Department of Education of the Kirov region. Ministry of General and Secondary Education
Municipal Educational Institution No. 204
"Elite school"
Scientific and technical direction.
Physics subject.
Pure black body
Performer: 11th grade student Maxim Karpov
Head: Bondina Marina Yurievna
Ekaterinburg 2007
Introduction page 2
Black body theory p.5
Practical part p.15
Conclusion p.17
Literature p.18
Introduction
At the end of the 19th century. Many scientists believed that the development of physics was completed for the following reasons:
1. For more than 200 years, the laws of mechanics, the theory of universal gravitation, and the laws of conservation (energy, momentum, angular momentum, mass and electric charge) have existed.
2. MKT was developed.
3. A solid foundation has been laid for thermodynamics.
4. Maxwell's theory of electromagnetism was formulated.
5. Relativistic law of conservation of energy - mass.
At the end of the 19th - beginning of the 20th centuries. discovered by V. Roentgen - X-rays (X-rays), A. Becquerel - the phenomenon of radioactivity, J. Thomson - electron. However, classical physics was unable to explain these phenomena.
A. Einstein's theory of relativity required a radical revision of the concept of space and time. Special experiments confirmed the validity of J. Maxwell's hypothesis about the electromagnetic nature of light. It could be assumed that the emission of electromagnetic waves by heated bodies is due to the oscillatory motion of electrons. But this assumption had to be confirmed by comparing theoretical and experimental data. To theoretically consider the laws of radiation, we used the black body model, i.e. a body that completely absorbs electromagnetic waves of any length and, accordingly, emits all lengths of electromagnetic waves.
I encountered the phenomenon of bodies absorbing energy while returning home on an autumn evening. That evening it was damp and I could hardly see the road I was walking on. And when snow fell a week later, the road was clearly visible. This is how I first encountered the phenomenon of an absolutely black body, a body that does not exist in nature, and I became interested in it. And since I spent a long time looking for the material that interested me, collecting it piece by piece, I decided to write a research paper in which all this would be connected and arranged in a logical order. Also, for a more convenient understanding of the theoretical part, I have given practical examples of experiments in which you can observe the above mentioned phenomenon.
While studying materials on the issue of reflection and absorption of light energy, I assumed that a completely black body is a body that absorbs all energy. However, is this possible in practice? I think I wasn’t the only one who found this question interesting. Therefore, the goal of my work is to prove that the emission of electromagnetic waves by heated bodies is due to the oscillatory motion of electrons. But this problem is relevant because it is not written about in our textbooks; in few reference books you can read about an absolutely black body. To do this, I set myself several tasks:
find as much information as possible on this problem;
study the black body theory;
experimentally confirm the theoretical concepts and phenomena presented in the abstract;
The abstract consists of the following parts:
introduction;
black body theory;
practical part;
conclusion.
Black body theory
1. History of the study of the issue.
Classical physics was unable to obtain a reasonable formula for spectral density (this formula is easily verified: an absolutely black body is an oven, a spectrometer is installed, the radiation is turned into a spectrum, and for each band of the spectrum one can find the energy in this wavelength interval). Classical physics could not only give the correct value of the function, it could not even give a reasonable value, namely, it turned out that this function increases with decreasing wavelength, and this is simply meaningless, this means that any body in the visible region emits, and at low frequencies it is even greater, and the total radiation energy tends to infinity. This means that there are phenomena in nature that cannot be described by the laws of classical physics.
At the end of the 19th century, the inconsistency of attempts to create a theory of black body radiation based on the laws of classical physics was revealed. From the laws of classical physics it followed that a substance should emit electromagnetic waves at any temperature, lose energy and lower the temperature to absolute zero. In other words. thermal equilibrium between matter and radiation was impossible. But this was in conflict with everyday experience.
This can be explained in more detail as follows. There is the concept of an absolutely black body - a body that absorbs electromagnetic radiation of any wavelength. The spectrum of its radiation is determined by its temperature. There are no absolutely black bodies in nature. The most accurate correspondence to an absolutely black body is a closed, opaque, hollow body with a hole. Any piece of a substance glows when heated and, with a further increase in temperature, becomes first red and then white. Color is almost independent of the substance; for an absolutely black body it is determined solely by its temperature. Let us imagine such a closed cavity, which is maintained at a constant temperature and which contains material bodies capable of emitting and absorbing radiation. If the temperature of these bodies at the initial moment differed from the temperature of the cavity, then over time the system (cavity plus bodies) will tend to thermodynamic equilibrium, which is characterized by the equilibrium between the energy absorbed and measured per unit time
G. Kirchhoff established that this state of equilibrium is characterized by a certain spectral distribution of the energy density of radiation contained in the cavity, and also that the function determining the spectral distribution (Kirchhoff function) depends on the temperature of the cavity and does not depend on the size of the cavity or its shape , nor from the properties of the material bodies placed in it. Since the Kirchhoff function is universal, i.e. is the same for any black body, then the assumption arose that its appearance is determined by some provisions of thermodynamics and electrodynamics. However, attempts of this kind turned out to be unsuccessful. From D. Rayleigh's law it followed that the spectral density of radiation energy should increase monotonically with increasing frequency, but the experiment indicated otherwise: at first the spectral density increased with increasing frequency, and then fell.
Solving the problem of black body radiation required a fundamentally new approach.
It was found by M. Planck.
In 1900, Planck formulated a postulate according to which matter can emit radiation energy only in finite portions proportional to the frequency of this radiation. This concept led to a change in the traditional principles underlying classical physics. The existence of discrete action indicated the relationship between the localization of an object in space and time and its dynamic state. L. de Broglie emphasized that “from the point of view of classical physics, this connection seems completely inexplicable and much more incomprehensible in the consequences to which it leads than the connection between spatial variables and time established by the theory of relativity. The quantum concept was destined to play a role in the development of physics huge role.
So, a new approach was found to explain the nature of the black body (in the form of a quantum concept).
2. Absorption capacity of the body.
To describe the process of absorption of radiation by bodies, we introduce the spectral absorption capacity of the body. To do this, having identified a narrow frequency interval from to , we will consider the radiation flux that falls on the surface of the body. If at the same time part of this flow is absorbed by the body, then the absorption capacity of the body at frequency will be defined as a dimensionless quantity
characterizing the fraction of frequency radiation incident on a body that is absorbed by the body.
Experience shows that any real body absorbs radiation of different frequencies differently depending on its temperature. Therefore, the spectral absorption capacity of a body is a function of frequency, the type of which changes with changes in body temperature.
By definition, the absorption capacity of a body cannot be greater than one. In this case, a body whose absorption capacity is less than unity and is the same over the entire frequency range is called a gray body.
