickel plated and the other is dark. Which kettle will cool down faster? Why?
Solution
According to Kirchhoff's law, the ratio of emission and absorption abilities is the same for all bodies. The nickel-plated teapot reflects almost all the light. Therefore, its absorption capacity is low. The emissivity is correspondingly low.
Answer: A dark kettle will cool down faster.
8. To destroy pest beetles, grain is exposed to infrared irradiation. Why do the bugs die but the grain does not?
Answer: bugs have black color, therefore they intensively absorb infrared radiation and die.
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 at the same temperature does not glow at all. Why?
Solution
See problem 7. A transparent body absorbs a small part of the light. Therefore, its emissivity is low.
Answer: the transparent body practically does not radiate, even when very heated.
10. Why do many animals sleep curled up in a ball in cold weather?
Answer: at the same time, the open surface of the body decreases and, accordingly, radiation losses decrease.
The energy that a body loses due to thermal radiation is characterized by the following quantities.
Radiation flux (F) - energy emitted 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 = W].
Energy luminosity (Re) - energy of thermal radiation emitted per unit time from a unit surface of a heated body:
In the SI system, energetic luminosity is measured - [W/m 2 ].
The radiation flux and energetic luminosity depend on the structure of the substance and its temperature: Ф = Ф(Т),
The distribution of energetic luminosity over the spectrum of thermal radiation characterizes it 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.
Spectral luminosity density (r) or emissivity The ratio of energetic luminosity in a narrow part of the spectrum (dRe) to the width of this part (dλ) is called:
Approximate form of spectral density and energetic luminosity (dRe) in the wavelength range from λ before λ + d λ, shown in Fig. 13.1.
Rice. 13.1. Spectral density of energetic luminosity
The dependence of the spectral density of energetic luminosity on wavelength is called body radiation spectrum.
Knowledge of this dependence allows one to calculate the energetic luminosity of a body in any wavelength range. The formula for calculating the energetic luminosity of a body in a range of wavelengths is: 
The total luminosity is: 
Bodies not only emit, but also absorb thermal radiation. The ability of a body to absorb radiation energy depends on its substance, temperature and wavelength of the radiation. The absorption capacity of the body is characterized by monochromatic absorption coefficient α.
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 magnitude 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: 
Monochromatic absorption coefficient is a dimensionless quantity. Its values lie between zero and one: 0 ≤ α ≤ 1.
Function α = α(λ,Τ) , expressing the dependence of the monochromatic absorption coefficient on wavelength and temperature, is called absorption capacity bodies. Its appearance can be quite complex. The simplest types of absorption are discussed below.
Pure black body is a body whose absorption coefficient is equal to unity for all wavelengths: α = 1.
Gray body is a body for which the absorption coefficient does not depend on the wavelength: α = const< 1.
Absolutely white body is a body whose absorption coefficient is zero for all wavelengths: α = 0.
Kirchhoff's law
Kirchhoff's law- the ratio of the emissivity of a body to its absorption capacity is the same for all bodies and is equal to the spectral density of the energy luminosity of an absolutely black body:
= /
Corollary of the law:
1. If a body at a given temperature does not absorb any radiation, then it does not emit it. Indeed, if for a certain wavelength the absorption coefficient α = 0, then r = α∙ε(λT) = 0
1. At the same temperature black body radiates more than any other. Indeed, for all bodies except black,α < 1, поэтому для них r = α∙ε(λT) < ε
2. If for a certain body we experimentally determine the dependence of the monochromatic absorption coefficient on wavelength and temperature - α = r = α(λT), then we can calculate the spectrum of its radiation.
