In which case the body is heated due to radiation. Thermal radiation wavelength. Law of absorption of radiant energy

Passing the radiation of a body through a device that decomposes it into a spectrum, one can judge the presence of waves of one or another length in the radiation, as well as evaluate the distribution of energy over parts of the spectrum. Such spectra are called emission spectra. It turns out that vapors and gases (especially monatomic ones), when heated or during an electric discharge, give (at low pressures, when the interaction of atoms is practically imperceptible) line spectra, consisting of relatively narrow "lines", i.e., narrow frequency intervals, where the radiation intensity is significant. So, hydrogen gives five lines in the visible part of the spectrum, sodium - one (yellow) line. When high-resolution spectral equipment is used, a complex structure is found in a number of lines. With an increase in pressure, when the interaction of atoms with each other affects, as well as with a complex structure of molecules, broader lines are obtained, turning into relatively broad bands of a complex structure (striped spectra). Such striped spectra, in particular, are observed in liquids. Finally, when heated, solids give practically continuous spectra, but the intensity distribution over the spectrum is different for different bodies.

The spectral composition of the radiation also depends on the temperature of the bodies. The higher the temperature, the more (ceteris paribus) the high frequencies predominate. So, as the temperature of the filament of an incandescent lamp increases, with changes in the current flowing through it, the color of the filament changes: at first, the filament glows faintly with red light, then the visible radiation becomes more intense and short-wavelength - the yellow-green part of the spectrum predominates. But, as will become clear later, in this case, too, most of the radiated energy corresponds to the invisible infrared range.

If radiation with a continuous spectrum is passed through a layer of matter, then partial absorption occurs, as a result of which lines with a minimum intensity are obtained on the continuous spectrum of radiation. In the visible part of the spectrum, they appear in contrast as dark bands (or lines); such spectra are called absorption spectra. Thus, the solar spectrum, cut by a system of thin dark lines (Fraunhofer lines), is an absorption spectrum; it takes place in the atmosphere of the sun.

The study of the spectra shows that with a change in body temperature, not only the emission of light changes, but also its absorption. In this case, it was found that well-radiating bodies also have a large absorption (Prevost), and the absorbed frequencies coincide with the emitted ones (Kirchhoff). Here we do not take into account the phenomena associated with frequency conversion (luminescence, Compton effect, Raman scattering), which usually play an insignificant role.

Of particular interest to physicists of the XIX century. caused the radiation of heated bodies. The fact is that during an electric discharge, during certain chemical reactions (chemiluminescence), during ordinary luminescence, a continuous expenditure of energy is required, due to which radiation occurs, i.e., the process is nonequilibrium.

The radiation of a heated body, under certain conditions, can be in equilibrium, since the radiated energy can be absorbed. In the 19th century thermodynamics was developed only for equilibrium processes; therefore, one could hope for the creation of only a theory of the radiation of a heated body.

So, let's imagine a body that has a cavity inside with mirrored (that is, completely reflecting radiation of any frequency) walls. Let two arbitrary bodies are placed in this cavity, giving a continuous spectrum of radiation; their temperature may initially be different. They will exchange radiation energy until an equilibrium state is established: the energy absorbed per unit time by an element of the surface of each body will be equal to the energy emitted by the same element. In this case, the entire cavity will be filled with radiation of various frequencies. According to the Russian physicist B. B. Golitsyn, this radiation should be assigned the same temperature that will be established for radiating bodies after reaching an equilibrium state.

For a quantitative description, we introduce the distribution function e(ν, T), called emissivity body. Work edv, where dv- an infinitely small frequency interval (near the frequency ν), gives the energy emitted by a unit surface of the body per unit time in the frequency interval (ν, ν+ dv).

Further we will call absorption capacity body function a(ν,T), which determines the ratio of the energy absorbed by an element of the surface of the body to the energy incident on it, contained in the frequency interval (v, ν + dv).

In the same way, one can define reflectivityr(ν , T) as the ratio of the reflected energy in the frequency range (ν, v+dν) to the incident energy.

Idealized mirror walls have a reflectivity equal to unity in the entire frequency range - from the smallest to arbitrarily large.

Let us assume that a state of equilibrium has come, while the first body per unit time radiates power from each unit of the surface

If radiation comes to this single surface from the cavity, Described by the function Ɛ(v, T) dv, then the part of the energy determined by the product a 1 (v, T) Ɛ(v, T) dv, will be absorbed, the rest of the radiation will be reflected. At the same time, a unit surface of the second body radiates power e 2 (v, T) dv, but absorbed a 2 (v, T)Ɛ(v, T) dv.

It follows that at equilibrium the following condition is satisfied:

It can be represented as

(11.1)

This entry emphasizes that the ratio of the emissivity of any body to its absorption capacity at a given temperature in a certain narrow frequency range is a constant value for all bodies. This constant is equal to the emissivity of the so-called black body(i.e., bodies with an absorbance equal to unity in the entire conceivable frequency range).

This black body turns out to be the cavity we are considering. Therefore, if a very small hole is made in the wall of a body with a cavity that does not noticeably disturb thermal equilibrium, then a weak radiation flux from this hole will be characteristic of blackbody radiation. At the same time, it is clear that radiation entering the cavity through such an opening has a negligibly small probability of escaping back, i.e., the cavity has complete absorption, as it should be for a black body. It can be shown that our reasoning remains valid even when the mirror walls are replaced by walls with a lower reflectivity; instead of two bodies, one can take several or one, or simply consider the radiation of the walls of the cavity itself (if they are not specular). The law expressed by formula (11.1) is called Kirchhoff's law. It follows from Kirchhoff's law that if the function Ɛ(v, T), characterizing the radiation of a black body, then the radiation of any other body could be determined by measuring its absorptive capacity.

We note that a small hole in the wall of, for example, a muffle furnace at room temperature appears black, since, while absorbing all the radiation that enters the cavity, the cavity almost does not radiate, being cold. But when the walls of the furnace are heated, the hole seems to glow brightly, since the flux of "black" radiation coming out of it at a high temperature (900 K and above) is quite intense. As the temperature rises, the intensity increases and red radiation is first perceived as yellow, and then as white.

If there is, for example, a cup made of white porcelain with a dark pattern in the cavity, then the pattern will not be noticeable inside the hot furnace, since its own radiation, together with the reflected one, coincides in composition with the radiation filling the cavity. If you quickly take the cup outside, into a bright room, then at first the dark pattern glows brighter than the white background. After cooling, when the cup's own radiation becomes vanishingly small, the room-filling light again produces a dark pattern on a white background.

Heated bodies radiate electromagnetic waves. This radiation is carried out by converting the energy of the thermal motion of body particles into radiation energy.

The electromagnetic radiation of a body in a state of thermodynamic equilibrium is called thermal (temperature) radiation. Sometimes thermal radiation is understood not only as equilibrium, but also as non-equilibrium radiation of bodies due to their heating.

Such equilibrium radiation occurs, for example, if the radiating body is inside a closed cavity with opaque walls whose temperature is equal to the temperature of the body.

In a thermally insulated system of bodies at the same temperature, heat exchange between bodies by emitting and absorbing thermal radiation cannot lead to a violation of the thermodynamic equilibrium of the system, since this would contradict the second law of thermodynamics.

Therefore, for the thermal radiation of bodies, Prevost's rule must be fulfilled: if two bodies at the same temperature absorb different amounts of energy, then their thermal radiation at this temperature must be different.

The radiant (radiative) ability or spectral density of the energy luminosity of a body is the value of En, m, numerically equal to the surface power density of the thermal radiation of the body and the frequency interval of unit width:

Where dW are the energies of thermal radiation per unit area of ​​the body surface per unit time in the frequency range from v to v + dr.

Emissivity En,m, is a spectral characteristic of the thermal radiation of the body. It depends on the frequency v, the absolute temperature T of the body, as well as on its material, shape and surface condition. In the SI system, En,t, is measured in j/m2.

The absorptivity or monochromatic absorption coefficient of a body is called the value An,t, which shows what fraction of the energy dWfall delivered per unit time per unit area of ​​the body surface by electromagnetic waves incident on it with frequencies from v to v + dv is absorbed by the body:

An,t is a dimensionless quantity. It depends, in addition to the radiation frequency and body temperature, on its material, shape and surface condition.

A body is called absolutely black if at any temperature it completely absorbs all the electromagnetic fields falling on it: An,t black = 1.

Real bodies are not absolutely black, but some of them are close to a completely black body in optical properties (soot, platinum black, black velvet in the visible light region have An,m, which differ little from unity)

A body is called gray if its absorptivity is the same for all frequencies n and depends only on the temperature, material and state of the surface of the body

Between the radiative En,t and absorbing An,t abilities of any opaque body, there is a relation (Kirhoff's law in differential form):

For an arbitrary frequency and temperature, the ratio of the emissivity of a body to its absorptivity is the same for all bodies and is equal to the emissivity en,m of a completely black body, which is a function of frequency and temperature only (the Kirchhoff function En,m = An,ten,m = 0).

Integral emissivity (energy luminosity) of the body:

is the surface power density of the thermal radiation of the body, i.e. energy of radiation of all possible frequencies emitted from a unit surface of a body per unit of time.

Integral emissivity eТ of a black body:

2. Laws of black body radiation

The laws of blackbody radiation establish the dependence of eT and e n,T on frequency and temperature.

Law of Cmefan - Boltsmap:

The value of σ is the universal constant of Stefan-Boltzmann, equal to 5.67 -10-8 W/m2*deg4.

The distribution of energy in the radiation spectrum of a black body, i.e., the dependence of en, T, on frequency at different temperatures, has the form shown in the figure:

Wine's Law:

where c is the speed of light in vacuum, and f(v/T) is the universal function of the ratio of the blackbody radiation frequency to its temperature.

The radiation frequency nmax, corresponding to the maximum value of the emissivity en, T of a completely black body, according to Wien's law is equal to

Where b1 is a constant value depending on the form of the function f(n/T).

Buna's displacement law: the frequency corresponding to the maximum value of the emissivity en,T of a completely black body is directly proportional to its absolute temperature.

From an energetic point of view, black radiation is equivalent to the radiation of a system of an infinite number of non-interacting harmonic oscillators, called radiative oscillators. If ε(ν) is the average energy of a radiative oscillator with natural frequency ν, then

ν= and

According to the classical law on the uniform distribution of energy over degrees of freedom, ε(ν) = kT, where k is the Boltzmann constant, and

This ratio is called the Rayleigh-Jeans formula. In the region of high frequencies, it leads to a sharp discrepancy with the experiment, which is called the “ultraviolet catastrophe: en, T monotonously increases with increasing frequency, without a maximum, and the integral emissivity of a completely black body turns to infinity.

The reason for the above difficulties that arose in finding the form of the Kirchhoff function en, T, is associated with one of the main provisions of classical physics, according to which the energy of any system can change continuously, i.e., it can take any arbitrarily close values.

According to Planck's quantum theory, the energy of a radiation oscillator with a natural frequency v can only take certain discrete (quantized) values ​​that differ by an integer number of elementary portions - energy quanta:

h \u003d b, 625-10-34 j * sec - Planck's constant (quantum of action). In accordance with this, the radiation and absorption of energy by particles of a radiating body (atoms, molecules or ions) exchanging energy with radiation oscillators should occur, not continuously, but discretely - in separate portions (quanta).

Description attempts:

The term was introduced by Gustav Kirchhoff in 1862.

The study of the laws of black body radiation was one of the prerequisites for the emergence of quantum mechanics. An attempt to describe the radiation of an absolutely black body based on the classical principles of thermodynamics and electrodynamics leads to the Rayleigh-Jeans law.
In practice, such a law would mean the impossibility of thermodynamic equilibrium between matter and radiation, since according to it, all thermal energy would have to be converted into radiation energy in the short-wavelength region of the spectrum. Such a hypothetical phenomenon has been called an ultraviolet catastrophe.
Nevertheless, the Rayleigh-Jeans radiation law is valid for the long-wavelength region of the spectrum and adequately describes the nature of the radiation. The fact of such a correspondence can be explained only by using the quantum mechanical approach, according to which the radiation occurs discretely. Based on quantum laws, you can get the Planck formula, which will coincide with the Rayleigh-Jeans Formula.
This fact is an excellent illustration of the operation of the correspondence principle, according to which the new physical theory must explain everything that the old one was able to explain.

The radiation intensity of a black body depending on temperature and frequency is determined by Planck's law.

The total energy of thermal radiation is determined by the Stefan-Boltzmann law. Thus, a black body at T = 100 K emits 5.67 watts per square meter of its surface. At a temperature of 1000 K, the radiation power increases to 56.7 kilowatts per square meter.

The wavelength at which the radiation energy of a black body is maximum is determined by Wynn's displacement law. So, if we assume in the first approximation that human skin is close in properties to an absolutely black body, then the maximum of the radiation spectrum at a temperature of 36 ° C (309 K) lies at a wavelength of 9400 nm (in the infrared region of the spectrum).

Electromagnetic radiation that is in thermodynamic equilibrium with an absolutely black body at a given temperature (for example, radiation inside a cavity in an absolutely black body) is called blackbody (or thermal equilibrium) radiation. Equilibrium thermal radiation is homogeneous, isotropic and non-polarized, there is no energy transfer in it, all its characteristics depend only on the temperature of an absolutely blackbody emitter (and since blackbody radiation is in thermal equilibrium with a given body, this temperature can be attributed to radiation).

Very close in its properties to the blackbody is the so-called relic radiation, or the cosmic microwave background - radiation filling the Universe with a temperature of about 3 K.