A special place in the theory of thermal radiation is occupied by the absolutely black body. This is what G. Kirchhoff called a body whose absorption capacity is equal to unity at all frequencies and at all temperatures. A real body always reflects part of the energy of the radiation incident on it (Fig. 1.2). Even soot approaches the properties of a completely black body only in the optical range.
1 - absolutely black body; 2 - gray body; 3 - real body
The black body is the reference body in the theory of thermal radiation. And, although there is no absolutely black body in nature, it is quite simple to implement a model for which the absorption capacity at all frequencies will differ negligibly from unity. Such a model of an absolutely black body can be made in the form of a closed cavity (Fig. 1.3), equipped with a small hole, the diameter of which is significantly smaller than the transverse dimensions of the cavity. In this case, the cavity can have almost any shape and be made of any material.
A small hole has the property of almost completely absorbing radiation incident on it, and as the size of the hole decreases, its absorption capacity tends to unity. Indeed, radiation through the hole hits the walls of the cavity, being partially absorbed by them. With small hole sizes, the beam must undergo many reflections before it can exit the hole, that is, formally, be reflected from it. With multiple repeated reflections on the walls of the cavity, the radiation entering the cavity is almost completely absorbed.
Note that if the walls of the cavity are maintained at a certain temperature, then the hole will radiate, and this radiation can be considered with a high degree of accuracy as the radiation of a black body having a temperature. By studying the distribution of the energy of this radiation over the spectrum oC. Langley, E. Pringsheim, O. Lümmer, F. Kurlbaum, etc.), it is possible to experimentally determine the emissivity of a black body and . The results of such experiments at different temperatures are shown in Fig. 1.4.
From these considerations it follows that absorption capacity and body color are interrelated.
3. Kirchhoff's law.
Kirchhoff's law. There must be a connection between the emissive and absorption properties of any body. Indeed, in an experiment with equilibrium thermal radiation (Fig. 1.1) p 
Equilibrium in the system can be established only if each body emits as much energy per unit time as it absorbs. This means that bodies that absorb radiation of any frequency more intensely will emit this radiation more intensely.
Therefore, according to this principle of detailed equilibrium, the ratio of emissive and absorptive powers is the same for all bodies in nature, including a black body, and at a given temperature is the same universal function of frequency (wavelength).
This law of thermal radiation, established in 1859 by G. Kirchhoff when considering the thermodynamic laws of equilibrium systems with radiation, can be written as the relation
where indices 1, 2, 3... correspond to various real bodies.
From Kirchhoff's law it follows that the universal functions are the spectral emissivity of a black body on a scale of frequencies or wavelengths, respectively. Therefore, the connection between them is determined by the formula 
.
Black body radiation has a universal character in the theory of thermal radiation. A real body always emits less energy at any temperature than an absolutely black body. Knowing the emissivity of a black body (the universal Kirchhoff function) and the absorptivity of a real body, from Kirchhoff’s law one can determine the energy emitted by this body in any frequency range or wavelength.
This means that this energy emitted by a body is defined as the difference between the emissive capacity of a black body and the absorption capacity of a real body.
4. Stefan-Boltzmann law
Stefan-Boltzmann law. Experimental (1879 by J. Stefan) and theoretical (1884 by L. Boltzmann) studies made it possible to prove the important law of thermal radiation of an absolutely black body. This law states that the energetic luminosity of a black body is proportional to the fourth power of its absolute temperature, that is
This law is often used in astronomy to determine the luminosity of a star based on its temperature. To do this, it is necessary to move from the radiation density to an observable quantity - flux. The formula for the radiation flux integrated over the spectrum will be derived in the third chapter.
According to modern measurements, the Stefan-Boltzmann constant 
W/(m2 (K4).
For real bodies, the Stefan-Boltzmann law is satisfied only qualitatively, that is, with increasing temperature, the energetic luminosities of all bodies increase. However, for real bodies the dependence of energetic luminosity on temperature is no longer described by simple relation (1.7), but has the form
The coefficient in (1.8), always less than unity, can be called the integral absorptive capacity of the body. Values of , which generally depend on temperature, are known for many technically important materials. So, in a fairly wide temperature range for metals, and for coal and metal oxides 
.
For real non-black bodies, one can introduce the concept of effective radiation temperature, which is defined as the temperature of a completely black body that has the same energetic luminosity as the real body. Radiation body temperature is always less than the true body temperature. Indeed, for a real body 
. From here we find that , that is, since for real bodies.
The radiation temperature of highly heated hot bodies can be determined using a radiation pyrometer (Fig. 1.5), in which the image of a sufficiently distant heated source I is projected using a lens onto the receiver P so that the image of the emitter completely overlaps the receiver. Metal or semiconductor bolometers or thermoelements are usually used to estimate the energy of radiation incident on the receiver. The action of bolometers is based on a change in the electrical resistance of a metal or semiconductor with a change in temperature caused by the absorption of an incident radiation flux. A change in the temperature of the absorbing surface of thermoelements leads to the appearance of thermo-EMF in them.
The reading of a device connected to a bolometer or thermoelement turns out to be proportional to the radiation energy incident on the pyrometer receiver. Having previously calibrated the pyrometer according to the radiation of a black body standard at different temperatures, it is possible to measure the radiation temperatures of various heated bodies using the instrument scale.
Knowing the integral absorption capacity of the emitter material, it is possible to convert the measured radiation temperature of the emitter into its true temperature using the formula
In particular, if a radiation pyrometer shows temperature K when observing the hot surface of a tungsten emitter (), then its true temperature is K.
From this we can conclude that the luminosity of any body can be determined by its temperature.
5. Wien's displacement law
In 1893, the German physicist W. Wien theoretically examined the thermodynamic process of compression of radiation confined in a cavity with perfectly mirror walls. Taking into account the change in the frequency of radiation due to the Doppler effect upon reflection from a moving mirror, Wien came to the conclusion that the emissivity of a completely black body should have the form
(1.9)
Here is a certain function, the specific form of which cannot be determined by thermodynamic methods.
Passing in this Wien formula from frequency to wavelength, in accordance with the transition rule (1.3), we obtain
(1.10)
As can be seen, the expression for emissivity includes temperature only in the form of a product. This circumstance alone makes it possible to predict some features of the function. In particular, this function reaches a maximum at a certain wavelength, which, when the body temperature changes, changes so that the condition is satisfied: .
Thus, V. Vin formulated the law of thermal radiation, according to which the wavelength at which the maximum emissivity of an absolutely black body occurs is inversely proportional to its absolute temperature. This law can be written in the form
The value of the constant in this law, obtained from experiments, turned out to be equal to m 
mK.