THERMAL RADIATION Stefan Boltzmann's law Relationship between the energy luminosity R e and the spectral density of the energy luminosity of a 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 solar energy luminosity occurs at wavelength = 0.48 microns. Assuming that the Sun radiates as a black body, determine: 1) the temperature of its surface; 2) the power emitted by its surface. According to Wien's displacement law, Power emitted by 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 minute, if the absorption capacity of platinum A T = 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 furnace 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. How much of the power consumption is dissipated by the walls? The total power is determined by the sum of the Power released through the hole 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 force I = 1 A to a temperature T 1 = 1000 K. At what current strength will the filament be heated to a temperature T 2 = 3000 K? The absorption coefficients of tungsten and its resistivity corresponding to temperatures T 1, T 2 are equal to: a 1 = 0.115 and a 2 = 0.334; 1 = 25, Ohm m, 2 = 96, Ohm m The power emitted is equal to the power consumed from the electrical circuit in steady state Electric 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 occurs at a wavelength of .0 = 0.47 microns. Assuming that the Sun emits as a completely black body, find the intensity of solar radiation (i.e., radiation flux density) near the Earth outside its atmosphere. Luminous intensity (radiation 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 black body radiation spectrum, is 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 Wien’s 2nd law. Temperature T is expressed from Wien’s displacement law value C is given in SI units, in which the unit wavelength interval = 1 m. According to the conditions of the problem, it is necessary to calculate the spectral luminosity density calculated for the 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 = 500 nm. Taking the Sun to be a black body, determine: 1) the energetic luminosity R e of the Sun; 2) energy flow F e emitted 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 (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 during time t, is equal to the product of energy flow Ф e ((radiation power) by time: E=Ф e t. Therefore, Ф e =ms 2, whence m=Ф e/s 2.
Energy luminosity of the body- - a physical quantity that is a function of temperature and is numerically equal to the energy emitted by a body per unit time from a unit surface area in all directions and across the entire frequency spectrum. J/s m²=W/m²
Spectral density of energetic 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 be written in terms of wavelength
It can be proven that the spectral density of energy luminosity, expressed in terms of frequency and wavelength, are related by the relation:
Absolutely black body- a physical idealization used in thermodynamics, a body that absorbs all electromagnetic radiation incident on it in all ranges and does not reflect anything. Despite the name, a completely black body can itself emit electromagnetic radiation of any frequency and visually have color. The radiation spectrum of an absolutely black body is determined only by its temperature.
The importance of an absolutely black body in the question of the spectrum of thermal radiation of any (gray and colored) bodies in general, in addition to the fact that it represents the simplest non-trivial case, also lies 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 the radiation of an absolutely black body (and historically this was already done by the end of the 19th century, when the problem of radiation of an absolutely black body came to the fore).
Absolutely black bodies do not exist in nature, so in physics a model is used for experiments. It is a closed cavity with a small hole. Light entering through this hole will, after repeated reflections, be completely absorbed, and the outside of the hole will appear completely black. But when this cavity is heated, it will develop its own visible radiation. Since the radiation emitted by the inner walls of the cavity, before it leaves (after all, the hole is very small), in the overwhelming majority of cases will undergo a huge amount of new absorption and radiation, we can say with confidence that the radiation inside the cavity is in thermodynamic equilibrium with the walls. (In fact, the hole is not important for this model 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 equilibrium has already been established and the measurement is being carried out).
2. Kirchhoff's radiation law- a physical law established by the German physicist Kirchhoff in 1859. In its 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 radiation absorbed at a given frequency is called absorption capacity body. On the other hand, every heated body emits energy according to some law called emissivity of the body.
The values of and can vary greatly when moving from one body to another, however, according to Kirchhoff’s law of radiation, the ratio of emissive and absorption abilities does not depend on the nature of the body and is a universal function of frequency (wavelength) and temperature:
By definition, an absolutely black body absorbs all radiation incident 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 black body radiation. Determines the dependence of the radiation power of an absolutely black body on its temperature. Statement of the law: The radiation power of an absolutely black body is directly proportional to the surface area and the fourth power of the 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- Boltzmann constant, c- 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 , on temperature T. According to Wien's displacement law,l max =b/T
i.e. wavelength l max corresponding to the maximum value of the spectral density of energy luminosity r l , T black body, is inversely proportional to its thermodynamic temperature, b- Wien's constant: its experimental value is 2.9 10 -3 m K. Expression (199.2) is therefore called the law offsets The fault is that it shows a shift in the position of the maximum of the function r l , T as the temperature increases into the region of short wavelengths. Wien's law explains why, as the temperature of heated bodies decreases, long-wave radiation increasingly dominates in their spectrum (for example, the transition of white heat to red heat when a 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 frequency distribution of energy at different temperatures.