24) Elementary quantum theory of radiation. The main thing here (briefly): 1) Radiation is a consequence of the transition of a quantum system from one state to another - with less energy. 2) Radiation does not occur continuously, but in portions of energy - quanta. 3) The quantum energy is equal to the energy difference between the levels. 4) The radiation frequency is determined by the well-known formula E=hf. 5) A radiation quantum (photon) exhibits the properties of both a particle and a wave. Detail: The quantum theory of radiation was used by Einstein to interpret the photoelectric effect. The quantum theory of radiation makes it possible to substantiate Einstein's theory. The quantum theory of radiation (taking into account certain assumptions about renormalization) describes quite fully the interaction of radiation with matter. Despite this, it is tempting to argue that the conceptual foundations of the quantum theory of radiation and the notion of the photon are best viewed in terms of the classical field and vacuum-related fluctuations. However, advances in quantum optics have advanced new arguments for quantizing the electromagnetic field, and with them a deeper understanding of the nature of photons. The quantum theory of light emission makes significant use of the fact that the interaction energy between a substance (atom, molecule, crystal) and an electromagnetic field is very small. This allows, in the zeroth approximation, to consider the field and matter independently of each other and talk about photons and stationary states of matter. Accounting for the interaction energy in the first approximation reveals the possibility of a substance transition from one stationary state to another. These transitions are accompanied by the appearance or disappearance of a single photon and are therefore those elementary acts that make up the processes of emission and absorption of light by matter. According to the quantum theory of radiation, the elementary process of photoluminescence should be considered as consisting of the act of electronic excitation of molecules of a luminescent substance by absorbed photons and subsequent emission of molecules during their transition from an excited state to a normal one. As experimental studies have shown, the elementary process of photoluminescence does not always occur within the limits of one emitting center. To construct a quantum theory of radiation, it turned out to be necessary to take into account the interaction of an electron with a second-quantized field of photons.
The beginning of the development of the quantum theory of radiation from a charge moving in the electromagnetic field of a plane wave was laid by the well-known work of Klein and Nishina, in which the scattering of a photon by an electron at rest was considered. Planck put forward the quantum theory of radiation, according to which energy is emitted and absorbed not continuously, but in certain portions - quanta called photons. Thus, the quantum theory of radiation not only leads to the conclusions that follow from the wave theory, but also supplements them with a new prediction, which has found brilliant experimental confirmation. A wave packet with minimal uncertainty at various times in the potential field of a harmonic oscillator (a. the corresponding electric field (b. As the quantum theory of radiation developed and with the advent of the laser, the field states that most closely described the classical electromagnetic field were studied to a large extent. Since time The question of how well the Planck and Stefan-Boltzmann equations describe the energy density inside real, finite cavities with semi-reflective walls has been the subject of repeated discussions, most of which took place in the first two decades of this century, but the question was not completely closed, and in recent years interest in this and some other related problems has been revived.Among the reasons for the revival of interest in this oldest subject of modern physics are the development of quantum optics, the theory of partial coherence and its application to the study of statistical x radiation properties; insufficient understanding of the processes of heat exchange by radiation between closely spaced bodies at low temperatures and the problem of standards for far infrared radiation, for which the wavelength cannot be considered small, as well as a number of theoretical problems related to the statistical mechanics of finite systems. He also showed that in the limit of large volumes or high temperatures, the Jeans number is valid for a cavity of any shape. Later, based on the results of Weyl's work, asymptotic approximations were obtained, where D0 (v) was simply the first term of the series, the total sum of which D (v) was the average mode density. The wave to Vroy - Gosya in a circular orbit, it is necessary that the sum-la associated with the electro-marma trajectory length Znr be a multiple in the circle hypothesis. z z orbit. Waves that break down the wavelength of the electron. otherwise, the shaking interference - if the wave will be destroyed due to the action, fat - interferences are shown (9. Condition of the essential line. the formation of a stable orbit of radius r you. By analogy with the quantum theory of radiation, de Broglie suggested in 1924 that the electron and, moreover, any material particle in general, simultaneously possess both wave and corpuscular properties. According to de Broglie, a moving particle with mass m and velocity v corresponds to a wavelength K h / mv, where h is Planck's constant. In accordance with the quantum theory of radiation, the energy of elementary emitters can only change in jumps that are multiples of some value that is constant for a given radiation frequency. The minimum portion of energy is called an energy quantum. The brilliant agreement between the fully quantum theory of radiation and matter and experiment, achieved by the example of the Lamb shift, provided a strong argument in favor of quantizing the radiation field. However, a detailed calculation of the Lamb shift would take us far from the mainstream of quantum optics. Mössbauer transitions, the most convenient in the experimental. These data confirm the conclusions of the quantum theory of radiation for the gamma range.
Having presented this brief substantiation of the quantum theory of radiation, we proceed to the quantization of the free electromagnetic field. The rest mass of a photon in the quantum theory of radiation is considered to be zero. However, this is only a postulate of the theory, because no real physical experiment can confirm this. Let us dwell briefly on the main provisions of the quantum theory of radiation. If we want to understand the action of a beam splitter and its quantum properties on the basis of the quantum theory of radiation, we must follow the above recipe: first find the eigenmodes, and then quantize, as described in the previous chapter. But what are the boundary conditions in our case that determine these modes. First, it is necessary to extend the quantum theory of radiation in order to consider non-quantum stochastic effects such as thermal fluctuations. This is an important component of the theory of partial coherence. In addition, such distributions make clear the connection between classical and quantum theories. The book is a manual for studying the courses Quantum Theory of Radiation and Quantum Electrodynamics. The principle of building the book: the presentation of the basics of the course occupies a small part of its volume, most of the factual material is given in the form of problems with solutions, the necessary mathematical apparatus is given in the appendices. All attention is focused on the non-relativistic nature of radiative transitions in atomic systems. Theoretically determine AnJBnm in the formula (11.32) elementary quantum theory of blackbody radiation is not able. Einstein showed, even before the development of the quantum theory of radiation, that a statistical equilibrium between radiation and matter is possible only when, along with stimulated emission proportional to the radiation density, there is spontaneous radiation that occurs even in the absence of external radiation. Spontaneous emission is due to the interaction of an atomic system with zero oscillations of the electromagnetic field. Einstein showed, even before the development of the quantum theory of radiation, that a statistical equilibrium between radiation and matter is possible only when, along with stimulated emission proportional to the density of radiation, there is spontaneous radiation that occurs even in the absence of external radiation. Spontaneous emission is due to the interaction of an atomic system with zero oscillations of the electromagnetic field. Stark and Einstein, based on the quantum theory of radiation, at the beginning of the 20th century formulated the second law of photochemistry: each molecule participating in a photochemical reaction absorbs one radiation quantum, which causes the reaction. The latter is due to the extremely low probability of repeated absorption of a quantum by excited molecules due to their low concentration in the substance. The expression for the absorption coefficient is obtained on the basis of the quantum theory of radiation. For the microwave region, it is a complex function depending on the square of the transition frequency, the line shape, temperature, the number of molecules at the lower energy level, and the square of the matrix element of the dipole moment of the transition

25 Einstein's radiation theory and light generation

Einstein begins by considering one difficulty in the theory of blackbody radiation. If we imagine that electromagnetic oscillators, which are body molecules, obey the laws of classical Maxwell-Boltzmann statistics, then each such oscillator will, on average, have an energy:

where R is Clapeyron's constant, N is Avogadro's number. Using Planck's relation between the average energy of an oscillator and the volumetric energy density, which is in equilibrium radiation with it:

where Eν is the average energy of the frequency v oscillator, L is the speed of light, ρ is the volume density of radiation energy, Einstein writes the equation:

From it, he finds the volumetric energy density:

“This relation,” writes Einstein, “found under the condition of dynamic equilibrium, not only contradicts experience, but also states that in our picture there can be no question of any unambiguous distribution of energy between ether and matter.” Indeed, the total radiation energy turns out to be infinite:

A similar conclusion was reached in the same year, 1905, independently by Rayleigh and Jean. Classical statistics leads to a law of radiation which is in sharp contrast to experiment. This difficulty has been called the "ultraviolet catastrophe".

Einstein points out that Planck's formula:

goes over for long wavelengths and high radiation densities into the formula he found:

Einstein emphasizes that the value of Avogadro's number coincides with the value found in another way. Turning further to Wien's law, which is well justified for large values ​​of ν/T, Einstein obtains an expression for the entropy of radiation:

"This equality shows that the entropy of monochromatic radiation of sufficiently low density depends on the volume in the same way as the entropy of an ideal gas or a dilute solution."

Rewriting this expression as:

and comparing it with Boltzmann's law:

S-S0= (R/N) lnW,

Einstein finds an expression for the probability that the radiation energy in the volume V0 will be concentrated in a part of the volume V:

Three light generation options

Fundamentally, there are three ways of generating light: thermal radiation, gas discharge of high and low pressure.

· Thermal radiation - radiation of a heated wire up to the maximum temperature during the passage of an electric current. The sample is the sun with a surface temperature of 6000 K. The element best suited for this is tungsten, with the highest melting point among metals (3683 K).

Example: Incandescent and halogen lamps are powered by thermal radiation.

· Gas arc discharge appears in a closed glass container filled with inert gases, metal vapors and rare earth elements when voltage is applied. The resulting glows of gaseous fillers give the desired color of light.

Example: Mercury, metal halide and sodium lamps operate due to gas arc discharge.

Luminescent process. Under the action of an electric discharge, mercury vapors pumped into a glass tube begin to emit invisible ultraviolet rays, which, falling on a phosphor deposited on the inner surface of the glass, are converted into visible light.

Example: Fluorescent lamps, compact fluorescent lamps are powered by the fluorescent process.

26) SPECTRAL ANALYSIS - a set of methods for determining the elemental and molecular composition and structure of substances by their spectra. With the help of S.<а. определяют как осн. компоненты, составляющие 50- 60% вещества анализируемыхобъектов, так и незначит. примеси в них (до и менее). С. а. - наиб. распространённый аналитич. метод, св. 20- 30% всеханализов выполняется с помощью этого метода, в т. ч. контроль состава сплавовв металлургии, автомоб. и авиац. пром-сти, технологии переработки руд, <анализ экологич. объектов и материалов высокой чистоты, хим., биол. и мед. <исследования. Особо важное значение С. а. имеет при поисках полезных ископаемых.

The basis of S. a. is the spectroscopy of atoms and molecules; it is classified according to the purposes of analysis and types of spectra. In atomic S. and. (ASA) determine the elemental composition of samples by atomic (ionic) emission and absorption spectra; in molecular S. and. (ISA) - the molecular composition of a substance according to the molecular spectra of absorption, emission, reflection, luminescence and Raman scattering of light. Emission S. a. carried out according to the emission spectra of excited atoms, ions and molecules. Absorption S. a. carried out according to the absorption spectra of the analyzed objects. In S. a. often combine multiple<спектральных методов, а также применяют др. аналитич. методы, что расширяетвозможности анализа. Для получения спектров используют разл. типы спектральныхприборов в зависимости от целей и условий анализа. Обработка эксперим. <данных может производиться на ЭВМ, встроенных в спектральный прибор. Atomic spectral analysis There are two basic atomic variant. a. - atomic emission (AESA) and atomic absorption (AAA). Atomic emission spectral analysis is based on the dependence 1 =f(c) of the intensity 1 of the spectral line of emission (emission) of the determined element x on its concentration in the analyzed object: where is the probability of a quantum transition from state q to state p, n q is the concentration of atoms in state q in the radiation source (substance under study), is the frequency of the quantum transition. If local thermodynamic equilibrium is satisfied in the radiation zone, the electron concentration p e 14 -10 15 and their velocity distribution is Maxwellian,<то where n a is the concentration of unexcited atoms of the element being determined in the radiation region, g q is the statistical weight of the q state, Z is the statistical sum over the q states, and level excitation energy q. Thus, the desired concentration n a is a f-tion of temperature, which practically cannot be strictly controlled. Therefore, usually measure the intensity of the analytical. lines relative to a certain ext.<стандарта, присутствующего в анализируемом объекте в известной концентрацииn ст. Если стандартная линия близка к аналитической, то (K - постоянная величина). Эта зависимость используется в С. а. в тех случаях, <когда отсутствует самообращение используемых линий.

In AESA, they are used in the main. spectral instruments with photo registration (spectrographs) and photoelectric. registration (quantometers). The radiation of the sample under study is directed to the entrance slit of the device using a lens system, falls on a dispersing device (prism or diffraction grating) and, after monochromatization, is focused by a lens system in the focal plane, where a photographic plate or a system of exit slits (quantometer) is located, behind which photocells or photomultipliers are installed. When photographing, the intensities of the lines are determined by the blackening density S, measured by a microphotometer: where p is the so-called. Schwarzschild constant, - contrast factor; t - exposure time. In AESA, the substance under study must be in the state of atomic gas.<Обычно атомизация и возбуждение атомов осуществляются одновременно - висточниках света. Для анализа металлов, сплавов и др. проводников чащевсего используют дуговой разряд или искровой разряд,гдев качестве электродов служат сами анализируемые пробы. Дуговой разряд применяетсяи для анализа непроводящих веществ. В этом случае порошкообразную пробупомещают в углубление в графитовом электроде (метод испарения) или с помощьюразл. устройств вводят порошок в плазму дугового разряда между горизонтальнорасположенными графитовыми электродами. Применяется также введение порошкообразныхпроб в дуговые плазмотроны. При АЭСА растворов в качестве источников возбуждающего света применяютпламя горючих газов (смеси ацетилен - кислород, ацетилен - закись азотаи др.). В качестве источников света начали использовать также безэлектродныйразряд и особенно индуктивносвязанную плазму. Во всех случаях растворв виде аэрозоля потоком аргона вводят в зону возбуждения спектра (темп-ра2500-3000 К в пламенах и 6000- 10000 К в плазме разряда), где происходитвысушивание, испарение и атомизация аэрозоля. Процесс атомизации в методах АЭСА обычно носит термич. характер, чтопозволяет сделать нек-рые обобщения. В реальных условиях, учитывающих кинетикупроцесса, для частиц, находящихся в зоне с темп-рой ТT кип (T кип - темп-pa кипения), зависимость кол-ва испарившихсячастиц от времени описывается ур-нием: where r is the radius of the particle, D is the coefficient. diffusion, - surface tension of the solution, p - saturated vapor pressure, M - mol. mass, - density. Using this equation, you can find the amount of substance evaporated during time t.

If in this case the molecule consists of elements n 1 and n 2, then the degree of atomization can be calculated from the equation: where M 1 and M 2 are at. masses of elements n 1 and n 2 ; Z 1 and Z 2 - statistical.<суммы по состояниям этих элементов, M МОЛ - мол. массаатомизирующейся молекулы, Z 3 - статистич. сумма по еёсостояниям, -энергия диссоциации молекулы. Такого типа расчёты позволяют найти концентрациюатомов определяемого элемента п а в ур-нии (2) и определитьеё связь с интенсивностью аналитич. линии. Необходимость учитывать взаимодействиеопределяемого элемента с окружающей средой, др. компонентами анализируемоговещества, ионизацию атомов определяемого элемента и др. эффекты значительноусложняет картину испарения и атомизации исследуемого вещества. С цельюоблегчения С. а. создаются спец. программы расчёта на ЭВМ достаточно сложныхреакций в газовой и конденсированных фазах при заданных темп-ре идавлении. В источниках излучения чаще всего не соблюдается термодинамич. равновесие, <поэтому эти расчёты могут использоваться лишь при выборе оптим. условийанализа. В АЭСА применяют эмпирич. метод, заключающийся в эксперим. построениианалитич. ф-ции с помощью серии стандартных образцов анализируемого материала с заранееточно известными содержаниями определяемого элемента. Такие образцы либоизготовляют специально, либо заранее в неск. образцах устанавливают концентрациюэтого элемента точными методами. Измеряя затем аналитич. сигнал , находят содержание определяемого элемента в пробе. Структура и физ.-хим. свойства анализируемого и стандартного объектовмогут оказаться неадекватными (различны, напр., условия парообразованиястепени атомизации, условий возбуждения). Эти различия приходится учитыватьпри С. а. В таких случаях используют метод факторного статистич. планированияэксперимента. В результате экспериментов получают т. н. ур-ния регрессии, <учитывающие влияние на интенсивность аналитич. линий концентраций всехэлементов, составляющих пробу, и устанавливают концентрацию анализируемогоэлемента с помощью этих ур-ний. Совр. многоканальные квантометры позволяютодновременно измерять интенсивность большого числа спектральных линий. <На основе этих эксперим. данных с помощью ЭВМ можно решать довольно сложныеслучаи анализа, однако за счёт измерения неск. линий случайная погрешностьопределения С. возрастает. Атомно-абсорбционный анализ (ААА) основан на зависимости аналитич. сигнала(абсорбционности) (где - интенсивности падающего и прошедшего сквозь образец света) от концентрации(Бугера- Ламберта - Берa закон): где k v - коэф. поглощения на частоте v, l - эфф. <длина светового пути в области поглощения, п - концентрация атомованализируемого элемента в парах. Схема установки ААА включает: независимый источник излучения света счастотой v, равной частоте аналитич. линии определяемого элемента; атомизатор, <преобразующий пробу в атомарный пар; спектрофотометр. Свет, прошедший сквозьатомный пар, системой линз направляется на входную щель спектрофотометра, <интенсивность аналитич. спектральной линии на выходе регистрируется фотоэлектрич. методом. Поскольку естественнаяширина спектральной линии, постоянна, зависит только от времени жизнивозбуждённого состояния и обычно пренебрежимо мала, разница контуров линиииспускания и поглощения определяется в осн. допплеровским и лоренцевским уширениями: (here p is pressure, c is the speed of light, m ​​is atomic, M is molecular mass, is the eff. cross section of collisions leading to broadening, K is a constant).T. Thus, the widths of the contours of the absorption and emission lines can be different depending on the pressure, temperature, and composition of the gas phase in the radiation source and in the absorbing cell, which will affect the form of the function and may lead to ambiguous results of S. a. To a certain extent, this can be eliminated by rather complex methods. In the Walsh method, lamps with a hollow cathode (HPC) are used, which emit spectral lines that are much narrower than the absorption lines of atoms of the elements being determined in conventional absorbing cells. As a result, the dependence in a fairly wide range of values ​​of A (0 -0.3) turns out to be a simple linear function. As an atomizer in AAA use decomp. flames based on mixtures of hydrogen - oxygen, acetylene - air, acetylene - nitrous oxide, etc. An aerosol of a sample solution blown into a burning flame is analyzed. The intensity and I 0 of the light transmitted through the flame during the aerosol supply and without it are successively measured. In modern instruments, the measurement is automated. In some cases, the processes of evaporation and subsequent atomization of the sample due to the low temperature of the flames (T ~ 3000 K) in the gas phase do not occur completely. The processes of evaporation of aerosol particles and the degree of atomization in the flame also strongly depend on the composition of the flame (the ratio of fuel and oxidizer), as well as on the composition of the aerosol solution. Good analytical reproducibility A signal (in the best cases, S r is 0.01-0.02) can be obtained by using CLP as sources, the radiation of which is highly stable, and by carrying out the processes of evaporation and atomization in the flame.