Wien's law is called the displacement law, thereby emphasizing that as the temperature of an absolutely black body increases, the position of the maximum of its emissivity shifts to the region of short wavelengths. The experimental results shown in Fig. 1.4 confirm this conclusion not only qualitatively, but also quantitatively, strictly in accordance with formula (1.11).
For real bodies, Wien's law is satisfied only qualitatively. As the temperature of any body increases, the wavelength near which the body emits the most energy also shifts toward shorter wavelengths. This displacement, however, is no longer described by the simple formula (1.11), which for the radiation of real bodies can only be used as an estimate.
From Wien's displacement law, it turns out that the temperature of a body and the wavelength of its emissivity are interrelated.
6. Rayleigh-Jeans formula
In the range of extremely low frequencies,
called the Rayleigh–Jeans region, the energy density is proportional to the temperature T and the square of the frequency ω:
In Fig. 2.1.1 this area is marked RD. The Rayleigh-Jeans formula can be derived purely
classically, without involving quantum concepts. The higher the temperature of the black body, the wider the frequency range in which this formula is valid. It is explained in the classical theory, but it cannot be extended to high frequencies (dashed line in Fig. 2.1.1), since the energy density summed over the spectrum in this case is infinitely large:
This feature of the Rayleigh-Jeans law is called the “ultraviolet catastrophe.”
From the Rayleigh-Jeans formula it is clear that body temperature does not extend to high frequencies.
7. Wine formula
In the high frequency range (region B in Fig. 2.1.1), Wien’s formula is valid:
It is clearly seen that the right side changes non-monotonically. If the frequency is not too high, then the factor ω3 prevails and the function Uω increases. As the frequency increases, the growth of Uω slows down, it passes through a maximum, and then decreases due to the exponential factor. The presence of a maximum in the emission spectrum distinguishes the Wien range from the Rayleigh-Jeans region.
The higher the body temperature, the higher the cutoff frequency, starting from which the Wien formula is performed. The value of the parameter a in the exponent on the right side depends on the choice of units in which temperature and frequency are measured.
This means that Wien’s formula requires the use of quantum ideas about the nature of light.
Thus I considered the questions posed to me. It is easy to see that the existing laws of physics of the 19th century. were superficial, they did not connect together all the characteristics (wavelength, temperature, frequency, etc.) of physical bodies. All of the above laws complemented each other, but to fully understand this issue it was necessary to involve quantum concepts about the nature of light.
Practical part
As I have already said many times, the phenomenon of an absolutely black body does not exist in practice today; in any case, we cannot create and see it. However, we can conduct a number of experiments that demonstrate the above theoretical calculations.
Can white be blacker than black? Let's start with a very simple observation. If you put pieces of white and black paper side by side and create darkness in the room. It is clear that then you will not see a single leaf, that is, both of them will be equally black. It would seem that under no circumstances can white paper be blacker than black. And yet this is not so. A body that, at any temperature, completely absorbs radiation of any frequency incident on it is called absolutely black. It is clear that this is an idealization: there are no absolutely black bodies in nature. The bodies that we usually call black (soot, soot, black velvet and paper, etc.) are actually gray, i.e. they partially absorb and partially scatter the light falling on them.
It turns out that a spherical cavity with a small hole can serve as a completely good model of an absolutely black body. If the diameter of the hole does not exceed 1/10 of the diameter of the cavity, then (as the corresponding calculation shows) the light beam entering the hole can exit back only after multiple scatterings or reflections from different points of the cavity wall. But with each “contact” of the beam with the wall, the light energy is partially absorbed, so that the fraction of radiation coming back out of the hole is negligibly small. Therefore, we can assume that the opening of the cavity almost completely absorbs light of any wavelength, just like a completely black body. And the experimental device itself can be made, for example, like this. From cardboard you need to glue a box measuring approximately 100X100X100 mm with an opening lid. The inside of the box should be covered with white paper, and the outside should be painted with black ink, gouache, or, even better, covered with paper from photo packages. A hole with a diameter of no more than 10 mm must be made in the lid. As an experiment, you need to illuminate the lid of the box with a table lamp, then the hole will look blacker than the black lid.
In order to simply observe a phenomenon, you can do it even simpler (but less interesting). You need to take a white porcelain cup and cover it with a black paper lid with a small hole - the effect will be almost the same.
Please note that if you look at the windows from the street on a bright sunny day, they appear dark to us.
By the way, Princeton University professor Eric Rogers, who wrote “Physics for the Curious”, published not only here, gave a unique “description” of an absolutely black body: “No black paint on a dog kennel looks blacker than the door open for a dog.”
By removing the stickers from two identical empty cans and smoking or painting one can with black paint, leaving the other light, pouring hot water into both cans and seeing in which of them the water cools down faster (the experiment can be carried out in the dark); You will observe the phenomenon of thermal radiation.
The phenomenon of thermal radiation can also be observed by watching the operation of an electric room heater, consisting of an incandescent coil and a well-polished concave metal surface.
It's interesting that:
The connection between light and heat rays has been known since antiquity. Moreover, the word “focus” means “fire”, “hearth” in Latin, which, when applied to concave mirrors and lenses, indicates a primary attention to the concentration of heat rather than light rays. Among the many experiments of the 16th-18th centuries, the experiment carried out by Edme Marriott, in which gunpowder was ignited by heat rays reflected by a concave mirror made of... ice, stands out.
William Herschel, famous for the discovery of the planet Uranus, having discovered invisible - infrared - rays in the spectrum of the Sun, was so amazed that he remained silent about it for twenty years. But he had no doubt that Mars is inhabited and populated...
after spectral analysis showed the presence of many chemical elements in the solar atmosphere, including gold, one banker said to Kirchhoff: “Well, what’s the use of your solar gold? After all, it can’t be delivered to Earth anyway!” Several years passed, and Kirchhoff received a gold medal and a cash prize from England for his remarkable research. Showing this money to the banker, he said: “Look, I finally managed to get some gold from the Sun.”
On the grave of Fraunhofer, who discovered dark lines in the spectrum of the Sun and studied the spectra of planets and stars, grateful compatriots erected a monument with the inscription “Brought the stars closer.”
The practical examples I have given confirm the theoretical part.
Conclusion
I considered the questions posed to me. It is easy to see that the existing laws of physics of the 19th century. were superficial, they did not connect together all the characteristics (wavelength, temperature, frequency, etc.) of physical bodies. All of the above laws complemented each other, but to fully understand this issue it was necessary to involve quantum concepts about the nature of light. The creation of quantum theory made it possible to explain many phenomena, such as the phenomenon of an absolutely black body, i.e. a body that completely absorbs electromagnetic waves of any length and, accordingly, emits all lengths of electromagnetic waves. It also made it possible to explain the relationship between absorptivity and body color, and the dependence of the luminosity of a body on its temperature. Subsequently, these phenomena were explained by classical physics. I fulfilled the goal of my work - I made everyone aware of the problem of a completely black body. To do this I completed the following tasks:
found as much information as possible on this problem;
studied the black body theory;
experimentally confirmed the theoretical concepts and phenomena presented in the abstract;
To theoretically consider the laws of radiation, we used the black body model, i.e. a body that completely absorbs electromagnetic waves of any length and, accordingly, emits all lengths of electromagnetic waves.