3. Let the walls of this cavity completely reflect the light falling on them. Let's place some body in the cavity that will emit light energy. An electromagnetic field will arise inside the cavity and, ultimately, it will be filled with radiation that is in a state of thermal equilibrium with the body. Equilibrium will also occur in the case when in some way the exchange of heat of the body under study with its surrounding environment is completely eliminated (for example, we will conduct this mental experiment in a vacuum, when there are no phenomena of thermal conductivity and convection). Only through the processes of emission and absorption of light will equilibrium be achieved: 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 surface of the body 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 a closed cavity, which, however, influence the time it takes to establish equilibrium. The energy density of the electromagnetic field in the cavity, as will be shown below, in a state of equilibrium is determined only by temperature.
To characterize equilibrium thermal radiation, not only the volumetric 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 radiation density, i.e., the average energy per unit volume of the electromagnetic field, distributed in the frequency interval from ω to ω + δω and related to the value of this interval. Obviously the meaning uω should depend significantly on temperature, so we denote it u(ω, T). Total Energy Density U(T) associated with u(ω, T) formula.
Strictly speaking, the concept of temperature is applicable only for equilibrium thermal radiation. Under equilibrium conditions, the temperature must remain constant. However, the concept of temperature is often also used to characterize incandescent bodies that are not in equilibrium with radiation. Moreover, with a slow change in the parameters of the system, at any given period of time it is possible to characterize its temperature, which will change slowly. So, for example, if there is no influx of heat and the radiation is due to a decrease in the energy of the luminous body, then its temperature will also decrease.
Let us establish a connection between the emissivity of a completely black body and the spectral density of equilibrium radiation. To do this, we calculate the energy flow incident on a single area located inside a closed cavity filled with electromagnetic energy of average density U ω . Let 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 propagating in a given solid angle is equal to the total energy filling the cavity. Flow of electromagnetic energy passing through a unit area per unit time
Replacing dΩ expression and integrating over ϕ within the limits (0, 2π) and over θ within the limits (0, π/2), we obtain the total energy flux incident on a unit area:
Obviously, under equilibrium conditions it is necessary to equate expression (13) of the emissivity of an absolutely black body rω, characterizing the energy flux emitted by the platform in a unit frequency interval near ω:
Thus, it is shown that the emissivity of a completely black body, up to a factor of 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 that f(ω, T)= u(ω, T) (15)
In conclusion, we point out that the radiation of an absolute black body (for example, light emitted by a small hole in a cavity) will no longer be in equilibrium. In particular, this radiation is not isotropic, since it does not propagate in all directions. But the energy distribution over the spectrum for such radiation will coincide with the spectral density of equilibrium radiation isotropically filling the space inside the cavity. This allows us to use relation (14), which is valid at any temperature. No other light source has a similar energy distribution across the spectrum. For example, an electric discharge in gases or a glow under the influence of chemical reactions have spectra that are significantly different from the glow of an absolutely black body. The distribution of energy across the spectrum of incandescent bodies also differs markedly from the glow of an absolutely black body, which was higher by comparing the spectra of a common light source (incandescent lamps with a tungsten filament) and an absolutely black body.
4. Based on the law of equidistribution of energy over degrees of freedom: for each electromagnetic oscillation there is, on average, an energy that is the sum of two parts kT. One half is contributed by the electrical component of the wave, and the second by the magnetic component. By itself, equilibrium radiation in a 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 set equal 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 vibration. Multiplying (2) by , we obtain the energy density that falls on the frequency interval dω:
Knowing the relationship between the emissivity of a completely black body f(ω, T) with equilibrium density of thermal radiation energy, 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 the agreement with experiment sharply diverges. 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 disaster, obviously contradicts experiment: the equilibrium between radiation and the radiating body must be established at finite values u(T).