27) Natural width of the emission line. Doppler broadening of the emission line in gaseous media.NATURAL WIDTH OF THE SPECTRAL LINE- the width of the spectral line due to spontaneous quantum transitions of an isolated quantum system (atom, molecule, nucleus, etc.). E. w. With. l. called also radiation. width. In accordance with the uncertainty principle, excited levels i energies of a quantum system that have a finite lifetime t i, are quasi-discrete and have a finite (small) width (see Level width). The energy of an excited level is - the total probability of all possible spontaneous quantum transitions from the level i (A ik- probability of transition to the level k; see Einstein coefficients). If the energy level j, to which the quantum system passes, is also excited, then E. sh. With. l. is equal to (G i+G j). Probability dwij photon emission in the frequency range d w at the i-j transition is determined by f-loy: For resonant lines of atoms and ions, E. sh. With. l. is equal to: where f ij- strength of the transition oscillator i-j, it is very small compared to the transition frequency w ij: h/w ij~ a 3 (z + 1) 2 (here a \u003d 1/137 is the fine structure constant, z is the multiplicity of the ion charge). Forbidden lines have a particularly small width. Natural line width classic. oscillator with charge e, mass t and own frequency w 0 is equal to: Г= 2еw 2 0 /3ms 3 . Radiation damping also leads to a very small shift of the line maximum towards lower frequencies ~ Г 2 /4w 0 . Spontaneous quantum transitions that determine the finite width of energy levels and E. sh. With. l., do not always occur with the emission of photons. Doppler broadening of the spectral line. This broadening is associated with the Doppler effect, i.e., with the dependence of the observed radiation frequency on the velocity of the emitter. If a source that creates monochromatic radiation with a frequency in a stationary state moves with a speed towards the observer so that the projection of the velocity on the direction of observation is, then the observer registers a higher frequency of radiation. where c is the phase velocity of wave propagation; 0 - the angle between the direction of the velocity of the emitter and observation. In quantum systems, radiation sources are atoms or molecules. In a gaseous medium at thermodynamic equilibrium, the particle velocities are distributed according to the Maxwell-Boltzmann law. Therefore, the shape of the spectral line of the entire substance will be associated with this distribution. In the spectrum recorded by the observer, there must be a continuous set of particles, since different atoms move at different speeds relative to the observer. Considering only the velocity projections in the Maxwell-Boltzmann distribution, we can obtain the following expression for the shape of the Doppler spectral line: This dependence is a Gaussian function. The line width corresponding to the value. As the particle mass M increases and the temperature T decreases, the line width decreases. Due to the Doppler effect, the spectral line of the entire substance does not coincide with the spectral line of an individual particle. The observed spectral line of a substance is a superposition of the spectral lines of all particles of the substance, i.e., lines with different central frequencies. For light particles at ordinary temperature, the width of the Doppler line in the optical range can exceed the natural linewidth by several orders of magnitude and reach values ​​of more than 1 GHz. The process in which the shape of the spectral line of the entire substance does not coincide with the shape of the spectral line of each particle is called inhomogeneous broadening of the spectral line. In the considered case, the reason for the inhomogeneous broadening was the Doppler effect. The shape of the Doppler spectral line is described by a Gaussian function. If the distribution of particle velocities differs from the Maxwellian one, then the shape of the Doppler spectral line will also differ from the Gaussian function, but the broadening will remain inhomogeneous.

28 Lasers: principles of operation, main characteristics and applications

The laser is a source of monochromatic coherent light with a highly directive light beam.

The main physical process that determines the action of a laser is the stimulated emission of radiation. It occurs when a photon interacts with an excited atom when the photon energy exactly coincides with the excitation energy of the atom (or molecule).

As a result of this interaction, the atom goes into an unexcited state, and the excess energy is emitted in the form of a new photon with exactly the same energy, propagation direction and polarization as the primary photon. Thus, the consequence of this process is the presence of two absolutely identical photons. With further interaction of these photons with excited atoms similar to the first atom, a “chain reaction” of reproduction of identical photons “flying” in exactly the same direction can occur, which will lead to the appearance of a narrowly directed light beam. For the emergence of an avalanche of identical photons, a medium is needed in which there would be more excited atoms than unexcited ones, since photons would be absorbed when photons interact with unexcited atoms. Such a medium is called a medium with an inverse population of energy levels.

Lasers have found wide application, and in particular they are used in industry for various types of material processing: metals, concrete, glass, fabrics, leather, etc.

Laser technological processes can be conditionally divided into two types. The first of them uses the possibility of extremely fine focusing of the laser beam and precise dosing of energy, both in pulsed and continuous modes. In such technological processes, lasers of relatively low average power are used: these are gas lasers of pulsed-periodic action. With the help of the latter, a technology was developed for drilling thin holes in ruby ​​and diamond stones for the watch industry and a technology for manufacturing dies for drawing thin wire. The main field of application of low-power pulsed lasers is associated with cutting and welding of miniature parts in microelectronics and the electrovacuum industry, with marking miniature parts, automatic burning of numbers, letters, and images for the needs of the printing industry.

The second type of laser technology is based on the use of lasers with a high average power: from 1 kW and above. Powerful lasers are used in such energy-intensive technological processes as cutting and welding of thick steel sheets, surface hardening, guiding and alloying large parts, cleaning buildings from surface contaminants, cutting marble, granite, cutting fabrics, leather and other materials. In laser welding of metals, a high quality of the seam is achieved and the use of vacuum chambers is not required, as in electron beam welding, and this is very important in conveyor production.

Powerful laser technology has found application in mechanical engineering, the automotive industry, and the building materials industry. It allows not only to improve the quality of material processing, but also to improve the technical and economic indicators of production processes.

Gas lasers are perhaps the most widely used type of laser today, and perhaps surpass even ruby ​​lasers in this respect. Among the various types of gas lasers, one can always find one that will satisfy almost any requirement for a laser, with the exception of very high power in the visible region of the spectrum in a pulsed mode. High powers are needed for many experiments in studying the nonlinear optical properties of materials.

The peculiarities of gas lasers are mostly due to the fact that, as a rule, they are sources of atomic or molecular spectra. Therefore, the wavelengths of the transitions are precisely known, they are determined by the atomic structure and usually do not depend on environmental conditions.

SEMICONDUCTOR LASERS - The main example of the operation of semiconductor lasers is a magneto-optical storage device (MO).

30 . Open optical resonators. Longitudinal modes. transverse modes. Diffraction stability

In 1958 Prokhorov A.M. (USSR) and independently R. Dicke, A. Shavlov, Ch. Towns (USA) substantiated the idea of ​​the possibility of using open resonators in the optical range instead of cavity ones. Such resonators called open optical or simply optical, L >> l

If m = n = const, then

The resulting set of resonant frequencies belongs to the so-called longitudinal(or axial) fashion. Axial modes are oscillations that propagate strictly along the optical axis of the resonator. They have the highest quality. Longitudinal modes differ from one another only in frequency and field distribution along the Z axis (i.e., the difference between adjacent frequencies is constant and depends only on the cavity geometry)

Modes with different indices m and n will differ in the field distribution in the plane perpendicular to the resonator axis, i.e. in the transverse direction. Therefore, they are called transverse(or non-axial) mods. For transverse modes differing in indices m and n, the field structure will be different in the direction of the x and y axes, respectively.

The frequency difference of transverse modes with indices m and n differing by 1 is equal to:

can be represented as:

where NF is the Fresnel number, .

Each transverse mode corresponds to an infinite number of longitudinal modes, differing in the index g.

Modes characterized by the same indices m and n, but different g, are combined under the general name transverse modes. The oscillation corresponding to a certain g is called the longitudinal mode related to the given transverse mode.

In the theory of open resonators, it is customary to designate individual modes as TEMmnq, where m, n are the transverse indices of the mode, and g is the longitudinal index. The designation TEM corresponds to the English phrase Transvers Electromagnetic (Transverse electromagnetic oscillations that have negligible projections of the vectors E and H on the Z axis). Since the number g is very large, often the index g is omitted and the cavity modes are denoted TEMmn. Each type of transverse mode TEMmn has a specific field structure in the resonator cross section and forms a specific light spot structure on the resonator mirrors (Fig. 1.8). In contrast to a cavity resonator, open modes can be visually observed.

The diffraction losses of real modes turn out to be much smaller due to the fact that during multiple passes of radiation between the mirrors there is a "natural" selection of those modes in which the maximum field amplitude is located at the center of the mirrors. Thus, in the presence of diffraction losses, true modes cannot exist in an open resonator; stationary configurations of the electromagnetic field such as standing waves, similar to those existing in a cavity resonator. However, there are a certain number of modes of oscillation that have low diffraction losses (they are sometimes called quasi-modes or open-cavity modes). The field of these oscillations (modes) is concentrated near the resonator axis and practically drops to zero in its peripheral regions.

31 Mode composition of radiation of laser generators. Operating modes of solid-state lasers

The mode composition of the radiation depends significantly on the design and dimensions of the resonator. A semiconductor laser, as well as on the magnitude of the radiation power. A semiconductor laser emits a narrow spectral line, which narrows with increasing radiation power if pulsations and multimode effects do not appear. Line narrowing is limited by phase fluctuations due to spontaneous emission. Evolution of the emission spectrum with increasing power in injection. laser is shown in Fig. 7. In the single-frequency mode, a narrowing of the spectral line to Hz is observed; min. linewidth value in a semiconductor laser with single-frequency mode stabilization using a selective ext. resonator is 0.5 kHz. In a semiconductor laser, it is possible to obtain modulators by modulating the pump. radiation, eg. in the form of sinusoidal pulsations with a frequency reaching in some cases 10-20 GHz, or in the form of ultraviolet pulses of subpicosecond duration. Information was transmitted using a semiconductor laser. at a speed of 2-8 Gbps.

solid state laser- a laser in which a substance in a solid state is used as an active medium (as opposed to gases in gas lasers and liquids in dye lasers).

The working schemes of active substances of solid-state lasers are divided into three- and four-level ones. According to which of the schemes this active element works is judged by the energy difference between the main and lower working levels. The greater this difference, the higher the temperatures at which efficient generation is possible. For example, the ground state of the Cr3+ ion is characterized by two sublevels, the distance between which is 0.38 cm-1. With such a difference in energies, even at a liquid helium temperature (~4K), the population of the upper sublevel is only ~13°/0 less than the lower one, i.e., they are occupied in the same way and, therefore, ruby ​​is an active substance with a three-level scheme at any temperature. For the neodymium ion, the lower laser level for radiation at =1.06 μm is located 2000 cm-1 higher than the main one. Even at room temperature, neodymium ions are 1.4 -104 times less at the lower level than at the main level, and active elements that use neodymium as an activator operate according to a four-level scheme.

Solid-state lasers can operate in pulsed and continuous modes. There are two pulsed operation modes of solid-state lasers: the free-running mode and the Q-switched mode. In the free-running regime, the duration of the radiation pulse is practically equal to the duration of the pump pulse. In the Q-switched regime, the pulse duration is much shorter than the pump pulse duration.

32) Nonlinear Optics - a section of optics that studies the totality of optical phenomena observed during the interaction of light fields with a substance that has a nonlinear response of the polarization vector P to the electric field strength vector E of the light wave. In most substances, this nonlinearity is observed only at very high light intensities, achieved with lasers. It is customary to consider both the interaction and the process itself to be linear if its probability is proportional to the first power of the radiation intensity. If this degree is greater than one, then both the interaction and the process are called nonlinear. Thus, the terms linear and nonlinear optics arose. Appearance nonlinear optics is associated with the development of lasers that can generate light with a large electric field, commensurate with the microscopic field strength in atoms. The main reasons causing differences in the effect of high-intensity radiation from low-intensity radiation on matter: At high radiation intensity, the main role is played by multiphoton processes, when several photons are absorbed in an elementary act. At high radiation intensity, self-action effects arise, leading to a change in the initial properties of the substance under the influence of radiation. One of the most commonly used frequency-changing processes is second harmonic generation. This phenomenon allows the output of a Nd:YAG laser (1064 nm) or a titanium-doped sapphire laser (800 nm) to be converted into visible light at 532 nm (green) or 400 nm (violet), respectively. In practice, to implement doubling the frequency of light, a nonlinear optical crystal is installed in the output beam of laser radiation, oriented in a strictly defined way.

33) Light scattering - scattering of electromagnetic waves in the visible range during their interaction with matter. In this case, there is a change in the spatial distribution, frequency, polarization of optical radiation, although scattering is often understood only as a transformation of the angular distribution of the light flux. Let and be the frequencies of the incident and scattered light. Then If - elastic scattering If - inelastic scattering - Stokes scattering - anti-Stokes scattering Scattered light provides information about the structure and dynamics of the material. Rayleigh scattering- coherent scattering of light without changing the wavelength (also called elastic scattering) on ​​particles, inhomogeneities or other objects, when the frequency of the scattered light is significantly less than the natural frequency of the scattering object or system. Equivalent formulation: scattering of light by objects smaller than its wavelength. model of interaction with the oscillator of Raman scattering of light in the spectrum of scattered radiation, spectral lines appear, which are absent in the spectrum of primary (exciting) light. The number and location of the lines that appear are determined by the molecular structure of the substance. The expression for the radiation intensity is where P is the induced dipole moment, defined as the coefficient of proportionality α in this equation is called the polarizability of the molecule. Consider a light wave as an electromagnetic field of intensity E with oscillation frequency ν 0 : where E0- amplitude, a t- time.

Radiation flux Ф  physical quantity equal to the amount of energy radiated by a heated body from the entire surface per unit time:

Energy luminosity (radiance) of the body R energy radiated per unit time per unit area of ​​a heated body in the entire range of wavelengths (0< < ∞).:

Spectral density of energy luminosity R  , T is the energy emitted in the wavelength range from  to +d per unit time per unit area

Energy luminosity R T, which is integral radiation characteristic, is related to spectral energy luminosity density ratio

Since the wavelength and frequency are related by the known relation  = c/, the spectral characteristics of radiation can also be characterized by frequency.

Radiation characteristics of bodies

Rice. 3. Black body model

; a completely white body

; - a completely black body.

The absorption coefficient depends on the wavelength and is characterized by the spectral absorbance - a dimensionless physical quantity showing what fraction of the energy incident per unit time per unit of body surface in the wavelength range from  to  + d, it absorbs:

A body for which the absorbance is the same for all wavelengths and depends only on temperature is called gray:

2. Laws of thermal radiation

2.1. There is a relationship between the spectral density of energy luminosity and the absorptivity of any body, which is expressed Kirchhoff's law:

The ratio of the spectral density of the energy luminosity of any body to its absorptivity at a given wavelength and temperature is a constant value for all bodies and equal to the spectral density of the energy luminosity of a completely black body r  , T at the same temperature and wavelength.

Here r  , T  universal Kirchhoff function, at BUT  , T= 1 , i.e. the universal Kirchhoff function is nothing but Withthe spectral density of the energy luminosity of a completely black body.

Consequences of Kirchhoff's law:

Because BUT  , T < 1, то: энергия излучения любо­го тела всегда меньше энергии излу­че­ния абсолютно черного тела;

If the body does not absorb energy in a certain range of wavelengths ( BUT  , T= 0), then it does not emit it in this range ().

Integrated energy luminosity

For the gray body

those. the absorption coefficient characterizes the ratio of the emissivities of the gray and black bodies. In technical literature it is called the degree of blackness of the gray body.

2.2. Stefan-Boltzmann law established by D. Stefan (1879) from the analysis of experimental data, and then by L. Boltzmann (1884) - theoretically.

 \u003d 5.6710 -8 W / (m 2  K 4) - Stefan-Boltzmann constant,

those. the energy luminosity of a black body is proportional to its absolute temperature to the fourth power.

Stefan-Boltzmann gray body law

Wien's displacement law established by the German physicist W. Wien (1893)

, b= 2.910 -3 m K- Constant Guilt. (ten)

The wavelength, which accounts for the maximum spectral density of the energy luminosity of an absolutely black body, is inversely proportional to the absolute temperature of this body, i.e. with increasing temperature, the maximum energy release shifts to the short-wavelength range.

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thermal radiation

Thermal radiation is electromagnetic radiation that occurs due to the energy of the rotational and vibrational motion of atoms and molecules in the composition of a substance. Thermal radiation is characteristic of all bodies that have a temperature exceeding the temperature of absolute zero.

The thermal radiation of the human body belongs to the infrared range of electromagnetic waves. For the first time such radiation was discovered by the English astronomer William Herschel. In 1865, the English physicist J. Maxwell proved that IR radiation has an electromagnetic nature and represents waves with a length of 760 nm to 1-2 mm. Most often, the entire range of IR radiation is divided into regions: near (750nm-2.500nm), middle (2.500nm-50.000nm) and far (50.000nm-2.000.000nm).

Let us consider the case when body A is located in cavity B, which is limited by an ideal reflective (radiation-impervious) shell C (Fig. 1). As a result of multiple reflection from the inner surface of the shell, the radiation will remain within the mirror cavity and be partially absorbed by body A. Under such conditions, the system cavity B - body A will not lose energy, but only a continuous exchange of energy will occur between body A and the radiation that fills cavity B.

Equilibrium thermal radiation has the following properties: homogeneous (the same energy flux density at all points of the cavity), isotropic (possible directions of propagation are equiprobable), non-polarized (directions and values ​​of the vectors of electric and magnetic fields at all points of the cavity change randomly).