List of used literature:
Myakishev G. Ya., Physics 11, M., 2000.
Kasyanov V. A., Physics 11, M., 2004.
Landsberg G.S., Elementary textbook of physics volume III, M., 1986.
http://ru.wikipedia.org/wiki/Absolutely_black_body.absolutely
Paradoxical. Black the hole behaves like body with a temperature equal to absolute zero... because with the help black holes... Thus, black the hole radiates as perfect black body(unexpectedly realized...
The spectral density of blackbody radiation is a universal function of wavelength and temperature. This means that the spectral composition and radiation energy of a completely black body do not depend on the nature of the body.
Formulas (1.1) and (1.2) show that knowing the spectral and integral radiation density of an absolutely black body, they can be calculated for any non-black body if the absorption coefficient of the latter is known, which must be determined experimentally.
Research led to the following laws of black body radiation.
1. Stefan-Boltzmann law: The integral radiation density of an absolutely black body is proportional to the fourth power of its absolute temperature
Magnitude σ called Stefan's constant- Boltzmann:
σ = 5.6687·10 -8 J m - 2 s - 1 K – 4.
Energy emitted over time t absolutely black body with a radiating surface S at constant temperature T,
W=σT 4 St
If the body temperature changes over time, i.e. T = T(t), That
The Stefan-Boltzmann law indicates an extremely rapid increase in radiation power with increasing temperature. For example, when the temperature increases from 800 to 2400 K (i.e. from 527 to 2127 ° C), the radiation of a completely black body increases by 81 times. If a completely black body is surrounded by a medium with a temperature T 0, then the eye will absorb the energy emitted by the environment itself.
In this case, the difference between the power of emitted and absorbed radiation can be approximately expressed by the formula
U=σ(T 4 – T 0 4)
The Stefan-Boltzmann law is not applicable to real bodies, as observations show a more complex relationship R on temperature, as well as on the shape of the body and the condition of its surface.
2. Wien's law of displacement. Wavelength λ 0, which accounts for the maximum spectral density of black body radiation, is inversely proportional to the absolute temperature of the body:
λ 0 = or λ 0 T = b.
Constant b, called Wien's law constant, equal to b = 0.0028978 m K ( λ expressed in meters).
Thus, with increasing temperature, not only the total radiation increases, but, in addition, the distribution of energy across the spectrum changes. For example, at low body temperatures, mainly infrared rays are studied, and as the temperature increases, the radiation becomes reddish, orange and, finally, white. In Fig. Figure 2.1 shows the empirical distribution curves of the radiation energy of a black body over wavelengths at different temperatures: it can be seen from them that the maximum spectral density of radiation shifts towards short waves with increasing temperature.
3. Planck's law. The Stefan-Boltzmann law and the Wien displacement law do not solve the main problem of how large the spectral radiation density is at each wavelength in the spectrum of a black body at temperature T. To do this, you need to establish a functional dependency And from λ And T.
Based on the idea of the continuous nature of the emission of electromagnetic waves and on the law of uniform distribution of energy over degrees of freedom (accepted in classical physics), two formulas were obtained for the spectral density and radiation of a black body:
1) Wine formula
Where a And b- constant values;
2) Rayleigh-Jeans formula
u λT = 8πkT λ – 4 ,
Where k- Boltzmann constant. Experimental testing has shown that for a given temperature Wien's formula is correct for short waves (when λT very small and gives sharp convergences from experience in the long wavelength region. The Rayleigh-Jeans formula turned out to be true for long waves and is completely inapplicable for short ones (Fig. 2.2).
Thus, classical physics was unable to explain the law of energy distribution in the radiation spectrum of an absolutely black body.
To determine the type of function u λТ completely new ideas about the mechanism of light emission were needed. In 1900, M. Planck hypothesized that absorption and emission of electromagnetic radiation energy by atoms and molecules is possible only in separate “portions”, which are called energy quanta. Magnitude of energy quantum ε proportional to the radiation frequency v(inversely proportional to wavelength λ ):
ε = hv = hc/λ
Proportionality factor h = 6.625·10 -34 J·s and is called Planck's constant. In the visible part of the spectrum for wavelength λ = 0.5 µm the value of the energy quantum is equal to:
ε = hc/λ= 3.79·10 -19 J·s = 2.4 eV
Based on this assumption, Planck obtained a formula for u λТ:
Where k– Boltzmann constant, With– speed of light in vacuum. l The curve corresponding to function (2.1) is also shown in Fig. 2.2.
From Planck's law (2.11) the Stefan-Boltzmann law and Wien's displacement law are obtained. Indeed, for the integral radiation density we obtain
Calculation using this formula gives a result that coincides with the empirical value of the Stefan-Boltzmann constant.
Wien's displacement law and its constant can be obtained from Planck's formula by finding the maximum of the function u λТ, why is the derivative of u λТ By λ , and is equal to zero. The calculation leads to the formula:
Calculation of constant b this formula also gives a result that coincides with the empirical value of the Wien constant.
Let us consider the most important applications of the laws of thermal radiation.
A. Thermal light sources. Most artificial light sources are thermal emitters (incandescent electric lamps, conventional arc lamps, etc.). However, these light sources are not very economical.
In § 1 it was said that the eye is sensitive only to a very narrow part of the spectrum (from 380 to 770 nm); all other waves do not produce a visual sensation. The maximum sensitivity of the eye corresponds to the wavelength λ = 0.555 µm. Based on this property of the eye, one should require from light sources such a distribution of energy in the spectrum at which the maximum spectral radiation density would fall on the wavelength λ = 0.555 µm or so. If we take an absolutely black body as such a source, then using Wien’s displacement law we can calculate its absolute temperature:
Thus, the most advantageous thermal light source should have a temperature of 5200 K, which corresponds to the temperature of the solar surface. This coincidence is the result of the biological adaptation of human vision to the distribution of energy in the solar radiation spectrum. But even this light source efficiency(the ratio of the energy of visible radiation to the total energy of all radiation) will be small. Graphically in Fig. 2.3 this coefficient is expressed by the ratio of areas S 1 And S; square S 1 expresses the energy of radiation in the visible region of the spectrum, S- all radiation energy.