Ultraviolet disaster- 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 paradox got its name due to the fact that the spectral power density of the radiation should have increased 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 which states that during thermal radiation energy is emitted and absorbed not continuously, but in separate quanta (portions). Each such quantum portion has energy , proportional to frequency ν radiation:
Where h or - the proportionality coefficient, 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's formula- expression for the spectral power density of black body radiation, which was obtained by Max Planck. For radiation energy density u(ω, T):
Planck's formula was obtained after it became clear that the Rayleigh-Jeans formula satisfactorily describes radiation only in the long-wave region. To derive the formula, Planck in 1900 made the assumption that electromagnetic radiation is emitted in the form of individual portions of energy (quanta), the magnitude of which is related to the frequency of the radiation by the expression:
The proportionality coefficient 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 limit in the bremsstrahlung X-ray spectrum.
X-ray radiation occurs when solid targets are bombarded by 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 is used for radiation, the rest is released at the anode in the form of heat, so the anodes are cooled with water. Once in the anode substance, the electrons experience strong inhibition 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– accelerating voltage.
>Noticeable emission is observed only with a sharp deceleration of fast electrons, starting from U~ 50 kV, while ( With– 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 short wavelength. This radiation has great penetrating power. According to classical electrodynamics, when an electron decelerates, radiation of all wavelengths from zero to infinity should arise. The wavelength at which the maximum radiation power occurs 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 of coordinates, but break off at finite values - this is short wavelength end of the X-ray spectrum.
It has been experimentally established that
The existence of the short-wave boundary directly follows from the quantum nature of radiation. Indeed, if radiation occurs due to the energy lost by the electron during braking, then the energy of the quantum cannot exceed the energy of the electron eU, i.e. , from here or .
In this experiment we can determine Planck's constant h. Of all the methods for determining Planck's constant, the method based on measuring the short-wavelength boundary of the X-ray bremsstrahlung spectrum is the most accurate.
7. Photo effect- this is the emission of electrons from a substance under the influence of light (and, generally speaking, any electromagnetic radiation). In condensed substances (solid and liquid) there is an external and internal photoelectric effect.
Laws of the photoelectric effect:
Formulation 1st law of photoelectric effect: the number of electrons emitted 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 limit of the photoelectric effect, that is, the minimum light frequency ν 0 (or 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 it, 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, performing a work function, leaves the metal: hν = A out + W e, Where W e- the maximum kinetic energy that an electron can have when leaving the metal.
From the law of conservation of energy, when representing light 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 the emitted electron (depending on the speed, either the kinetic energy of a relativistic particle can be calculated or not), ν is the frequency of the incident photon with energy hν, h- Planck's constant.
Work function- the difference between the minimum energy (usually measured in electron volts) that must be imparted to an electron for its “direct” removal from the volume of a solid body, and the Fermi energy.
“Red” border of the photo 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 output function A out electron: , where A out- work function for a specific photocathode, h is Planck's constant, and With- speed of light. Work function A out depends on the material of the photocathode and the condition of its surface. The emission of photoelectrons begins as soon as light of frequency or wavelength λ is incident on the photocathode.
d Φ e (\displaystyle d\Phi _(e)), emitted by a small area of the surface of the radiation source, to its area d S (\displaystyle dS) : M e = d Φ e d S . (\displaystyle M_(e)=(\frac (d\Phi _(e))(dS)).)It is also said that energetic luminosity is the surface density of the emitted radiation flux.
Numerically, the energetic luminosity is equal to the time-average modulus of the Poynting vector component perpendicular to the surface. In this case, averaging is carried out over a time significantly exceeding the period of electromagnetic oscillations.