The main quantitative characteristics of thermal radiation are:

Energy luminosity is the amount of electromagnetic radiation energy in the entire wavelength range of thermal radiation, which is emitted by a body in all directions per unit surface area per unit time: R = E / (S t), [J / (m2s)] = [W /m2] Energy luminosity depends on the nature of the body, the temperature of the body, the state of the surface of the body and the wavelength of the radiation.

The spectral density of energy luminosity is the energy luminosity of a body for given wavelengths (λ + dλ) at a given temperature (T + dT): Rλ, T = f(λ, T).

The luminosity of a body within certain wavelengths is calculated by integrating Rλ, T = f(λ, T) for T = const:

The absorption coefficient is the ratio of the energy absorbed by the body to the incident energy. So, if the radiation of the flow dФfall falls on the body, then one part of it is reflected from the surface of the body - dФоtr, the other part passes into the body and is partially converted into heat dФabs, and the third part, after several internal reflections, passes through the body outward dФpr: α = dФabs /dFfall.

Monochromatic absorption coefficient - absorption coefficient of thermal radiation of a given wavelength at a given temperature: αλ, T = f(λ, T)

Among the bodies there are such bodies that can absorb all the thermal radiation of any wavelength that falls on them. Such perfectly absorbing bodies are called absolutely black bodies. For them α =1.

There are also gray bodies for which α<1, но одинаковый для всех длин волн инфракрасного диапазона.

The blackbody model is a small opening of the cavity with a heat-impervious shell. The hole diameter is not more than 0.1 of the cavity diameter. At a constant temperature, some energy is emitted from the hole, corresponding to the energy luminosity of a completely black body. But ABB is an idealization. But the laws of thermal radiation of a black body help to get closer to real patterns.

2. Laws of thermal radiation

Consequences from Kirchhoff's law:

A systematic study of the spectra of a number of elements allowed Kirchhoff and Bunsen to establish an unambiguous relationship between the absorption and emission spectra of gases and the individuality of the corresponding atoms. Thus, spectral analysis was proposed, with the help of which it is possible to identify substances whose concentration is 0.1 nm.

The distribution of the spectral density of energy luminosity for a black body, a gray body, an arbitrary body. The last curve has several maxima and minima, which indicates the selectivity of radiation and absorption of such bodies.

2. Stefan-Boltzmann law.

The German physicist Wilhelm Wien in 1893 formulated a law that determines the position of the maximum spectral density of the energy luminosity of a body in the radiation spectrum of a black body depending on temperature. According to the law, the wavelength λmax, which accounts for the maximum spectral density of the energy luminosity of a blackbody, is inversely proportional to its absolute temperature T: λmax \u003d w / t, where w \u003d 2.9 * 10-3 m K is Wien's constant.

Thus, with an increase in temperature, not only the total radiation energy changes, but also the very shape of the distribution curve of the spectral density of energy luminosity. The spectral density maximum shifts towards shorter wavelengths with increasing temperature. Therefore, Wien's law is called the law of displacement.

Wien's law is used in optical pyrometry - a method for determining temperature from the emission spectrum of highly heated bodies that are far from the observer. It was by this method that the temperature of the Sun was determined for the first time (for 470nm T = 6160K).

4. Planck's theory. A German scientist in 1900 put forward a hypothesis that bodies do not emit continuously, but in separate portions - quanta. The quantum energy is proportional to the radiation frequency: E = hν = h·c/λ, where h = 6.63*10-34 J·s is Planck's constant.

Thermal radiation and its characteristics

thermal radiation- this is the electromagnetic radiation of bodies, arising due to a change in their internal energy (the energy of the thermal motion of atoms and molecules).

The thermal radiation of the human body belongs to the infrared range of electromagnetic waves.

infrared rays occupy the range of electromagnetic waves with a wavelength from 760 nm to 1-2 mm.

Source of thermal radiation: any body whose temperature exceeds the temperature of absolute zero.

Flux (F)- the amount of energy that is emitted (absorbed) from the selected area (surface) in all directions per unit of time.

2. Integral emissivity (R)– radiation flux per unit surface area.

3. Spectral emissivity() - integral emissivity, related to the unit of the spectral interval

where is the integral emissivity;

is the width of the wavelength interval ().

4. Integral absorption capacity (absorption coefficient) is the ratio of the energy absorbed by the body to the incident energy.

is the radiation flux absorbed by the body;

- the flux of radiation that falls on the body.

5. Spectral absorbance - absorption coefficient related to a single spectral interval:

Completely black body. gray bodies

A black body is a body that absorbs all incident energy.

The absorption coefficient of a completely black body does not depend on the wavelength.

Examples of a completely black body: soot, black velvet.

Gray bodies are bodies in which.

Example: The human body is considered a gray body.

Black and gray bodies are a physical abstraction.

The laws of thermal radiation

1. Kirchhoff's law (1859): The ratio of the spectral emissivity of bodies to their spectral absorptivity does not depend on the nature of the radiating body and is equal to the spectral emissivity of a blackbody at a given temperature:

where is the spectral emissivity of a black body.

Thermal radiation is equilibrium - how much energy is emitted by the body, so much of it is absorbed by it.

Rice. 41. Curves of energy distribution in the spectra of thermal radiation

various bodies (1 - absolutely black body, 2 - gray body,

3 - arbitrary body)

2. Stefan-Boltzmann law (1879, 1884): the integral emissivity of a completely black body () is directly proportional to the fourth power of its thermodynamic temperature (T).

where - Stefan–Boltzmann constant

3. Wien's law (1893): the wavelength at which the maximum spectral emissivity of a given body falls is inversely proportional to temperature.

Where = - Constant guilt.

Rice. 42. Spectra of thermal radiation of a black body at various temperatures

Thermal radiation of the human body

The human body has a constant temperature due to thermoregulation. The main part of thermoregulation is the heat exchange of the body with the environment.

Heat transfer occurs through the following processes:

a) thermal conductivity (0%), b) convection (20%), c) radiation (50%), d) evaporation (30%).

The range of thermal radiation of the human body

Human skin surface temperature: .

The wavelength corresponds to the infrared range, therefore it is not perceived by the human eye.

Emissivity of the human body

The human body is considered a gray body, as it partially radiates energy () and absorbs radiation from the environment ().

The energy () that a person loses in 1 second from 1 of his body due to radiation is:

where ambient temperature: , human body temperature: .

Contact methods for determining temperature

Thermometers: mercury, alcohol.

Celsius scale: t°C

Kelvin scale: T = 273 + t°C

Thermography is a method for determining the temperature of a part of the human body remotely by assessing the intensity of thermal radiation.

Devices: thermograph or thermal imager (registers the temperature distribution in a selected area of ​​\u200b\u200ba person).

Lecture number 16. thermal radiation

1. The concept of thermal radiation and its characteristics

So what is thermal radiation?

Fig.1. Multiple reflection of thermal waves from the mirror walls of cavity B

If the distribution of energy remains unchanged for each wavelength, then the state of such a system will be in equilibrium, and the radiation will also be in equilibrium. The only type of equilibrium radiation is thermal. If, for some reason, the balance between radiation and the body shifts, then such thermodynamic processes begin to take place that will return the system to a state of equilibrium. If body A begins to radiate more than it absorbs, then the body begins to lose internal energy and the temperature of the body (as a measure of internal energy) will begin to fall, which will reduce the amount of radiated energy. The temperature of the body will drop until the amount of energy emitted becomes equal to the amount of energy absorbed by the body. Thus, an equilibrium state will come.

The absorption coefficient is the ratio of the energy absorbed by the body to the incident energy. So, if the radiation of the flow dФ fall falls on the body, then one part of it is reflected from the surface of the body - dФ neg, the other part passes into the body and is partially converted into heat dФ absorb, and the third part, after several internal reflections, passes through the body outward dФ pr : α = dФ absorb /dФ fall.

The absorption coefficient α depends on the nature of the absorbing body, the wavelength of the absorbed radiation, the temperature and the state of the surface of the body.

The blackbody model is a small opening of the cavity with a heat-impervious shell. The hole diameter is not more than 0.1 of the cavity diameter. At a constant temperature, some energy is emitted from the hole, corresponding to the energy luminosity of a completely black body. But ABB is an idealization. But the laws of thermal radiation of a black body help to get closer to real patterns.

2. Laws of thermal radiation

1. Kirchhoff's law. Thermal radiation is equilibrium - how much energy is emitted by the body, so much of it is absorbed by it. For three bodies in a closed cavity, we can write:

The indicated ratio will be true even when one of the bodies is AF:

This is Kirchhoff's law: the ratio of the spectral density of the energy luminosity of a body to its monochromatic absorption coefficient (at a certain temperature and for a certain wavelength) does not depend on the nature of the body and is equal for all bodies of the spectral density of the energy luminosity at the same temperature and wavelength.

1. The spectral energy luminosity of a blackbody is a universal function of the wavelength and body temperature.

2. The spectral energy luminosity of the blackbody is the largest.

3. The spectral energy luminosity of an arbitrary body is equal to the product of its absorption coefficient and the spectral energy luminosity of a completely black body.

4. Any body at a given temperature emits waves of the same wavelength that it emits at a given temperature.

In 1879, Austrian scientists Josef Stefan (experimentally for an arbitrary body) and Ludwig Boltzmann (theoretically for a black body) established that the total energy luminosity over the entire wavelength range is proportional to the fourth power of the absolute body temperature:

The German physicist Wilhelm Wien in 1893 formulated a law that determines the position of the maximum spectral density of the energy luminosity of a body in the radiation spectrum of a black body depending on temperature. According to the law, the wavelength λ max , which accounts for the maximum spectral density of the energy luminosity of a blackbody, is inversely proportional to its absolute temperature T: λ max \u003d w / t, where w \u003d 2.9 * 10 -3 m K is Wien's constant.

The presented laws did not make it possible to theoretically find the equations for the distribution of the spectral density of energy luminosity over wavelengths. The works of Rayleigh and Jeans, in which scientists studied the spectral composition of blackbody radiation based on the laws of classical physics, led to fundamental difficulties called the ultraviolet catastrophe. In the range of UV waves, the energy luminosity of the blackbody should have reached infinity, although in experiments it decreased to zero. These results contradicted the law of conservation of energy.

4. Planck's theory. A German scientist in 1900 put forward a hypothesis that bodies do not emit continuously, but in separate portions - quanta. The energy of a quantum is proportional to the radiation frequency: E = hν = h·c/λ, where h = 6.63*J·s is Planck's constant.

This formula is in agreement with experimental data over the entire range of wavelengths at all temperatures.

3. Radiation of real bodies and the human body

Thermal radiation from the surface of the human body plays an important role in heat transfer. There are such methods of heat transfer: thermal conductivity (conduction), convection, radiation, evaporation. Depending on the conditions in which a person finds himself, each of these methods can be dominant (for example, at very high environmental temperatures, the leading role belongs to evaporation, and in cold water, conduction, and a water temperature of 15 degrees is a deadly environment for a naked person, and after 2-4 hours fainting and death occur due to hypothermia of the brain). The share of radiation in the total heat transfer can be from 75 to 25%. Under normal conditions, about 50% at physiological rest.

There are features of the spectral density of the energy luminosity of real bodies: at 310K, which corresponds to the average temperature of the human body, the maximum of thermal radiation falls on 9700nm. Any change in body temperature leads to a change in the power of thermal radiation from the surface of the body (0.1 degree is enough). Therefore, the study of skin areas associated with certain organs through the central nervous system helps to identify diseases, as a result of which the temperature changes quite significantly (thermography of the Zakharyin-Ged zones).

4. Biological and therapeutic effect of heat and cold

The human body constantly emits and absorbs heat radiation. This process depends on the temperature of the human body and the environment. The maximum IR radiation of the human body falls on 9300nm.

5. Physical foundations of thermography. Thermal imagers

Thermography, or thermal imaging, is a functional diagnostic method based on the registration of infrared radiation from the human body.

Many companies have recently recognized the fact that it is sometimes quite difficult to “get through” to a potential client, his information field is so loaded with various kinds of advertising messages that they simply cease to be perceived.

Active phone sales are becoming one of the most effective ways to increase sales in a short time. Cold calls are aimed at attracting customers who have not previously applied for a product or service, but for a number of factors are potential customers. Having dialed the phone number, the active sales manager must clearly understand the purpose of the cold call. After all, telephone conversations require special skill and patience from the sales manager, as well as knowledge of the technique and methodology of negotiating.

Characteristics of thermal radiation

The main questions of the topic:

1. Characteristics of thermal radiation.

2. Laws of thermal radiation (Kirchhoff's law, Stefan-Boltzmann's law, Wien's law); Planck's formula.

3. Physical foundations of thermography (thermal imaging).

4. Body heat transfer.

Any body at temperatures above absolute zero (0 K) is a source of electromagnetic radiation, which is called thermal radiation. It arises due to the internal energy of the body.

The range of wavelengths of electromagnetic waves (spectral range) emitted by a heated body is very wide. In the theory of thermal radiation, it is often believed that here the wavelength varies from 0 to ¥.

The distribution of the energy of thermal radiation of a body over wavelengths depends on its temperature. At room temperature, almost all energy is concentrated in the infrared region of the electromagnetic wave scale. At a high temperature (1000°C), a significant part of the energy is emitted in the visible range as well.

Characteristics of thermal radiation

1. Flux (power) of radiation Ф(sometimes referred to as R) is the energy emitted in 1 second from the entire surface of the heated body in all directions in space and in the entire spectral range:

2. Energy luminosity R- energy radiated for 1 sec from 1 m 2 of the body surface in all directions in space and in the entire spectral range. If a S is the surface area of ​​the body

3. Spectral density of energy luminosity r λ- energy radiated in 1 sec from 1m 2 of the body surface in all directions at wavelength λ in a single spectral range , →

The dependence of r l on l is called spectrum thermal radiation of the body at a given temperature (at T= const). The spectrum gives the distribution of the energy emitted by the body over wavelengths. It is shown in fig. one.

It can be shown that the energy luminosity R is equal to the area of ​​the figure bounded by the spectrum and the axis (Fig. 1).

4. The ability of a heated body to absorb the energy of external radiation is determined by monochromatic absorption coefficient a l,

those. a l the ratio of the radiation flux with a wavelength l, absorbed by the body, to the radiation flux of the same wavelength, incident on the body. From (3.) it follows that and l - dimensionless quantity.

By type of addiction a from l all bodies are divided into 3 groups:

a= 1 at all wavelengths at any temperatures (Fig. 3, 1 ), i.e. A black body completely absorbs all radiation incident on it. There are no “absolutely black” bodies in nature; a closed opaque cavity with a small hole can serve as a model for such a body (Fig. 2). The beam that fell into this hole, after multiple reflections from the walls, will be almost completely absorbed.

The sun is close to an absolutely black body, its T = 6000 K.

2). gray bodies: their absorption coefficient a < 1 и одинаков на всех длинах волн при любых температурах (рис. 3, 2 ). For example, a human body can be considered a gray body in problems of heat exchange with the environment.

for them, the absorption coefficient a < 1 и зависит от длины волны, т.е. a l = f(l), this dependence is the absorption spectrum of the body (Fig. 3 , 3 ).

Thermal radiation wavelength

The laws of thermal radiation. Radiant warmth.

Maybe for someone it will be news, but the transfer of temperature occurs not only by heat conduction through the touch of one body to another. Each body (solid, liquid and gaseous) emits thermal rays of a certain wave. These rays, leaving one body, are absorbed by another body, and take on heat. And I will try to explain to you how this happens, and how much heat we lose by this radiation at home for heating. (I think many will be interested to see these figures). At the end of the article, we will solve a problem from a real example.

I was convinced of this more than once that sitting by the fire (usually large) my face was burned by these rays. And if I covered the fire with my palms and at the same time my arms were outstretched, it turned out that my face stopped burning. It is not difficult to guess that these rays are straight as light. It is not the air circulating around the fire that burns me, and not even the thermal conductivity of the air, but the direct invisible heat rays coming from the fire.

In space, there is usually a vacuum between the planets and therefore the transfer of temperatures is carried out exclusively by thermal rays (All rays are electromagnetic waves).

Thermal radiation has a nature such as light and electromagnetic rays (waves). Simply, these waves (rays) have different wavelengths.

For example, wavelengths in the range of 0.76 - 50 microns are called infrared. All bodies having a room temperature of + 20 °C emit mainly infrared waves with wavelengths close to 10 microns.

Any body, if only its temperature is different from absolute zero (-273.15 ° C), is capable of sending radiation into the surrounding space. Therefore, any body radiates rays to the surrounding bodies and, in turn, is influenced by the radiation of these bodies.

Thermal radiation can be absorbed or passed through the body, or it can simply be reflected off the body. The reflection of heat rays is similar to the reflection of a light beam from a mirror. The absorption of heat radiation is similar to how a black roof gets very hot from the sun's rays. And the penetration or passage of rays is similar to how rays pass through glass or air. The most common type of electromagnetic radiation in nature is thermal radiation.