Calculations show that at a temperature of about 5000-6000 K, the light efficiency is only 14-15% (for an absolutely black body). At the temperature of existing artificial light sources (3000 K), this efficiency is only about 1-3%. Such a low “light output” of a thermal emitter is explained by the fact that during the chaotic movement of atoms and molecules, not only light (visible) waves are excited, but also other electromagnetic waves that do not have a light effect on the eye. Therefore, it is impossible to selectively force the body to emit only those waves to which the eye is sensitive: invisible waves are also emitted.
The most important of modern temperature light sources are incandescent electric lamps with tungsten filament. The melting point of tungsten is 3655 K. However, heating the filament to temperatures above 2500 K is dangerous, since tungsten at this temperature is very quickly atomized and the filament is destroyed. To reduce filament sputtering, it was proposed to fill the lamps with inert gases (argon, xenon, nitrogen) at a pressure of about 0.5 atm. This made it possible to raise the temperature of the filament to 3000-3200 K. At these temperatures, the maximum spectral density of radiation lies in the region of infrared waves (about 1.1 microns), therefore all modern incandescent lamps have an efficiency of slightly more than 1%.
B. Optical pyrometry. The laws of black body radiation outlined above make it possible to determine the temperature of this body if the wavelength is known λ 0 , corresponding to the maximum u λТ(according to Wien's law), or if the value of the integral radiation density is known (according to the Stefan-Boltzmann law). These methods of determining body temperature from its thermal radiation in the cabin optical pyrometry; they are especially useful when measuring very high temperatures. Since the mentioned laws apply only to an absolutely black body, optical pyrometry based on them gives good results only when measuring the temperatures of bodies that are close in their properties to an absolutely black body. In practice, these are factory furnaces, laboratory muffle furnaces, boiler furnaces, etc. Let's consider three ways to determine the temperature of thermal emitters:
A. Method based on Wien's displacement law. If we know the wavelength at which the maximum spectral density of radiation falls, then the body temperature can be calculated using formula (2.2).
In particular, the temperature on the surface of the Sun, stars, etc. is determined in this way.
For non-black bodies, this method does not give the true body temperature; if there is one maximum in the emission spectrum and we calculate T according to formula (2.2), then the calculation gives us the temperature of an absolutely black body, which has almost the same energy distribution in the spectrum as the body under test. In this case, the color of the radiation of an absolutely black body will be the same as the color of the radiation under study. This body temperature is called its color temperature.
The color temperature of an incandescent lamp filament is 2700-3000 K, which is very close to its true temperature.
b. Radiation method of measuring temperatures based on measuring the integral radiation density of the body R and calculating its temperature using the Stefan-Boltzmann law. The corresponding devices are called radiation pyrometers.
Naturally, if the radiating body is not absolutely black, then the radiation pyrometer will not give the true temperature of the body, but will show the temperature of an absolutely black body at which the integral radiation density of the latter is equal to the integral radiation density of the test body. This body temperature is called radiation, or energy, temperature.
Among the disadvantages of a radiation pyrometer, we point out the impossibility of using it to determine the temperatures of small objects, as well as the influence of the medium located between the object and the pyrometer, which absorbs part of the radiation.
V. I brightness method for determining temperatures. Its operating principle is based on a visual comparison of the brightness of the hot filament of the pyrometer lamp with the brightness of the image of the heated test body. The device is a telescope with an electric lamp placed inside, powered by a battery. Equality, visually observed through a monochromatic filter, is determined by the disappearance of the image of the thread against the background of the image of the hot body. The filament is regulated by a rheostat, and the temperature is determined by the ammeter scale, graduated directly to the temperature.
Pure black body- this is a body for which the absorption capacity is identically equal to unity for all frequencies or wavelengths and for any temperature, i.e.:
From the definition of an absolutely black body it follows that it must absorb all radiation incident on it.
The concept of "absolutely black body" is a model concept. Absolute black bodies do not exist in nature, but it is possible to create a device that is a good approximation to an absolutely black body - black body model .
Black body model- this is a closed cavity with a small hole compared to its size (Fig. 1.2). The cavity is made of a material that absorbs radiation quite well. The radiation entering the hole is reflected many times from the inner surface of the cavity before leaving the hole.
With each reflection, part of the energy is absorbed, as a result, the reflected flux dФ comes out of the hole, which is a very small part of the radiation flux dФ that entered it. As a result, the absorption capacity holes in the cavity will be close to unity.
If the inner walls of the cavity are maintained at temperature T, then radiation will emerge from the hole, the properties of which will be very close to the properties of black body radiation. Inside the cavity, this radiation will be in thermodynamic equilibrium with the cavity matter.
By definition of energy density, the volumetric energy density w(T) of equilibrium radiation in a cavity is:
where dE is the radiation energy in the volume dV. Spectral distribution of volume density is given by the functions u(λ,T) (or u(ω,T)), which are introduced similarly to the spectral density of energetic luminosity ((1.6) and (1.9)), i.e.:
Here dw λ and dw ω are the volumetric energy density in the corresponding interval of wavelengths dλ or frequencies dω.
Kirchhoff's law states that the relationship emissivity body ((1.6) and (1.9)) to its absorption capacity (1.14) is the same for all bodies and is a universal function of frequency ω (or wavelength λ) and temperature T, i.e.:
It is obvious that the absorption capacity aω (or a λ) is different for different bodies, then from Kirchhoff’s law it follows that the stronger a body absorbs radiation, the stronger it should emit this radiation. Since for an absolute black body aω ≡ 1 (or aλ ≡ 1), then it follows that in the case of a completely black body:
In other words, f(ω,T) or φ(λ,T) , is nothing more than the spectral energy luminosity density (or emissivity) of a completely black body.
The function φ(λ,T) and f(ω,T) are related to the spectral energy density of black body radiation by the following relations:
where c is the speed of light in vacuum.
Installation diagram for experimental determination of the dependence φ(λ,T) is shown in Figure 1.3.
Radiation is emitted from the opening of a closed cavity heated to a temperature T, then hits a spectral device (prism or grating monochromator), which emits radiation in the frequency range from λ to λ + dλ. This radiation hits a receiver, which allows the radiation power incident on it to be measured. By dividing this power per interval from λ to λ + dλ by the area of the emitter (the area of the hole in the cavity!), we obtain the value of the function φ(λ,T) for a given wavelength λ and temperature T. The experimental results obtained are reproduced in Figure 1.4.
Results of lecture No. 1
1. German physicist Max Planck in 1900 put forward a hypothesis according to which electromagnetic energy is emitted in portions, energy quanta. The magnitude of the energy quantum (see (1.2):
ε = h v,
where h=6.6261·10 -34 J·s is Planck’s constant, v- frequency of oscillations of an electromagnetic wave emitted by a body.