The emitted radiation can arise in the surface itself, then they speak of a self-luminous surface. Another option is observed when the surface is illuminated from the outside. In such cases, some part of the incident flux necessarily returns back as a result of scattering and reflection. Then the expression for the energetic luminosity has the form:
M e = (ρ + σ) ⋅ E e , (\displaystyle M_(e)=(\rho +\sigma)\cdot E_(e),)Where ρ (\displaystyle \rho ) And σ (\displaystyle \sigma )- reflection coefficient and scattering coefficient of the surface, respectively, and - its irradiance.
Other names of energetic luminosity, sometimes used in the literature, but not provided for by GOST: - emissivity And integrated emissivity.
Spectral density of energetic luminosity
Spectral density of energetic luminosity M e , λ (λ) (\displaystyle M_(e,\lambda )(\lambda))- ratio of the magnitude of energetic luminosity d M e (λ) , (\displaystyle dM_(e)(\lambda),) falling on a small spectral interval d λ , (\displaystyle d\lambda ,), concluded between λ (\displaystyle \lambda) And λ + d λ (\displaystyle \lambda +d\lambda ), to the width of this interval:
M e , λ (λ) = d M e (λ) d λ . (\displaystyle M_(e,\lambda )(\lambda)=(\frac (dM_(e)(\lambda))(d\lambda )).)The SI unit is W m−3. Since wavelengths of optical radiation are usually measured in nanometers, in practice W m −2 nm −1 is often used.
Sometimes in literature M e , λ (\displaystyle M_(e,\lambda )) are called spectral emissivity.
Light analogue
M v = K m ⋅ ∫ 380 n m 780 n m M e , λ (λ) V (λ) d λ , (\displaystyle M_(v)=K_(m)\cdot \int \limits _(380~nm)^ (780~nm)M_(e,\lambda )(\lambda)V(\lambda)d\lambda ,)Where K m (\displaystyle K_(m))- maximum luminous radiation efficiency equal to 683 lm / W in the SI system. Its numerical value follows directly from the definition of candela.
Information about other basic energy photometric quantities and their light analogues is given in the table. Designations of quantities are given according to GOST 26148-84.
Energy photometric SI quantities| Name (synonym) | Quantity designation | Definition | SI units notation | Luminous magnitude |
|---|---|---|---|---|
| Radiation energy (radiant energy) | Q e (\displaystyle Q_(e)) or W (\displaystyle W) | Energy transferred by radiation | J | Light energy |
| Radiation flux (radiant flux) | Φ (\displaystyle \Phi ) e or P (\displaystyle P) | Φ e = d Q e d t (\displaystyle \Phi _(e)=(\frac (dQ_(e))(dt))) | W | Light flow |
| Radiation intensity (light energy intensity) | I e (\displaystyle I_(e)) | I e = d Φ e d Ω (\displaystyle I_(e)=(\frac (d\Phi _(e))(d\Omega ))) | W sr −1 | The power of light |
| Volumetric radiation energy density | U e (\displaystyle U_(e)) | U e = d Q e d V (\displaystyle U_(e)=(\frac (dQ_(e))(dV))) | J m −3 | Volumetric density of light energy |
| Energy brightness | L e (\displaystyle L_(e)) | L e = d 2 Φ e d Ω d S 1 cos ε (\displaystyle L_(e)=(\frac (d^(2)\Phi _(e))(d\Omega \,dS_(1)\, \cos \varepsilon ))) | W m−2 sr−1 | Brightness |
| Integral energy brightness | Λ e (\displaystyle \Lambda _(e)) | Λ e = ∫ 0 t L e (t ′) d t ′ (\displaystyle \Lambda _(e)=\int _(0)^(t)L_(e)(t")dt") | J m −2 sr −1 | Integral brightness |
| Irradiance (irradiance) | E e (\displaystyle E_(e)) | E e = d Φ e d S 2 (\displaystyle E_(e)=(\frac (d\Phi _(e))(dS_(2)))) | W m−2 |