Very close in its properties to a black body is the so-called relic radiation, or the cosmic microwave background - radiation filling the Universe with a temperature of about 3 K.

In general, in the science of heat engineering, in order to explain the processes of thermal radiation, it is convenient to use the concept of a black body in order to qualitatively explain the processes of thermal radiation. Only a black body is capable of facilitating calculations in some way.

As described above, any body is capable of:

2. Absorb thermal energy.

3. Reflect thermal energy.

A black body is a body that completely absorbs thermal energy, that is, it does not reflect rays and thermal radiation does not pass through it. But do not forget that the black body radiates thermal energy.

What difficulties arise in the calculation if the body is not a black body?

A body that is not a black body has these factors:

2. Reflects some part of the thermal radiation.

These two factors complicate the calculation so much that "mom don't cry." It's very difficult to count. And scientists on this occasion did not really explain how to calculate the gray body. By the way, a gray body is a body that is not a black body.

Thermal radiation has different frequencies (different waves), and each individual body can have a different radiation wave. In addition, when the temperature changes, this wavelength can change, and its intensity (radiation strength) can also change.

Consider an image that confirms the complexity of emissivity calculation.

The figure shows two balls that have particles of this ball in themselves. The red arrows are the rays emitted by the particles.

Consider a black body.

Inside the black body, deep inside, there are some particles that are indicated in orange. They emit rays that absorb nearby other particles, which are indicated in yellow. The rays of the orange particles of the black body are not able to pass through other particles. And therefore, only the outer particles of this ball emit rays over the entire area of ​​the ball. Therefore, the calculation of the black body is easy to calculate. It is also commonly believed that a black body emits the entire spectrum of waves. That is, it emits all available waves of various lengths. A gray body can emit part of the wave spectrum, only of a certain wavelength.

Consider a gray body.

Inside the gray body, the particles inside emit some part of the rays that pass through other particles. And that's why the calculation becomes much more complicated.

Thermal radiation is electromagnetic radiation resulting from the conversion of the energy of the thermal motion of body particles into radiation energy. It is the thermal nature of the excitation of elementary emitters (atoms, molecules, etc.) that opposes thermal radiation to all other types of luminescence and determines its specific property to depend only on the temperature and optical characteristics of the radiating body.

Experience shows that thermal radiation is observed in all bodies at any temperature other than 0 K. Of course, the intensity and nature of the radiation depend on the temperature of the radiating body. For example, all bodies with a room temperature of + 20 ° C emit mainly infrared waves with wavelengths close to 10 microns, and the Sun emits energy, the maximum of which falls on 0.5 microns, which corresponds to the visible range. At T → 0 K, bodies practically do not radiate.

Thermal radiation leads to a decrease in the internal energy of the body and, consequently, to a decrease in body temperature, to cooling. A heated body, due to thermal radiation, gives off internal energy and cools down to the temperature of the surrounding bodies. In turn, by absorbing radiation, cold bodies can heat up. Such processes, which can also occur in a vacuum, are called radiative heat transfer.

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

(Temperature range in Kelvin and their Color)

up to 1000 Red

5500-7000 Pure white

The blackest real substances, for example, soot, absorb up to 99% of the incident radiation (i.e., have an albedo equal to 0.01) in the visible wavelength range, but they absorb infrared radiation much worse. The deep black color of some materials (charcoal, black velvet) and the pupil of the human eye is explained by the same mechanism. Among the bodies of the solar system, the Sun has the properties of an absolutely black body to the greatest extent. By definition, the Sun reflects practically no radiation at all. The term was introduced by Gustav Kirchhoff in 1862.

According to the spectral classification, the Sun belongs to the type G2V (“yellow dwarf”). The surface temperature of the Sun reaches 6000 K, so the Sun shines with almost white light, but due to the absorption of part of the spectrum by the Earth's atmosphere near the surface of our planet, this light acquires a yellow tint.

Absolutely black body - absorbs 100% and at the same time heats up, and vice versa! a heated body - 100% radiates, which means that there is a strict pattern (the radiation formula of an absolutely black body) between the temperature of the Sun - and its spectrum - since both the spectrum and temperature have already been determined - yes, the Sun has no deviations from these parameters!

In astronomy, there is such a diagram - “Spectrum-Luminosity”, and so our Sun belongs to the “main sequence” of stars, to which most other stars belong, that is, almost all stars are “absolutely black bodies”, as it is not strange. Exceptions are white dwarfs, red giants and New, Super-New.

This is someone who did not study physics at school.

A black body absorbs ALL radiation and emits more than all other bodies (the more the body absorbs, the more it heats up; the more it heats up, the more it radiates).

Suppose we have two surfaces - gray (with a blackness factor of 0.5) and absolutely black (coefficient of 1).

The emissivity is the absorption coefficient.

Now on these surfaces by directing the same flux of photons, say, 100 pieces.

A gray surface will absorb 50 of them, a black surface will absorb all 100.

Which surface emits more light - in which "sits" 50 photons or 100?

The radiation of a completely black body was first correctly calculated by Planck.

The radiation of the Sun approximately obeys Planck's formula.

And so we begin to study the theory.

Under the radiation (radiation) understand the emission and propagation of electromagnetic waves of any kind. Depending on the wavelength, there are: X-ray, ultraviolet, infrared, light (visible) radiation and radio waves.

X-ray radiation - electromagnetic waves, the photon energy of which lies on the scale of electromagnetic waves between ultraviolet radiation and gamma radiation, which corresponds to wavelengths from 10−2 to 103 Angstroms. 10 Angstroms = 1 nm. (0,nm)

Ultraviolet radiation (ultraviolet, UV, UV) - electromagnetic radiation, occupying the range between the violet border of visible radiation and X-ray radiation (10 - 380 nm).

Infrared radiation - electromagnetic radiation occupying the spectral region between the red end of visible light (with a wavelength λ = 0.74 μm) and microwave radiation (λ

Now the entire range of infrared radiation is divided into three components:

Shortwave region: λ = 0.74-2.5 µm;

Medium wave region: λ = 2.5-50 µm;

Long-wavelength region: λ = 50-2000 µm;

Visible radiation - electromagnetic waves perceived by the human eye. The sensitivity of the human eye to electromagnetic radiation depends on the wavelength (frequency) of the radiation, with the maximum sensitivity at 555 nm (540 terahertz), in the green part of the spectrum. Since the sensitivity drops to zero gradually with distance from the maximum point, it is impossible to indicate the exact boundaries of the spectral range of visible radiation. Usually, a section of 380-400 nm (750-790 THz) is taken as a short-wave boundary, and 760-780 nm (385-395 THz) as a long-wave boundary. Electromagnetic radiation with such wavelengths is also called visible light, or simply light (in the narrow sense of the word).

Radio emission (radio waves, radio frequencies) - electromagnetic radiation with wavelengths of 5 10−5-1010 meters and frequencies, respectively, from 6 1012 Hz and up to several Hz. Radio waves are used in the transmission of data in radio networks.

Thermal radiation is a process of propagation in space of the internal energy of a radiating body by means of electromagnetic waves. The causative agents of these waves are the material particles that make up the substance. The propagation of electromagnetic waves does not require a material medium; in vacuum they propagate at the speed of light and are characterized by a wavelength λ or an oscillation frequency ν. At temperatures up to 1500 °C, the main part of the energy corresponds to infrared and partly to light radiation (λ=0.7÷50 µm).

It should be noted that the radiation energy is not emitted continuously, but in the form of certain portions - quanta. The carriers of these portions of energy are the elementary particles of radiation - photons, which have energy, number of motions and electromagnetic mass. When it hits other bodies, the radiation energy is partially absorbed by them, partially reflected, and partially passes through the body. The process of conversion of radiation energy into the internal energy of an absorbing body is called absorption. Most solid and liquid bodies emit energy of all wavelengths in the range from 0 to ∞, that is, they have a continuous emission spectrum. Gases emit energy only in certain wavelength ranges (selective emission spectrum). Solids radiate and absorb energy by the surface, and gases by volume.

The energy radiated per unit time in a narrow range of wavelengths (from λ to λ+dλ) is called the flux of monochromatic radiation Qλ. The radiation flux corresponding to the entire spectrum in the range from 0 to ∞ is called the integral, or total, radiant flux Q(W). The integral radiant flux emitted from a unit surface of the body in all directions of the hemispherical space is called the integral radiation density (W / m 2).

To understand this formula, consider an image.

It was not by chance that I depicted two versions of the body. The formula is valid only for a square-shaped body. Since the radiating area must be flat. Provided that it radiates only the surface of the body. Internal particles do not radiate.

Q is the energy (W) radiated by the rays from the entire area.

Knowing the radiation density of the material, it is possible to calculate how much energy is spent on radiation:

It must be understood that the rays emanating from the plane have different radiation intensities with respect to the normal of the plane.

Lambert's Law. The radiant energy emitted by the body propagates in space in different directions with different intensities. The law that establishes the dependence of the intensity of radiation on the direction is called Lambert's law.

Lambert's law states that the amount of radiant energy emitted by a surface element in the direction of another element is proportional to the product of the amount of energy emitted along the normal and the spatial angle made by the direction of radiation with the normal

The intensity of each ray can be found using the trigonometric function:

That is, it is a kind of angle coefficient and it strictly obeys the trigonometry of the angle. The coefficient only works for a black body. Since nearby particles will absorb side rays. For a gray body, it is necessary to take into account the number of rays passing through the particles. The reflection of the rays must also be taken into account.

Consequently, the largest amount of radiant energy is emitted in a direction perpendicular to the radiation surface. Lambert's law is completely valid for a completely black body and for bodies that have diffuse radiation at a temperature of °C. For polished surfaces, Lambert's law does not apply. For them, radiation at an angle will be greater than in the direction normal to the surface.

A little about definitions. Definitions come in handy to express yourself correctly.

Note that most solid and liquid bodies have a continuous (continuous) emission spectrum. This means that they have the ability to emit rays of all wavelengths.

The radiant flux (or radiation flux) is the ratio of radiant energy to the radiation time, W:

where Q is the radiation energy, J; t - time, s.

If a radiant flux emitted by an arbitrary surface in all directions (i.e. within a hemisphere of arbitrary radius) is carried out in a narrow wavelength range from λ to λ + Δλ, then it is called a monochromatic radiation flux

The total radiation from the surface of the body over all wavelengths of the spectrum is called the integral or total radiation flux Ф

The integral flux emitted from a unit surface is called the surface flux density of the integral radiation or emissivity, W / m 2,

The formula can also be applied to monochromatic radiation. If thermal monochromatic radiation falls on the surface of a body, then in the general case, a part equal to B λ of this radiation will be absorbed by the body, i.e. will turn into another form of energy as a result of interaction with matter, part of F λ will be reflected, and part of D λ will pass through the body. If we assume that the radiation incident on the body is equal to unity, then

where B λ , F λ , D λ are the absorption and reflection coefficients, respectively

and transmission of the body.

When B, F, D remain constant within the spectrum, i.e. do not depend on the wavelength, then there is no need for indices. In this case

If B \u003d 1 (F \u003d D \u003d 0), then a body that completely absorbs all radiation incident on it, regardless of the wavelength, direction of incidence and state of radiation polarization, is called a black body or a full radiator.

If F=1 (B=D=0), then the radiation incident on the body is completely reflected. In the case when the surface of the body is rough, then the rays are reflected diffusely (diffuse reflection), and the body is called white, and when the surface of the body is smooth and the reflection follows the laws of geometric optics, then the body (surface) is called mirror. In the case when D \u003d 1 (B \u003d F \u003d 0), the body is permeable to thermal rays (diathermic).

Solids and liquids are practically opaque to thermal rays (D = 0), i.e. athermic. For such bodies

Absolutely black, as well as transparent or white bodies, do not exist in nature. Such bodies must be regarded as scientific abstractions. But still, some real bodies can come close enough in their properties to such idealized bodies.

It should be noted that some bodies have certain properties with respect to rays of a certain wavelength, and others with respect to rays of a different wavelength. For example, a body may be transparent to infrared rays and opaque to visible (light) rays. The surface of a body can be smooth for rays of one wavelength and rough for rays of another wavelength.

Gases, especially those under low pressure, in contrast to solids and liquids, emit a line spectrum. Thus, gases absorb and emit rays of only a certain wavelength, while they can neither emit nor absorb other rays. In this case, one speaks of selective (selective) absorption and emission.

In the theory of thermal radiation, an important role is played by a quantity called the spectral density of the radiation flux, or spectral emissivity, which is the ratio of the density of the radiant flux emitted in an infinitely small interval of wavelengths from λ to λ + Δλ, to the size of this interval of wavelengths Δλ, W / m 2,

where E is the surface density of the radiant flux, W/m 2 .

Why is there no such material guide? Because the heat loss by thermal radiation is very small, and I think it is unlikely to exceed 10% in our living conditions. Therefore, they are not included in the calculation of heat losses. That's when we often fly into space, then all the calculations will appear. Rather, in our astronautics, data on materials have accumulated, but they are not yet freely available.

Law of absorption of radiant energy

If a radiant flux falls on any body of thickness l (see figure), then in the general case, when passing through the body, it decreases. It is assumed that the relative change in the radiant flux along the path Δl is directly proportional to the path of the stream:

The coefficient of proportionality b is called the absorption index, which generally depends on the physical properties of the body and the wavelength.

Integrating from l to 0 and keeping b constant, we get

Let us establish the relationship between the spectral absorption coefficient of the body B λ and the spectral absorption index of the substance b λ .

From the definition of the spectral absorption coefficient B λ we have

After substituting the values ​​into this equation, we obtain the relationship between the spectral absorption coefficient B λ and the spectral absorption index B λ .

The absorption coefficient B λ is zero for l 1 = 0 and b λ = 0. For a large value of bλ, a very small value of l is sufficient, but still not equal to zero, so that the value of B λ is arbitrarily close to unity. In this case, we can say that absorption occurs in a thin surface layer of the substance. Only in this understanding is it possible to speak of surface absorption. For most solids, due to the large value of the absorption index b λ, “surface absorption” takes place in the indicated sense, and therefore the state of its surface has a great influence on the absorption coefficient.

Bodies, although with a small value of the absorption index, such as gases, can, with their sufficient thickness, have a large absorption coefficient, i.e. are made opaque to rays of a given wavelength.

If b λ \u003d 0 for the interval Δλ, and for other wavelengths b λ is not equal to zero, then the body will absorb the incident radiation only of certain wavelengths. In this case, as mentioned above, one speaks of a selective (selective) absorption coefficient.

Let us emphasize the fundamental difference between the absorption index of a substance b λ and the absorption coefficient B λ of a body. The first characterizes the physical properties of matter in relation to rays of a certain wavelength. The value of В λ depends not only on the physical properties of the substance of which the body consists, but also on the shape, size and condition of the surface of the body.

Laws of radiation of radiant energy

Max Planck theoretically, on the basis of electromagnetic theory, established a law (called Planck's law), expressing the dependence of the spectral emissivity of a black body E 0λ on wavelength λ and temperature T.

where E 0λ (λ, T) is the emissivity of the black body, W / m 2; T - thermodynamic temperature, K; C 1 and C 2 are constant; C 1 \u003d 2πhc 2 \u003d (3.74150 ± 0.0003) 10-16 W m 2; C 2 =hc/k=(1.438790±0.00019) 10 -2; m K (here h=(6.626176±0.000036) J s is Planck's constant; c=(±1.2) m/s is the propagation velocity of electromagnetic waves in free space: k is Boltzmann's constant.)

It follows from Planck's law that the spectral emissivity can be zero at a thermodynamic temperature equal to zero (T=0), or at a wavelength λ = 0 and λ→∞ (at T≠0).

Consequently, a black body radiates at any temperature greater than 0 K. (T> 0) rays of all wavelengths, i.e. has a continuous (continuous) emission spectrum.

From the above formula, you can get the calculated expression for the emissivity of the black body:

Integrating within the range of λ from 0 to ∞, we obtain

As a result of expanding the integrand into a series and integrating it, a calculated expression for the blackbody radiance is obtained, called the Stefan-Boltzmann law:

where E 0 is the emissivity of the black body, W / m 2;

σ - Stefan Boltzmann's constant, W / (m 2 K 4);

σ = (5.67032 ± 0.00071) 10 -8;

T is thermodynamic temperature, K.

The formula is often written in a more convenient form for calculation:

where E 0 is the emissivity of a black body; C 0 \u003d 5.67 W / (m 2 K 4).

The Stefan-Boltzmann law is formulated as follows: the emissivity of a black body is directly proportional to its thermodynamic temperature to the fourth power.