This hypothesis allowed Planck to solve the problem of black body radiation.
2. And Einstein, developing Planck’s concept of energy quanta, introduced in 1905 the concept of “quantum of light” or photon. According to Einstein, quantum of electromagnetic energy ε = h v moves in the form of a photon localized in a small region of space. The idea of photons allowed Einstein to solve the problem of the photoelectric effect.
3. English physicist E. Rutherford, based on experimental studies conducted in 1909-1910, built a planetary model of the atom. According to this model, at the center of the atom there is a very small nucleus (r I ~ 10 -15 m), in which almost the entire mass of the atom is concentrated. The nuclear charge is positive. Negatively charged electrons move around the nucleus like the planets of the solar system in orbits whose size is ~ 10 -10 m.
4. The atom in Rutherford’s model turned out to be unstable: according to Maxwell’s electrodynamics, electrons, moving in circular orbits, should continuously emit energy, as a result of which they should fall onto the nucleus in ~ 10 -8 s. But all our experience testifies to the stability of the atom. This is how the problem of atomic stability arose.
5. The problem of atomic stability was solved in 1913 by the Danish physicist Niels Bohr on the basis of two postulates he put forward. In the theory of the hydrogen atom, developed by N. Bohr, Planck's constant plays a significant role.
6. Thermal radiation is electromagnetic radiation emitted by a substance due to its internal energy. Thermal radiation can be in thermodynamic equilibrium with surrounding bodies.
7. The energetic luminosity of a body R is the ratio of the energy dE emitted during a time dt by the surface dS in all directions to dt and dS (see (1.5)):
8. Spectral density of energy luminosity r λ (or emissivity of a body) is the ratio of energy luminosity dR, taken in an infinitesimal wavelength interval dλ, to the value dλ (see (1.6)):
9. Radiation flux Ф is the ratio of the energy dE transferred by electromagnetic radiation through any surface to the transfer time dt, which significantly exceeds the period of electromagnetic oscillations (see (1.13)):
10. Body absorption capacity a λ is the ratio of the radiation flux dФ λ "absorbed by a body in the wavelength interval dλ to the flux dФ λ incident on it in the same interval dλ, (see (1.14):
11. An absolutely black body is a body for which the absorption capacity is identically equal to unity for all wavelengths and for any temperature, i.e.
A completely black body is a model concept.
12. Kirchhoff’s law states that the ratio of the emissivity of a body r λ to its absorption capacity a λ is the same for all bodies and is a universal function of wavelength λ (or frequency ω) and temperature T (see (1.17)):
LECTURE N 2
The problem of black body radiation. Planck's formula. Stefan-Boltzmann law, Wien's law
§ 1. The problem of black body radiation. Planck's formula
The problem with black body radiation was to theoretically get addictedφ(λ,Т)- the spectral density of the energy luminosity of an absolutely black body.
It seemed that the situation was clear: at a given temperature T, the molecules of the substance of the radiating cavity have a Maxwellian velocity distribution and emit electromagnetic waves in accordance with the laws of classical electrodynamics. Radiation is in thermodynamic equilibrium with matter, which means that the laws of thermodynamics and classical statistics can be used to find the spectral radiation energy density u(λ,T) and the associated function φ(λ,T).
However, all attempts by theorists to obtain the law of black body radiation based on classical physics have failed.
Partial contributions to the solution of this problem were made by Gustav Kirchhoff, Wilhelm Wien, Joseph Stefan, Ludwig Boltzmann, John William Rayleigh, James Honwood Jeans.
The problem of blackbody radiation was solved by Max Planck. To do this, he had to abandon classical concepts and make the assumption that a charge oscillating with a frequency v, can receive or give energy in portions, or quanta.
The magnitude of the energy quantum in accordance with (1.2) and (1.4):
where h is Planck's constant; 
v- frequency of oscillations of an electromagnetic wave emitted by an oscillating charge; ω = 2π v- circular frequency.
Based on the concept of energy quanta, M. Planck, using the methods of statistical thermodynamics, obtained an expression for the function u(ω,T), giving distribution of energy density in the radiation spectrum of an absolute black body:
The derivation of this formula will be given in Lecture No. 12, § 3 after we become acquainted with the basics of quantum statistics.
To go to the spectral density of energy luminosity f(ω,T), we write the second formula (1.19):
Using this relation and Planck’s formula (2.1) for u(ω,T), we obtain that:
This is Planck's formula for spectral density of energetic luminosity f(ω ,T).
Now we get Planck's formula for φ(λ,T). As we know from (1.18), in the case of a completely black body f(ω,T) = r ω, and φ(λ,T) = r λ.
The relationship between r λ and r ω is given by formula (1.12), applying it we get:
Here we expressed the argument ω of the function f(ω,T) in terms of the wavelength λ. Substituting here Planck’s formula for f(ω,T) from (2.2), we obtain Planck’s formula for φ(λ,T) - the spectral density of energy luminosity depending on the wavelength λ:
The graph of this function coincides well with the experimental graphs of φ(λ,T) for all wavelengths and temperatures.
This means that the problem of black body radiation has been solved.
§ 2. Stefan-Boltzmann law and Wien's law
From (1.11) for an absolutely black body, when r ω = f(λ,T), we obtain the energy luminosity R(T) , integrating the function f(ω,Т) (2.2) over the entire frequency range.
Integration gives:
Let us introduce the notation:
then the expression for the energetic luminosity R will take the following form:
That's what it is Stefan-Boltzmann law .
M. Stefan, based on an analysis of experimental data, came to the conclusion in 1879 that the energetic luminosity of any body is proportional to the fourth power of temperature.
L. Boltzmann in 1884 found from thermodynamic considerations that such a dependence of energetic luminosity on temperature is valid only for an absolutely black body.
The constant σ is called Stefan-Boltzmann constant . Its experimental significance:
Calculations using the theoretical formula give a result for σ that is in very good agreement with the experimental one.
Note that graphically the energetic luminosity is equal to the area limited by the graph of the function f(ω,T), this is illustrated in Figure 2.1.
The maximum of the graph of the spectral density of energy luminosity φ(λ,T) shifts to the region of shorter waves with increasing temperature (Fig. 2.2). To find the law according to which the maximum φ(λ,T) shifts depending on temperature, it is necessary to study the function φ(λ,T) to the maximum. Having determined the position of this maximum, we obtain the law of its movement with temperature change.