Spectral distribution of black body radiation at different temperatures

λ - wavelength from 0 to 10 µm (nm)

E 0λ - should be understood as follows: As if in the volume (m 3) of a black body there is a certain amount of energy (W). This does not mean that it radiates such energy only from the outer particles. Simply, if we collect all the particles of a black body in a volume and measure the emissivity of each particle in all directions and add them all, then we will get the total energy on the volume, which is indicated on the graph.

As can be seen from the location of the isotherms, each of them has a maximum, and the higher the thermodynamic temperature, the greater the value of E0λ corresponding to the maximum, and the maximum point itself moves to the region of shorter waves. The shift of the maximum spectral emissivity E0λmax to shorter wavelengths is known as

Wien's displacement law, according to which

T λ max \u003d 2.88 10 -3 m K \u003d const and λ max \u003d 2.88 10 -3 / T,

where λ max is the wavelength corresponding to the maximum value of the spectral emissivity E 0λmax .

So, for example, at T = 6000 K (the approximate temperature of the surface of the Sun), the maximum E 0λ is located in the region of visible radiation, on which about 50% of the solar radiation falls.

The elementary area under the isotherm, shaded on the graph, is equal to E 0λ Δλ. It is clear that the sum of these areas, i.e. the integral is the black body emissivity E 0 . Therefore, the area between the isotherm and the x-axis depicts the black body emissivity on a conventional scale of the diagram. At low values ​​of the thermodynamic temperature, the isotherms pass in close proximity to the abscissa axis, and the indicated area becomes so small that it can practically be considered equal to zero.

The concepts of so-called gray bodies and gray radiation play an important role in technology. Gray is a non-selective thermal emitter capable of emitting a continuous spectrum, with a spectral emissivity E λ for waves of all wavelengths and at all temperatures, which is a constant fraction of the spectral emissivity of a black body E 0λ i.e.

The constant ε is called the emissivity of the heat emitter. For gray bodies emissivity ε E - Emissivity, W;

B - absorption coefficient;

F - reflection coefficient;

D - transmittance;

T - Temperature K.

It can be assumed that all the rays sent by one body completely fall on the other. Let us assume that the transmission coefficients of these bodies are D 1 = D 2 = 0 and there is a heat-transparent (diathermic) medium between the surfaces of two planes. Denote by E 1 , B 1 , F 1 , T 1 , and E 2 , B 2 , F 2 , T 2 respectively the emissivities, absorption coefficients, reflections and temperatures of the surfaces of the first and second bodies.

The flux of radiant energy from surface 1 to surface 2 is equal to the product of the radiance of surface 1 and its area A, i.e. E 1 A, from which part of E 1 B 2 A is absorbed by surface 2, and part of E 1 F 2 A is reflected back to surface 1. From this reflected flow E 1 F 2 A, surface 1 absorbs E 1 F 2 B 1 A and reflects E 1 F 1 F 2 A. FROM the reflected energy flow E 1 F 1 F 2 A, surface 2 will again absorb E 1 F 1 F 2 B 2 A and reflect E 1 F 1 F 2 A, etc.

Similarly, there is a transfer of radiant energy by the flow E 2 from surface 2 to surface 1. As a result, the radiant energy flux absorbed by surface 2 (or given away by surface 1)

The flux of radiant energy absorbed by surface 1 (or given off by surface 2),

Ultimately, the flux of radiant energy transmitted by surface 1 to surface 2 will be equal to the difference between the radiant fluxes Ф 1→2 and Ф 2→1 i.e.

The resulting expression is valid for all temperatures T 1 and T 2 and, in particular, for T 1 = T 2 . In the latter case, the system under consideration is in dynamic thermal equilibrium, and on the basis of the second law of thermodynamics, it is necessary to put Ф 1→2 = Ф 2→1, from which it follows

The resulting equality is called Kirchhoff's law: the ratio of the emissivity of a body to its absorption coefficient for all gray bodies at the same temperature is the same and equal to the emissivity of a black body at the same temperature.

If a body has a small absorption coefficient, such as a well-polished metal, then this body also has a low emissivity. On this basis, in order to reduce heat loss by radiation to the external environment, heat-releasing surfaces are covered with sheets of polished metal for thermal insulation.

When deriving Kirchhoff's law, gray radiation was considered. The conclusion remains valid even if the thermal radiation of both bodies is considered only in a certain part of the spectrum, but nevertheless has the same character, i.e. both bodies emit rays whose wavelengths lie in the same arbitrary spectral region. In the limiting case, we arrive at the case of monochromatic radiation. Then

those. for monochromatic radiation, Kirchhoff's law should be formulated as follows: the ratio of the spectral emissivity of a body at a certain wavelength to its absorption coefficient at the same wavelength is the same for all bodies at the same temperatures, and is equal to the spectral emissivity of a black body at the same wavelength waves at the same temperature.

We conclude that for a gray body B = ε, i.e. the concepts of "absorption coefficient" B and "blackness coefficient" ε for a gray body coincide. By definition, the blackness coefficient does not depend on either temperature or wavelength, and, consequently, the absorption coefficient of a gray body also does not depend on either wavelength or temperature.

The radiation of gases differs significantly from the radiation of solid bodies. Absorption and emission of gases - selective (selective). Gases absorb and emit radiant energy only in certain, rather narrow intervals Δλ of wavelengths - the so-called bands. In the rest of the spectrum, gases do not emit or absorb radiant energy.

Diatomic gases have a negligible ability to absorb radiant energy, and consequently, a small ability to radiate it. Therefore, these gases are usually considered diathermic. Unlike diatomic gases, polyatomic gases, including triatomic gases, have a significant ability to emit and absorb radiant energy. Of the triatomic gases in the field of heat engineering calculations, carbon dioxide (CO 2) and water vapor (H 2 O), which each have three emission bands, are of the greatest practical interest.

In contrast to solids, the absorption coefficient for gases (of course, in the region of absorption bands) is small. Therefore, for gaseous bodies it is no longer possible to speak of "surface" absorption, since the absorption of radiant energy occurs in a finite volume of gas. In this sense, the absorption and emission of gases are called volumetric. In addition, the absorption coefficient b λ for gases depends on temperature.

According to the absorption law, the spectral absorption coefficient of a body can be determined from:

For gaseous bodies, this dependence is somewhat complicated by the fact that the gas absorption coefficient is affected by its pressure. The latter is explained by the fact that absorption (radiation) proceeds the more intensely, the more molecules the beam meets on its way, and the volumetric number of molecules (the ratio of the number of molecules to volume) is directly proportional to pressure (at t = const).

In technical calculations of gas radiation, usually absorbing gases (CO 2 and H 2 O) are included as components in the mixture of gases. If the pressure of the mixture is p, and the partial pressure of the absorbing (or emitting) gas is p i, then it is necessary to substitute the value p i 1 instead of l. The value p i 1, which is the product of the gas pressure and its thickness, is called the effective layer thickness. Thus, for gases, the spectral absorption coefficient

The spectral absorption coefficient of a gas (in space) depends on the physical properties of the gas, the shape of the space, its dimensions, and the temperature of the gas. Then, in accordance with the Kirchhoff law, the spectral radiance

Emissivity within one band of the spectrum

This formula determines the radiance of a gas into free space (emptiness). (Free space can be considered as a black space at 0 K.) But the gas space is always limited by the surface of a solid, in the general case having a temperature T st ≠ T g and emissivity ε st

The spectral composition of the radiation of individual excited atoms is a set of relatively narrow lines. This means that the light emitted by rarefied gases or vapors is concentrated in narrow spectral intervals near certain frequencies characteristic of atoms of each type.

Thermal radiation. The radiation spectrum of solid and liquid bodies heated to a high temperature has a completely different form. In this radiation, called thermal, there are electromagnetic waves of all frequencies from a very wide range, i.e., its spectrum is continuous.

To get an idea of ​​the nature of thermal radiation, let us consider several bodies heated to different temperatures and placed in a closed cavity, the inner walls of which completely reflect the radiation incident on them. Experience shows that such a system, in accordance with the provisions of thermodynamics, sooner or later comes to a state of thermal equilibrium, in which all bodies acquire the same temperature. This also happens if there is an absolute vacuum inside the cavity and the bodies can exchange energy only by

radiation and absorption of electromagnetic waves. This makes it possible to apply the laws of thermodynamics in the study of such a system.

In equilibrium, all bodies absorb the same amount of electromagnetic wave energy per unit time as they emit, and the energy density of the radiation filling the cavity reaches a certain definite value corresponding to the steady temperature. Such radiation, which is in thermodynamic equilibrium with bodies having a certain temperature, is called equilibrium or black radiation. Not only the energy density, i.e., the total energy per unit volume, but also the spectral composition of the equilibrium radiation filling the cavity depends only on the temperature and is completely independent of the properties of the bodies in the cavity.

Spectral composition of thermal radiation. The universal nature of the spectral composition of equilibrium radiation, as first shown by Kirchhoff back in 1860, follows directly from the second law of thermodynamics. Indeed, let us assume the opposite, i.e., that the spectral composition depends on the nature of the body with which the radiation is in equilibrium. Let us take two cavities in which the radiation is in equilibrium with different bodies, which, however, have the same temperature. Let us connect the cavities with a small hole so that they can exchange radiation. If the radiation energy densities in them are different, then a directed transfer of radiant energy occurs, which will lead to a spontaneous violation of the thermal equilibrium between the bodies, i.e., to the appearance of a certain temperature difference. This contradicts the second law of thermodynamics.

To experimentally study the spectral composition of equilibrium radiation, a small hole can be made in the shell surrounding the cavity. The radiation escaping through the hole, although not equilibrium, nevertheless has exactly the same spectral composition as the equilibrium radiation filling the cavity. The radiation emerging from the hole differs from the equilibrium one only in that it is not isotropic, since it propagates in a certain direction.

If the temperature in the cavity is increased, then the energy carried away by the radiation emerging from the hole will increase. This means that the volume energy density of equilibrium radiation increases with temperature. This growth is very fast, as we shall see below, in proportion to the fourth power of the thermodynamic temperature. With increasing temperature, the spectral composition of the radiation also changes, and in such a way that the maximum shifts to shorter wavelengths: the light coming out of a hole in a hot furnace has a reddish tint at a relatively low temperature and becomes yellow and even white as it rises.

What can be seen when looking through a hole into a cavity in which radiation is in equilibrium with bodies? Because

Since the properties of the radiation emerging from the hole at thermal equilibrium do not depend on the nature of the bodies inside the cavity, then the radiation cannot carry any information about these bodies, except for their temperature. And indeed, looking inside the furnace, we will not see any objects against the background of the walls of the cavity, nor the walls themselves, although a lot of light will enter the eye. The contours of objects inside the cavity will not be visible, everything will appear equally light.

The ability to distinguish objects appears only when using non-equilibrium radiation. Even if this radiation comes from hot bodies and its spectral composition is close to equilibrium, the temperature of the radiating surface must be higher than the temperature of the illuminated objects.

All regularities of black radiation observed in experience are described by Planck's formula, obtained on the basis of the rejection of the continuous nature of the radiation process.

Rice. Fig. 96. Frequency distribution of energy in the spectrum of equilibrium radiation (a) and spectral density of equilibrium radiation at different temperatures (b)

The frequency distribution of energy given by the Planck formula in the spectrum of equilibrium radiation

shown in fig. 96a. On fig. 96b shows the spectral density of equilibrium radiation as a function of wavelength at several temperatures.

Radiation as a gas of photons. Equilibrium thermal radiation can be considered as a gas consisting of photons. The photon gas is ideal, since different electromagnetic waves in vacuum do not interact with each other. Therefore, the establishment of thermal equilibrium in a photon gas is possible only when it interacts with matter.

The mechanism for establishing thermal equilibrium consists in the absorption of some and the emission of other photons by matter.

The possibility of absorption and emission of photons leads to a characteristic feature of a photon gas: the number of particles in it is not constant, but is itself determined from the condition of thermodynamic equilibrium.

The idea of ​​a photon gas makes it very easy to find the dependence of the energy density of equilibrium radiation on the thermodynamic temperature T. This can be done using dimensional considerations. The energy of a unit volume of radiation can be represented as the product of the average number of photons per unit volume uniformly filling the cavity by the average energy of one photon

The quantities on which the average photon energy and the number of photons per unit volume of equilibrium radiation can depend are the thermodynamic temperature T, the Boltzmann constant k, the speed of light c, and the Planck constant. Since the equilibrium radiation in a cavity does not depend on either the size and shape of the cavity or the nature of the bodies in the cavity, or the substance of its walls, then such parameters as the dimensions of the bodies and the cavity, and such constants as the charges and masses of electrons and nuclei, cannot appear in the expressions for

Dependence of energy density on temperature. The average energy of a photon of thermal radiation is equal in order of magnitude.

where is some dimensionless factor.

Formula (2) shows that the volume energy density of equilibrium radiation is proportional to the fourth power of the temperature in the cavity. Such a rapid increase in energy density with temperature is due not so much to an increase in the average photon energy (which is proportional to T) as to an increase in the number of photons in the cavity, which is proportional to the cube of temperature.

If there is a small hole in the wall of the cavity, then the radiation energy flux y through the unit area of ​​the hole is proportional to the product of the energy density in the cavity and the speed of light c:

where a is called the Stefan-Boltzmann constant. An exact calculation based on the application of statistical mechanics to a photon gas gives a value for it equal to

Thus, the total intensity of radiation from the hole is proportional to the fourth power of the thermodynamic temperature in the cavity.

Radiation from the surface of heated bodies differs from radiation from a hole in the cavity wall. The intensity and spectral composition of this radiation depend not only on temperature, but also on the properties of the radiating body. However, in many cases, the estimates can be considered that these differences are small.

Earth surface temperature. As an example of applying the law of thermal radiation (3), consider the question of the average temperature of the earth's surface. Let us assume that the heat balance of the Earth is determined mainly by the absorption of the energy of solar radiation and the radiation of energy into space, and the role of the processes taking place inside the Earth is not great. The total flux of energy radiated by the Sun, in accordance with (3), is equal to - the temperature of the surface of the Sun, - its radius. We will assume that all the energy of solar radiation incident on the Earth is absorbed. With the help of fig. 97 it is easy to understand that the amount of energy absorbed by the Earth per unit time is equal to

In conclusion, we note that the radiation spectrum of heated bodies is so wide that the efficiency of incandescent lamps and other lighting devices based on the radiation of hot bodies is completely negligible. The region of visible light corresponds only to a narrow band in the spectrum of thermal radiation.

Why do the energy density and spectral composition of the equilibrium radiation filling the cavity depend only on temperature? Why can't these quantities depend on the properties of the bodies in the cavity and on the material of its walls?

Why does the radiation emerging from the hole in the cavity, although not equilibrium, nevertheless have the same spectral composition as the equilibrium radiation inside the cavity? After all, gas molecules flying out through a hole in the wall of the vessel, on average, have more energy than the molecules in the vessel.

Why, looking through the hole into the red-hot furnace, we do not see the clear contours of the objects located there?

Why can radiation in a cavity, i.e., the totality of photons located there, be considered as an ideal gas?

Why is the interaction of photons with matter necessary to establish thermodynamic equilibrium in a gas of photons?

How does the concentration of photons in equilibrium radiation depend on temperature?

How, using dimensional considerations, to show that the energy of thermal radiation emitted by a body is proportional to the fourth power of the body's thermodynamic temperature?

If all the energy that comes to Earth from the Sun is ultimately radiated into space, then what is the meaning of the statement that the Sun gives life to everything that exists on Earth?

It has been experimentally found that thermal radiation from a heated body attracts - and does not repel! - nearby atoms. Although the phenomenon is based on the well-known effects of atomic physics, it went unnoticed for a long time and was theoretically predicted only four years ago.

Shift of energy levels due to thermal radiation

Recently appeared in the archive of electronic preprints, reporting experimental confirmation that thermal radiation from a hot body is able to attract nearby atoms to the body. The effect looks, at first glance, unnatural. Thermal radiation emitted by a heated body flies away from the source - so why is it capable of causing force attraction?!

Show comments (182)

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In the discussion, as is almost always the case now, one version of the "explanation" is postulated. In fact, its applicability had to be substantiated.
Igor! You are a very good person. For more than one year you have been rolling the stone of your mission.
What is gravity? Has its mechanical consideration again become scientific?
In the described experiment, a change in inertia was registered.
The rest is from the evil one, right?
The train of thought about the board on the waves is very interesting. (I myself am from the former).
Still, there may be different simple effects. For example, movement towards lowering of the bottom. In this situation, each subsequent wave may be slightly lower, and still have a vertical component.

I wonder if adding nanotubes to asphalt has nothing to do with topology premium?
Not?
Waves are not drawn on the EM plane?
Well, yes, ... yes.
And again these whirlwinds are at the level of Descartes

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The main value of this article is that it destroys some stereotypes and makes you think, which contributes to the development of creative thinking. I am very glad that such articles have started to appear here.

You can fantasize a little. If we further reduce the energy of the body (object), including the energy of internal interactions in elementary particles, then the energy of the object will become negative. Such an object will be pushed by ordinary gravity and will have the property of antigravity. In my opinion, the modern vacuum of our World does not have an absolute zero energy - because it is a well-structured environment, as opposed to absolute chaos. It's just that the level of vacuum energy in the energy scale is taken equal to zero. Therefore, there may be an energy level less than the vacuum energy level - there is nothing mystical about this.

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"Returning to the original theoretical paper of 2013, we mention the potential importance of this effect not only for atomic experiments, but also for cosmic phenomena. The authors considered the forces acting inside a dust cloud with a density of 1 g/cm3, heated to 300 K and consisting of particles of size 5 micron."
Is there an error here? The density of the dust cloud is too high, like that of the upper layer of regolith.
And by the phenomenon itself: and if we take a more non-trivial version of the problem - the action of thermal radiation on a non-polarizable particle, for example, an electron. Where will the force be directed? The heater is 100% dielectric.

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• Yes, this is a high density, on the verge of agglomeration of dust particles.

  An isolated electron has no energy levels, it has nothing to lower. Well, it does not have a dipole moment, within the limits of errors (there is a link in the text to the search for the electron EDM). Therefore, this force does not act on him. In addition, it is charged, photons are well scattered on it, so in general it will simply be repelled due to pressure.

  Reply

The far IR spectrum is convenient in that the photon energies are still small, so all requirements are met. Lower temperatures are also suitable, but there the effect is already very weak. At temperatures of thousands of degrees, the scattering of photons is already much stronger, and it interrupts this effect.

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• I'm not talking about a heated body. And about other emitters and spectra.
  All we're discussing here is wave effects. So they can't be limited to IR only.
  Do I understand correctly that, depending on the size of the particle, it is necessary to select the appropriate wavelength?
  For heavy atoms or hydrogen atoms, do you need to select your frequency so that the attraction is maximum?

  Now a cool idea is spinning in my head how to check it, for example, on the waves in the pool or the sea.
  Those. make a mechanical toy that will swim against the waves.
  What do you think about this possibility?

  Reply

  • 1) The wavelength must be significantly larger than the particle size.
    2) The system itself should not interact with an external influence as a whole, the interaction is carried out only due to induced polarization.
    3) There must be a discrete spectrum of excitations, and the photon energies must be significantly less than the distances between the levels, otherwise the waves will easily scatter and thereby exert pressure. When these conditions are met, the effect no longer depends on the wavelength.
    4) The force must be vector, not scalar, to lower the energy of the system.

    Now imagine if this can be implemented for waves on the water.

    Reply

    • Part of this effect I see well in the real world. I love yacht racing. And masters of sports in yachting win regattas precisely due to the ability to walk correctly against the wave. Those. if everything is done correctly, then the oncoming waves give the yacht additional energy.
      In fact, this is a paradox. But he is well seen in the races. As soon as the waves rise, "quantization" by skill levels immediately occurs)) Amateurs slow down, while the pros, on the contrary, get an additional advantage.

      So such a toy is quite real.
      I set up my yacht so that it went without control and any interference against the wind and against the waves without problems.
      If you dig deeper, then it is this setting that gives the maximum advantage.

      Let's just say, if you imagine a point source of strong wind in the middle of the lake, then my yacht will tend to it and go in circles indefinitely ...
      very beautiful and real analogy, for example, the movement of the earth around the sun)))
      and it seems that there is a certain force that drags the yacht to the source of the wind.

      By the way, you can put the problem on the elements and estimate, for example, the minimum distance at which the yacht can approach the source of the wind.

      Let me remind you that a sailing yacht sails against the wind with tacks, describing a semblance of a sinusoid. She turns only through the nose. If it is turned around, then the magic will disappear and it will go back with the wind.

      Reply

      I think you are a little confused. There are no similar effects in tacking. There is a complex sum of well-defined forces that gives a net force that has a non-zero negative projection along the wind direction axis.

      Reply

  • At first glance, far ... because there are waves and wind. But on the example of a yacht, everything works. If it is balanced, then it tends to the source of the wind with tacks. You just sit and enjoy the physics of the process while drinking cognac. It is especially cool to observe the moments of acceleration and the dynamics of the process at different points of the trajectory. Hands did not reach the truth to evaluate the approximate function that describes the trajectory.

    We built similar particle models and ran them on the computer.

    I propose another experiment.
    We take balls or balls of different sizes and put vibrators inside with a customizable frequency.
    We throw them on the smooth surface of the water and observe the effect of wave attraction or repulsion. No wind. Only due to vibrations and interference of waves on the water. You just need to pick up the frequency. Standing waves and resonance will do their job))
    I think I've seen this video somewhere.

    Reply

    • I don't think the waves have anything to do with it. And the physics is different. It is like jet propulsion, which acts perpendicular to the direction of the wind due to the sail (the sail turns the wind). At the same time, if the yacht is turned a little against the wind, then it will go there, because. the resistance of the water in this direction will be less than the direct drift of the yacht by the wind. I wish you a good rest, and more cognac!

      Reply

      • There is no jet thrust of course. Rather, your idea is clear, but this is not the correct definition.
        In the same way, say that a glider that flies due to air currents creates jet thrust.
        Sails against the wind work like an airplane wing.
        The skill of the sailor influences how he sets the sail and gives it the most efficient shape to generate power. Everything there is not very trivial. Sometimes a shift of 1 cm of the sheet (rope) is critical. At first, I even drew notches to keep up with the general company.

        As for physics.
        There are no ordinary waves without wind. On this idea, my colleague got his doctorate in physics. I also got a piece of doctor's sausage as a workhorse for programming the model and optimization. But the work was interesting.
        The analogy is the following. In the early days of wind exploration and sailing, there was only one way to go - walking with the wind. With a side wind without a keel, the ship has a huge drift. This is where the expression "wait for a fair wind" comes from.
        But then the keel and triangular sails appeared and it turned out to go against the wind with tacks.

        The same is true for solar sailing. Those. you can walk not only with the wind, but also with tacks to go to a source of radiation, such as a star.
        Cool?

        Reply

      • In the real world there is)) And the question is what is the keel. But this is all patented or closed by the NDA and I do not even have the right to speak and hint at specific solutions.
        But analogies can be discussed openly.
        Solve this puzzle and enjoy. You won't earn money.
        A yacht with a keel and sails is a system on a flat surface with vibrations in the 3rd dimension. She uses 2 environments.
        When we move into space, everything is the same but plus one dimension.
        If you are familiar with TRIZ (the theory of inventive problem solving), then there are clear methods for solving such problems. Rather, there are tips on how to think.

        Reply

        • With a tackling yacht, everything is banal: the yacht gains kinetic energy in the wind (the sails are "opened"), when moving against, due to interaction with the already aquatic environment, it turns against the wind (the sail is then placed in the position of minimum wind resistance). After that, the yacht can actually travel much further than at the acceleration stage, gradually losing kinetic energy to friction (in liquid helium, one could drive at least to infinity). Thus, in your task, the only question concerns how to deploy a knowingly folded (or placed edge to the sun) sail. Of course, there are a lot of options: the gravitational field of the planet, the magnetic (or electromagnetic) field from an external source, etc., etc., but alas, they all require some kind of external source. If you have it to solve a specific navigation task, fly. If not... You will not receive it by the forces of the installation itself. The law of conservation of momentum, damn it))

          Reply

          • In order to go against the wind, the yacht does not have to go with the wind. All race starts are against the wind.
            I repeat that a triangular sail is an aircraft wing with a lifting force directed at an angle to the boat's hull. And the projection is strong enough to go at an angle of 30 degrees to the wind. If you put the yacht even sharper, then the headwind already slows it down and the sail begins to oscillate and loses its aerodynamic shape. And those who better feel this limit win the race.
            It's not fun to ride in the wind.

            Reply

And here is a simple experiment on our topic. Can you explain?


What makes a curved path faster than a straight line?

It is obvious that if we observe this on our scale, then in the quantum world it will be exactly the same. And in the macro world too.

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• Banal school problem in physics. We simplify the model to one rectilinear trajectory with a small angle to the horizontal - and a trajectory in the form of a line with a break, where the first section is inclined to the horizon much more strongly, and the second one has an even smaller slope than the first trajectory. The beginning and end of the trajectories are the same. Let's ignore the friction. And we calculate the time of arrival to the "finish" for the cargo on one and the other way. 2nd z-n N. (eighth graders know what it is) will give that the time of arrival to the finish line on the second trajectory is less. If you now complete the problem with the second part of the installation, which represents a mirror image relative to the vertical at the end of the trajectory, slightly round the edges, then you will get your own case. Banality. Level "C" at the exam in physics. Not even an Olympiad task in terms of complexity

  Reply

  • I like your simplified idea. Maybe this will help the kids. Give me time to think and try to talk to teenagers.

    And if without simplification and everything is so banal, then what form of the trajectory is the fastest?

    Reply

"At temperatures of thousands of degrees, the scattering of photons is already much stronger, and it interrupts this effect."...

That's it!!!
Presumably, this effect works in a limited area and the corresponding types of energy interactions. "Frequency dispersion" and the dynamics corresponding to it - prevail in the boundary zones. Volodya Lisin tried to unearth some of the nuances of these processes in 1991, but
probably didn't make it. (I just couldn't get through to him.). In my opinion, this effect fades as the temperature gradients and (intensity of convection currents) decrease in the analyzed zone.
http://maxpark.com/community/5302/content/3334997#comment-44 797112
#10 MAG » 04.09.2015, 22:02
http://globalwave.tv/forum/viewtopic.php?f=20&t=65
Centuries have flown by, but without miracles... - "neither here nor there": (Film 7. Warmth and temperature)
https://www.youtube.com/watch?v=FR45i5WXGL8&index=7& list=PLgQC7tmTSjqTEDDVkR38piZvD14Kde
rYw

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Funny effect. It can shed light on the problem of the first gram in the formation of planets - how microscopic dust can stick together in a gas-dust cloud. As long as an atom, say, of hydrogen, is far from the particles, it is practically in isotropic thermal radiation. But if two dust particles inadvertently approach it, then, interacting with the atom with their radiation, they will receive an impulse to each other! The force is many times greater than gravitational force.

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• For sticking of dust particles, it is not necessary to fence such a cool physics. But what about "dust particles", we all understand that we are most likely talking about H2O, as the main solid component in many clouds? Compounds of carbon with hydrogen are extremely volatile (up to pentane), I won’t say anything about ammonia at all, substances other than H, He, C, N, O are in the minority, there are also few hopes for complex organics. So the solid will be mostly water. It is likely that in real clouds of gas, ice-snowflakes move quite chaotically and relatively quickly, I believe that with speeds of at least centimeters per second. Such an effect, as in the article, simply will not create such a potential for snowflakes to collide - the characteristic relative speeds of snowflakes are too high and snowflakes pass through each other's potential hole in a split second. But it doesn't matter. Snowflakes already often collide and, purely mechanically, lose energy on this. At some point, they will stick together due to molecular forces at the moment of contact and remain together, so that snow flakes will form. Here, in order to roll up small and very loose snowballs, neither thermal nor gravitational attraction is needed - only gradual mixing of the cloud is required.

  I also believe that the calculation in the article has a gross error. The pairwise attraction of dust grains was taken into account. But the dust in a dense cloud is opaque and gives uniform heat from all sides, i.e. we have a speck of dust inside a warm hollow chamber. And why would she fly into the area of ​​​​the nearest pollen? Those. for attraction to work, cold space is needed, and in a dense cloud it is not visible, which means there is no thermal gradient.

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  • >I also believe that the calculation in the article has a gross error. The pairwise attraction of dust grains was taken into account. But the dust in a dense cloud is opaque and gives uniform heat from all sides, i.e. we have a speck of dust inside a warm hollow chamber.

    Here I disagree. Here we can draw an analogy with plasma. In the approximation of an ideal collisionless plasma, everything is approximately as you say: the average field is considered, which, in the absence of external charges and currents, is equal to zero - the contributions from charged particles completely compensate each other. Nevertheless, when we begin to consider individual ions, it turns out that the influence from the nearest neighbors is still present, and it must be taken into account (which is done through the Landau collision integral). The characteristic distance beyond which one can forget about pairwise interaction is the Debye radius.

    For the interaction under consideration, I believe, a similar parameter will be infinite: the integral of 1/r^2 converges. For a rigorous proof, it would be necessary to construct a kinetic equation for the "fog" of droplets with such an interaction. Well, or use the Boltzmann equation: the scattering cross section is finite, which means that you don’t have to be so sophisticated, as in a plasma, by introducing an average field.

    Well, I thought, an interesting idea for an article, but everything is trivial. :(

    And in the article under discussion, they acted very simply: they estimated the total potential energy of a spherical cloud of microparticles with a Gaussian distribution. There is a ready-made formula for gravity, for this interaction (on the asymptotics r>>R) they calculated it. And it turned out that there is a noticeable area where the contribution of gravity is much smaller.

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    • > For the interaction under consideration, I believe that a similar parameter will be infinite

      Maybe zero? In general, I didn’t really understand your post, there is an overabundance of mathematics in it that I don’t know when it’s easier - in order to have an unbalanced force, you need a radiation density gradient, when there is no gradient, consider there is no force, because it is the same in all directions.

      > And it turned out that there is a noticeable area where the contribution of gravity is much smaller.

      Can't you be a little more specific? I don't really understand how this effect can help form anything in space to make any difference. For me, this is a useless value. It's like proving that the effect is more than 100500 times stronger than the gravitational interaction between neighboring atoms in Jupiter's atmosphere - I agree, but this is only because the gravitational interaction of individual dust particles is generally not interesting at all. But gravity is at least not shielded.

      The effect, I believe, increases in the near field when the distance approaches 0, but this is already a description of how exactly the dust grains collide if they have already collided.

      PS: the potential of a dust particle in thermal radiation, as I understand it, does not depend on the size of the cloud in order of magnitude - this potential depends only on the radiation density, i.e. on temperature and degree of opacity of the cloud. The degree of opacity in order of magnitude can be taken as 1. It turns out that no matter what kind of cloud we have, only the average temperature around is important. How big is this potential if it is expressed in terms of kinetic energy m/s? (I can and can calculate, but maybe there is a ready-made solution?) Also, if the cloud is opaque, then the potential of the cloud as a whole will be a function of the surface area of ​​the cloud. Curiously, we got the same surface tension, but in a slightly different way. And inside the cloud the dust will be free.

      Reply

You open the article of 2013, look, it is not difficult there, everything is described there in ordinary human language.

For illustration, they took a cloud with a finite radius of 300 meters and stupidly substituted numbers into the formulas for the situation inside and outside the cloud. The main observation is that even outside, at a distance of almost a kilometer from the center, thermal attraction is still stronger than gravitational attraction. This is just to get a feel for the scale of the effect. They acknowledge that the real situation is much more complex and needs to be modeled carefully.

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The dust is mainly represented (at 400°K) by olivine, soot, and silicon particles. They are "smoked" by red supergiants.
Dust particles convert kinetic energy into thermal energy. And they do not interact with each other, but with nearby atoms or molecules that are transparent to radiation. Since r is cubed, then the dust particles that are a millimeter, a centimeter away from the ATOM, each pull it towards themselves, and a resulting force appears that brings the dust particles together. At the same time, dust particles in a meter are ignored due to a decrease in the interaction force by billions (or even trillions) of times.

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“This radiation diverges in all directions, so its energy density decreases with distance as 1/r2. An atom, being nearby, feels this radiation - because it lowers its energy. And since the atom seeks to lower its interaction energy as much as possible, it is energetically beneficial for it to approach the ball - after all, the decrease in energy is most significant there!”
But, excuse me, if an atom rushes towards a heated ball, then it will not lower its energy in any way, but, on the contrary, will only increase it. I don't think this is the correct explanation.

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Here I came up with a problem. Let there be a thermally stabilized chamber composed of two black hemispheres of different radii, oriented in different directions, and an additional flat ring. Let the left hemisphere have a smaller radius than the right, a flat partition makes the chamber area closed. Let the atom be at the center of curvature of each of the two hemispheres and be motionless. Let the hemispheres be warm. The question is - will the atom experience a thermal force in one of the directions?

Here I see 2 solutions: 1) thermal equilibrium will quickly arise in such a chamber, i.e. the radiation density will be the same from all sides, and the same at any point of the chamber. If the density of thermal radiation in the chamber does not depend on the chosen point, then the potential of interaction with radiation does not change, and therefore there is no force.
2) Wrong decision. We divide the wall into surface elements of equal area and integrate the interaction force of the atom with the surface element. It turns out that the flat ring makes a zero contribution, and the closer left surface has quadratically fewer points, each of which drags a cube times stronger - i.e. a grain of dust flies to the nearest surface, i.e. left.