As is known from mathematics, to study a function to its maximum, you need to find its derivative and equate it to zero:
Substituting here φ(λ,Т) from (1.23) and taking the derivative, we obtain three roots of the algebraic equation with respect to the variable λ. Two of them (λ = 0 and λ = ∞) correspond to zero minima of the function φ(λ,T). For the third root, an approximate expression is obtained:
Let us introduce the notation:
then the position of the maximum of the function φ(λ,T) will be determined by a simple formula:
That's what it is Wien's displacement law .
It is named after V. Wien, who theoretically obtained this ratio in 1894. The constant in Wien's displacement law has the following numerical value:
Results of lecture No. 2
1. The problem of black body radiation was that all attempts to obtain, on the basis of classical physics, the dependence φ(λ,T) - the spectral density of the energy luminosity of a black body failed.
2. This problem was solved in 1900 by M. Planck on the basis of his quantum hypothesis: a charge oscillating with a frequency v, can receive or give out energy in portions or quanta. Energy quantum value:
here h = 6.626 10 -34 is Planck’s constant, the value 
J s is also called Planck's constant ["ash" with a bar], ω is the circular (cyclic) frequency.
3. Planck’s formula for the spectral density of the energy luminosity of an absolutely black body has the following form (see (2.4):
here λ is the wavelength of electromagnetic radiation, T is the absolute temperature, h is Planck’s constant, c is the speed of light in vacuum, k is Boltzmann’s constant.
4. From Planck’s formula follows the expression for the energy luminosity R of an absolutely black body:
which allows us to theoretically calculate the Stefan-Boltzmann constant (see (2.5)):
the theoretical value of which coincides well with its experimental value:
in the Stefan-Boltzmann law (see (2.6)):
5. From Planck’s formula follows Wien’s displacement law, which determines λ max - the position of the maximum of the function φ(λ,T) depending on the absolute temperature (see (2.9):
For b - the Wien constant - the following expression is obtained from Planck’s formula (see (2.8)):
Wien's constant has the following value b = 2.90 ·10 -3 m·K.
LECTURE N 3
Photoelectric effect problem . Einstein's equation for the photoelectric effect
§ 1. The photoelectric effect problem A
The photoelectric effect is the emission of electrons by a substance under the influence of electromagnetic radiation.
This photoelectric effect is called external. This is what we will talk about in this chapter. There is also internal photoelectric effect . (see lecture 13, § 2).
In 1887, German physicist Heinrich Hertz discovered that ultraviolet light shining on the negative electrode in a spark gap facilitated the passage of the discharge. In 1888-89 Russian physicist A. G. Stoletov is engaged in a systematic study of the photoelectric effect (a diagram of its installation is shown in the figure). The research was carried out in a gas atmosphere, which greatly complicated the processes taking place.
Stoletov discovered that:
1) ultraviolet rays have the greatest impact;
2) the current increases with increasing intensity of light illuminating the photocathode;
3) charges emitted under the influence of light have a negative sign.
Further studies of the photoelectric effect were carried out in 1900-1904. German physicist F. Lenard in the highest vacuum achieved at that time.
Lenard was able to establish that the speed of electrons escaping from the photocathode does not depend on light intensity and directly proportional to its frequency . This is how I was born photoelectric effect problem . It was impossible to explain the results of Lenard's experiments on the basis of Maxwell's electrodynamics!
Figure 3.2 shows a setup that allows you to study the photoelectric effect in detail.
Electrodes, photocathode And anode , placed in balloon, from which the air has been pumped out. Light is supplied to the photocathode through quartz window . Quartz, unlike glass, transmits ultraviolet rays well. The potential difference (voltage) between the photocathode and anode measures voltmeter . The current in the anode circuit is measured by a sensitive microammeter . To regulate voltage power battery connected to rheostat with a midpoint. If the rheostat motor is opposite the midpoint connected through a microammeter to the anode, then the potential difference between the photocathode and the anode is zero. When the slider is shifted to the left, the anode potential becomes negative relative to the cathode. If the rheostat slider is moved to the right from the midpoint, then the anode potential becomes positive.
The current-voltage characteristic of the installation for studying the photoelectric effect allows one to obtain information about the energy of electrons emitted by the photocathode.
The current-voltage characteristic is the dependence of the photocurrent i on the voltage between the cathode and anode U. When illuminated with light, the frequency v which is sufficient for the photoelectric effect to occur, the current-voltage characteristic has the form of the graph shown in Fig. 3.3:
From this characteristic it follows that at a certain positive voltage at the anode, the photocurrent i reaches saturation. In this case, all electrons emitted by the photocathode per unit time fall on the anode during the same time.
At U = 0, some electrons reach the anode and create a photocurrent i 0 . At some negative voltage at the anode - U back - the photocurrent stops. At this voltage value, the maximum kinetic energy of the photoelectron at the photocathode (mv 2 max)/2 is completely spent on doing work against the forces of the electric field:
In this formula, m e is the mass of the electron; v max - its maximum speed at the photocathode; e is the absolute value of the electron charge.
Thus, by measuring the retarding voltage U back, you can find the kinetic energy (and speed of the electron) immediately after its departure from the photocathode.
Experience has shown that
1)the energy of the electrons emitted from the photocathode (and their speed) did not depend on the light intensity! When the frequency of light changes v U back also changes, i.e. maximum kinetic energy of electrons leaving the photocathode;
2)maximum kinetic energy of electrons, at the photocathode,(mv 2 max)/2 , is directly proportional to the frequency v of the light illuminating the photocathode.
Problem, as in the case of black body radiation, was that theoretical predictions made for the photoelectric effect based on classical physics (Maxwellian electrodynamics) contradicted the experimental results. Light intensity I in classical electrodynamics is the energy flux density of a light wave. Firstly, from this point of view, the energy transferred by a light wave to an electron must be proportional to the intensity of the light. Experience does not confirm this prediction. Secondly, in classical electrodynamics there are no explanations for the direct proportionality of the kinetic energy of electrons,(mv 2 max)/2 , light frequency v.
Thermal radiation is electromagnetic radiation that is emitted by heated bodies due to their internal energy. Thermal radiation reduces the internal energy of the body, and, consequently, its temperature. The spectral characteristic of thermal radiation is the spectral density of energy luminosity.
2. What body is called absolutely black? Give examples of absolutely black bodies.
A completely black body is a body that absorbs all the energy of radiation incident on it of any frequency at an arbitrary temperature (black hole).
3. What is ultraviolet catastrophe? Formulate Planck's quantum hypothesis.
An ultraviolet catastrophe is the discrepancy between experimental results and classical wave theory. Planck's quantum hypothesis: Energy and frequency of radiation are related to each other. Radiation from molecules and atoms of a substance occurs in separate portions - quanta.
4. What microparticle is called a photon? List the main physical characteristics of a photon.
Photon is a quantum of electromagnetic radiation.
1) its energy is proportional to the frequency of electromagnetic radiation.
3) its speed in all reference systems is equal to the speed of light in vacuum.
4) its rest mass is 0.
5) the photon momentum is equal to:
6) Electromagnetic radiation pressure:
5. Formulate the laws of black body radiation: Wien’s and Stefan-Boltzmann’s laws.
Stefan-Boltzmann law: the integral luminosity of a completely black body depends only on its temperature
Kikoin A.K. Absolutely black body // Quantum. - 1985. - No. 2. - P. 26-28.
By special agreement with the editorial board and editors of the journal "Kvant"
Light and color
When we look at various bodies around us in daylight (sunlight), we see them painted in different colors. So, grass and tree leaves are green, flowers are red or blue, yellow or purple. There are also black, white, gray bodies. All this cannot but cause surprise. It would seem that all bodies are illuminated by the same light - the light of the Sun. Why are their colors different? Let's try to answer this question.
We will proceed from the fact that light is an electromagnetic wave, that is, a propagating alternating electromagnetic field. Sunlight contains waves in which electric and magnetic fields oscillate at different frequencies.
Every substance consists of atoms and molecules containing charged particles that interact with each other. Since particles are charged, under the influence of an electric field they can move, and if the field is variable, then they can oscillate, and each particle in the body has a certain natural frequency of oscillation.
This simple, although not very accurate, picture will allow us to understand what happens when light interacts with matter.
When light falls on a body, the electric field “brought” by it causes the charged particles in the body to perform forced oscillations (the field of the light wave is variable!). In this case, for some particles, their natural frequency of oscillations may coincide with some frequency of oscillations of the light wave field. Then, as is known, the phenomenon of resonance will occur - a sharp increase in the amplitude of oscillations (this is discussed in § 9 and 20 of Physics 10). During resonance, the energy brought by the wave is transferred to the atoms of the body, which ultimately causes it to heat up. Light whose frequency resonates is said to be absorbed by the body.
But some waves from the incident light do not resonate. However, they also cause particles in the body to vibrate, but to vibrate with a small amplitude. These particles themselves become sources of so-called secondary electromagnetic waves of the same frequency. Secondary waves, adding to the incident wave, make up reflected or transmitted light.
If the body is opaque, then absorption and reflection are all that can happen to the light falling on the body: light that does not resonate is reflected, and light that does reach is absorbed. This is the “secret” of the color of bodies. If, for example, vibrations corresponding to the red color are included in the resonance from the composition of the incident sunlight, then they will not be present in the reflected light. And our eye is designed in such a way that sunlight, deprived of its red part, causes the sensation of green. The color of opaque bodies thus depends on which frequencies of the incident light are absent in the light reflected by the body.
There are bodies in which charged particles have so many different natural frequencies of vibration that each or almost every frequency in the incident light falls into resonance. Then all the incident light is absorbed, and there is simply nothing to be reflected. Such bodies are called black, that is, bodies of black color. In reality, black is not a color, but the absence of any color.
There are also bodies in which not a single frequency in the incident light hits resonance, then there is no absorption at all, and all the incident light is reflected. Such bodies are called white. White is also not a color, it is a mixture of all colors.
Emitting light
It is known that any body can itself become a source of light. This is understandable - after all, in every body there are oscillating charged particles that can become sources of emitted waves. But under normal conditions - at low temperatures - the frequencies of these vibrations are relatively small, and the emitted wavelengths significantly exceed the wavelengths of visible light (infrared light). At a high temperature, vibrations of higher frequencies “turn on” in the body, and it begins to emit light waves visible to the eye.
What kind of light does a body emit, what frequency vibrations can be “turned on” when heated? Obviously, only oscillations with natural frequencies can arise. At low temperatures, the number of charged particles with high natural vibration frequencies is small, and their radiation is imperceptible. As the temperature increases, the number of such particles increases, and the emission of visible light becomes possible.
Relationship between emission and absorption of light
Absorption and emission are opposite phenomena. However, there is something in common between them.
To absorb means to “take”, to emit means to “give”. What does the body “take” when it absorbs light? Obviously, what it can take is light of those frequencies that are equal to the natural frequencies of vibration of its particles. What does the body “give” when it emits light? What it has is light corresponding to its own frequencies of vibration. Therefore, there must be a close connection between the body's ability to emit light and its ability to absorb it. And this connection is simple: the more a body emits, the more it absorbs. In this case, naturally, the brightest emitter should be a black body, which absorbs vibrations of all frequencies. This connection was established mathematically in 1859 by the German physicist Gustav Kirchhoff.
Let us call the emissivity of a body the energy emitted per unit area of its surface per unit time, and denote it by Eλ,T . It is different for different wavelengths ( λ ) and different temperatures ( T), hence the indices λ And T. The absorption capacity of a body is the ratio of the light energy absorbed by the body per unit time to the incident energy. Let us denote it by Aλ,T - it is also different for different λ And T.
Kirchhoff's law states that the ratio of emissive and absorptive abilities is the same for all bodies:
\(~\frac(E_(\lambda, T))(A_(\lambda, T)) = C\) .
Magnitude WITH does not depend on the nature of the bodies, but depends on the wavelength of light and temperature: C = f(λ , T). According to Kirchhoff's law, a body that absorbs better at a given temperature should radiate more intensely.
Pure black body
Kirchhoff's law is valid for all bodies. This means that it can also be applied to a body that absorbs all wavelengths without exception. Such a body is called completely black. For it, the absorption capacity is equal to unity, so Kirchhoff’s law takes the form
\(~E_(\lambda, T) = C = f(\lambda, T)\) .
Thus, the meaning of the function becomes clear f(λ , T): it is equal to the emissivity of a completely black body. Function Finding Problem C = f(λ , T) turned into the problem of finding the dependence of the radiation energy of a completely black body on temperature and wavelength. Finally, after two decades of futile attempts, it was solved. Its solution, given by the German theoretical physicist Max Planck, became the beginning of a new physics - quantum physics.
Note that absolutely black bodies do not exist in nature. Even the blackest of all known substances - soot - absorbs not 100, but 98% of the light falling on it. Therefore, an artificial device was used to experimentally study black body radiation.
It turned out that the properties of an absolutely black body are possessed by... a closed cavity with a small hole (see figure). In fact, when a ray of light enters a hole, it experiences many successive reflections inside the cavity, so that it has very little chance of leaving the hole to the outside. (For the same reason, an open window in the house seems dark even on a bright sunny day). If such a body is heated, then the radiation emanating from the hole is practically no different from the radiation of a completely black body.
A pipe, one end of which is closed, can also serve as a good imitation of a completely black body. If the pipe is heated, its open end shines as a completely black body. At normal temperatures, it looks completely black, like the hole in the cavity.