As you can see, the answer is completely different.

Explanation of the contradiction. If we have a radiating element of a non-spherical shape, then it does not shine equally in all directions. As a result, we have a radiation density gradient, the direction of which is not directed to the emitter. Then we get this - to break a complex surface into points, and to consider them as ROUND specks of dust becomes completely incorrect.

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Here an even more interesting problem came to mind. Let us have a heat emitter in the form of a flat black ring, whose outer and inner radii are equal to R and r. And exactly on the axis of the ring, at a distance h is an atom. Count h<

Solution 1 (wrong!). Break the ring into "motes", then take the integral of the attractive force of the atom and the elements of the ring over the surface. The calculation is not interesting, because one way or another, we get that the atom is drawn into the ring.
Solution 2. The ring cannot shine from the end or it shines vanishingly little, i.e. the energy potential of the atom at the points of the plane of the ring turns to 0 (potential maximum). The radiation of the ring will be non-zero at points whose height h above the plane of the ring is different from 0, at these points there will be a non-zero potential (less than 0). Those. we have a radiation density gradient, which locally (for h~=0, h<

It seems to me that solution 1 contains an error, I seem to understand where, but I can’t explain in simple words.

This task shows this. The atom is not attracted to the heat-radiating object, i.e. the force vector is not directed to the radiating surface. It doesn't matter to us WHERE the radiation comes from, it is important for us HOW MUCH radiation is at a particular point and what is the radiation density gradient. The atom goes in the direction of the radiation density gradient, and this gradient can be directed even to that half-plane in which there is not a single point of the emitter.

Problem 3. The same ring as in item 2, but the atom is initially at the point h=0. This state is balanced and symmetrical, but unstable. The solution is spontaneous symmetry breaking. The atom will be pushed out from the position of the center of symmetry, since it is unstable.

I also pay attention - it is not necessary to replace the cloud with attracting dust particles. It will turn out bad. If 3 dust particles stand on one straight line and slightly shade one another, then the symmetry will be spontaneously broken, this is not in gravitational forces, because gravity is not shielded.

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I have a question (not only to Igor, but to everyone). How does potential energy enter the gravitational mass of the system? I want to sort out this issue. For example, the universe consists of grains of dust evenly spaced in space, which gravitationally interact with each other. It is obvious that such a system has a large potential energy, since there is a state of the system in which these dust grains are concentrated into galaxies, each of which has a lower potential energy in comparison with the dust grains scattered over space of which they are composed. The specific question is the following - does the potential energy of this system enter into the gravitational mass of the universe?
It seems to me that this question is related to the topic that PavelS brought up. In an infinite universe, it is impossible to single out a sphere that encompasses it. And inside any other sphere, for example, enclosing a galaxy, the gravitational potential created by matter located behind the sphere (located on large scales almost uniformly in space) does not affect the behavior of bodies inside this sphere. Therefore, it is possible to speak about the entry of potential energy into the gravitational mass only in relation to local inhomogeneities in the distribution of matter.

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• I didn't raise this question. :) It also seemed to me that the expansion of the universe, taking into account dark energy and the reddening of photons, violates the law of conservation of energy, but with a strong desire, you can turn around and say that the total energy of the universe is still 0, because the substance is in a potential well, and the more substance, the deeper the well. For what I bought, for that I sell - I myself am not strong in details.

  About potential energy, it is usually considered to be less than zero. Those. free particles are zero, bound ones are already less than 0. So the negative potential energy works like a negative mass (mass defect) - the mass of the system is less than the mass of the individual components. For example, during the collapse of a supernova, the potential energy goes into a big minus, and the difference in the masses of what was and what has become can radiate outward in the form of photons (rather, not photons, but neutrinos in fact).

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  • The article discusses the manifestations of potential energy in the system. If there is a potential gradient of this energy in the system, then a force arises. You quite rightly noticed that in some conditions there is no gradient, due to complete symmetry (the atom is inside the sphere). I continued the analogy in relation to the universe, where as a whole there is no potential gravitational energy gradient. There are only local manifestations.

    There is a statement that the mass of matter mainly consists of the kinetic energy of quarks and gluons plus a small particle due to the Higgs field. If we assume that negative potential energy is also mixed in this mass, then this statement is not true.

    The proton mass is 938 MeV. The total mass of quarks, as physicists define it, is approximately 9.4 MeV. There is no mass defect here. I want to understand, in general, potential energy is somehow taken into account by the general theory of relativity, as a mass generator, or not. Or there is just energy - which is the sum of kinetic energy and potential.

    “For example, during the collapse of a supernova, the potential energy goes into a big minus, and the difference in the masses of what was and became can be radiated outward in the form of photons (rather, not photons, but actually neutrinos).”

    So what - a hole from the fact that the substance that got into it and is in a deep potential well does not become lighter, perhaps by the amount of the mass of energy - the substance that it returned back.

    Reply

    • "unless by the size of the mass of energy - the substance that she returned back"

      This "unless" can be arbitrarily large. So, having thrown off a kilogram into a black hole, it will be less than 1 kg more massive. In practice, up to 30% of the incident mass is emitted by an accretion disk in the form of X-rays, but the number of incident protons does not decrease. It is not a substance that is emitted, but X-rays. X-ray is not usually called the term substance.

      Read the news about the collision of two black holes, so there, too, the result is noticeably worse than the original holes in total.

      Finally, the question is WHERE are you with your weights. In what frame of reference and at what point? The measurement method is everything. Depending on this, you intend a different mass, but this IMHO is more of a terminological issue. If an atom is inside a neutron star, then you can't measure its mass except by comparing it with a neighboring test body that is nearby. In this regard, the mass of an atom does not decrease when falling into a well, but the mass of the total system is not equal to the sum of the masses of the components. I believe this is the most accurate terminology. In this case, the mass of the system is always measured relative to an observer outside this system.

      Reply

      • The term "the value of the mass of energy - matter" here means "the value of the mass of energy and the mass of matter." X-rays have a rest mass when trapped in a box of mirrors or in a black hole. Gravitational waves also carry energy, and must be taken into account in the mass generator in general relativity. I apologize for the inaccurate wording.

        Although, as I know, the practically stationary gravitational field in general relativity is not taken into account as part of the mass. Therefore, the potential energy of the field should not be taken into account either. Besides, potential energy is always relative. Or am I wrong? In this connection, the statement that the mass of the universe is 0 due to the negative energy (and mass) of the gravitational field is nonsense.

        In the black hole example, if we assume that in the process of falling into the hole, for example, a kilogram of potatoes, nothing flew back, I think that the black hole increases its mass by this kilogram. If the potential energy of the potato is not taken into account in the composition of the mass, then the arithmetic is as follows. When falling into a hole, the potato acquires a large kinetic energy. Due to which, if you look outside the hole, it increases its mass. But at the same time, when viewed from the outside, all processes in the potato slow down. If we make a correction for time dilation, then the mass of the potato when looking at it from an external reference system will not change. A black hole will increase its mass by exactly 1 kilogram.

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"For example, the universe consists of grains of dust evenly spaced in space, which gravitationally interact with each other."

Your model is already contradictory and out of touch with reality. You can come up with a bunch of such examples and each time come to any conclusions.
And the factor of order in your system will be entropy. And the potential energy will not give you any interesting results, since it is relative to the chosen reference point and the Observer.

In the real world, a similar model is a crystal. In it, atoms are evenly distributed in space and interact with each other.
Correct me if I'm wrong.

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• "Your model is already inconsistent and out of touch with reality."

  With regard to inconsistency, this must be proven. In relation to reality - maybe. This is a hypothetical model. It is slightly simplified for better understanding.

  “And entropy will be the factor of order in your system…”

  I agree.

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  • If you enjoy wave physics theories and like to model them, then try to explain this effect in our amazing universe.
    It manifests itself on all scales.
    https://cs8.pikabu.ru/post_img/2017/01/30/0/1485724248159285 31.webm

    I posted this for the AI ​​above too. It will be interesting to see his rationale too.

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    Sorry for being direct, but this is a banal mechanics of the first year of the university. However, the phenomenon itself should be clear even to a strong student. Understand, I can't waste time on arbitrary requests. In general, it is better to stick to the topic of the news in the comments to the news.

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    • • Do you seriously believe that physics comes down to listing all possible problems and a list of solutions to them? And that a physicist, seeing a problem, opens this magic list, looks for the problem number one million in it, and reads the answer? No, to understand physics is to see a phenomenon, to understand it, to write formulas that describe it.

        When I say that this is a banal first-year physics, it means that a student of the physics department after a normal course in mechanics is able to solve it on his own. A normal student does not look for a solution, he solves the problem himself.

        Sorry for the rebuff, but this common attitude is very depressing. This is the basis of most people's misunderstanding of what and how science does in general.

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        • I absolutely agree with you. There is no greater pleasure than solving the problem yourself. It's like a drug
          I was just asking a friendly question.
          I have an average level in general in solving problems in physics. At the All-Union Physics Olympiads, I was in the middle. But in programming and modeling, it turned out to climb higher. but here another way of thinking is at work.

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          • • I can not clearly formulate the essence of this phenomenon in simple words. (some kind of stupor in the head). It's the essence. To transfer it to another model and also to explain to schoolchildren.

              
              This experiment can be considered as a signal passage. And on a curved trajectory, it passes faster.
              Where does this gain in time come from?
              It is obvious that the shape of the trajectory also affects this delay. If you make very deep holes, then the ball simply will not overcome the hole, losing energy on air resistance at high speeds.

              If we set the task as determining the optimal form of the trajectory, then the task seems to cease to be a school one. We already get into many different functions and forms of the trajectory.

              Can you take this problem to the elements? It seems to me that many would be useful judging by the reaction of people. And this task reflects reality well.

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              • Honestly, I do not understand how, when participating in the All-Union Olympiads, you do not see this phenomenon. Especially coupled with the fact that, according to you, you cannot clearly articulate the essence of this phenomenon.

                Do you understand that the time it takes to complete a trajectory depends not only on its length, but also on its speed? Do you understand that at the bottom the speed is greater than at the top? Can you combine these two facts into a general understanding that a longer trajectory does not necessarily mean more time? It all depends on the increase in speed with increasing length.

                It is enough to understand this phenomenon in order to stop being surprised at the effect. And a specific calculation for an arbitrary trajectory will already require an accurate recording of the integral (and this is where 1 course of the university is needed). There, of course, it will be different for different trajectories, but it can be shown that for a sufficiently _flat_ trajectory of any shape, going strictly below the straight line, the travel time will always be less.

                > I'm having fun now with the theory of Time.

                This is a very dangerous wording. So dangerous that I proactively ask you not to write anything on such topics in the comments on the elements. Thanks for understanding.

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                • I see this phenomenon, I understand it, and I can take the integral over any form of the trajectory and easily write a program for the calculation.
                  But when I go with teenagers to the experimentarium and explain to them in simple terms how everything works, then it is on this phenomenon that I fail. Maybe it's the age.)
                  And the skill to quickly and easily see the final answer goes away if you do not constantly train. Probably like in sports. At 40, it’s hard to spin on the horizontal bar like in your youth ... and do somersaults)))

                  I never thought that the discussion of Time is taboo))). Especially since it's the foundation. Reading Hawking and seeing how they popularize these ideas, I was sure that they capture the minds of world researchers.
                  Maybe you misunderstood me?

                  But this is just a conversation... and of course I'm not going to break the rules and promote any heresy and unsubstantiated personal theories)) This is at least not decent...

                  But the brain needs food and something new)))

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                  As for the Olympics. My experience has shown that the really cool guys are not those who solve new problems, but those who come up with them. Their units. This is a different dimension and view of the world. A random 5-minute conversation with such a person at one of the Olympiads completely changed my life and brought me out of deep illusions and actually saved my life.
                  He joked that the "doctor of science" is precisely what gets his title for treating injured colleagues who could not climb one of the slides.

                  This person claimed that the top winners of Olympiads then dissolve in the scientific community and do not bring new discoveries and results. Therefore, without the constant wide development of one's knowledge and real skills, the path to the new will not be visible.
                  And in general, the Olympiad is a pure sport with luck, courage, tricks, with a lot of injuries and crippling of the psyche of children, including me. But this is life

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The destroyers of myths and legends have already refuted your assumption.
https://www.youtube.com/watch?v=XsKhzk4gn3A

The effect is independent of materials and friction.
Also, according to your version, if we replace the balls with sliding weights, then the effect will disappear.

Also, faster balls experience more air resistance. Drag is proportional to the square of speed. Still, it doesn't stop them from coming first.

Let's get more realistic ideas. Such things directly reflect the essence of the work of our world.

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• • In general, rolling friction has nothing to do with it ...))
    The effect works in models without friction and air.
    You can make magnets and pump out air.

    But to calculate the shape of the trajectory which is the fastest is kind of a cool problem.
    Professionals in classical mechanics can probably intuitively predict the answer.

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    • It dawned on me that the experiment in your video resembles a Foucault pendulum. Obviously, the fastest trajectory for the ball will be an arc of a circle with the smallest possible radius (up to a half-circle path = 1 half-wave crest down). For a pendulum, the paradox of a longer trajectory and, at the same time, a higher speed is solved due to the smaller radius of the described arc, i.e. the length of the arm of the pendulum, on which the period of its oscillation depends.
      In this case, any deviation of the ball's motion from strictly circular is undesirable, since it should have a negative effect on its average speed. The rectilinear motion of the ball in the video is akin to the oscillations of a pendulum with a very long arm, which, as everyone understands, has the largest oscillation period. Therefore, there is the lowest speed of the ball.
      It seems to have done without integrals;)
      An interesting problem!

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      • It is necessary to prove mathematically and test the hypothesis. But it sounds interesting ... one of the latest versions was that this is an inverted cycloid.

        I have a lot of these in stock.

        For example:

        The most seemingly banal energy conservation problem for the school, but it shows exactly the understanding of potential energy and kinetic energy that nicolaus spoke about. The task for him but broke the brain of many, even serious guys in physics.

        We take a machine with a clockwork spring. We put it on the floor and let go. Due to the spring, it accelerates to a speed V. We write down the law of conservation of energy and calculate the energy of the spring.
        0 + E(springs) = mV^2/2

        And now attention! We pass into an equal inertial system that moves towards the machine. Roughly speaking, we go towards the machine with a speed V.
        Relative to us, at the beginning the speed of the machine was V, after acceleration it will be 2V.
        We calculate the energy of the spring.
        E(springs) + mV^2/2 = m(2v)^2/2
        E(springs) = 3mV^2/2
        The energy of the spring suddenly increased relative to another inertial frame of reference.
        and the faster you move towards the machine, the greater the energy of the spring.
        How is this possible?

        Nicolaus is for you. The law of conservation has been violated. Hooray! it happened!)))

        This is also a fundamental understanding of processes and energy transfer.
        Kids love to throw problems

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        Your expression after "We calculate the energy of the spring" is incorrect.

        "And kids who ask questions are very rare."
        Kids who ask questions are not rare. All children have a "why" period.

        In general, I will refrain from discussing with you so as not to offend you inadvertently. I love to make jokes that can be misunderstood.

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No not like this. Vacuum energy level, i.e. empty space determines the dynamics of the recession of galaxies. Whether they scatter with acceleration or vice versa, they slow down. This does not allow you to move the scale too freely. The vacuum potential cannot be chosen arbitrarily, it is quite measurable.

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Dear Igor! Of course, I understand that you are sick of the commentators after the publication of each news article. We should thank you for giving information about foreign developments, and not gouging, but we are who we are. Your right to generally send to the original source, tk. this is a rewrite or Copy Paste with a technically correct translation, for which once again a separate ATP.
And now, on the topic, if an atom, particle, any body without kinetics is moved closer to the source of electromagnetic radiation, then its total energy increases. And how it is redistributed inside the body (which increases (decreases) more kinetic or potential), this does not affect the final result. Therefore, I spoke out that the explanation of the authors of the article is not correct. In fact, there is no thermal force - it is the force of gravity. How does this happen? The answer is in the article: "Gravity of the Earth Photon-quantum gravity", published in the Hungarian journal (p. 79-94):
http://tsh-journal.com/wp-content/uploads/2016/11/VOL-1-No-5-5-2016.pdf

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Igor, I don’t know if this is bad manners. But, in the light of numerous comments on this topic, it seems to me that there is a need to write a good popular science text, including on the concept of potential energy. Because I think people are a little confused. Maybe you will try, if you have time, and write about Lagrangians in a scientifically popular way? It seems to me that with your talent and experience there will be a very necessary article. It is the hardest thing to write about such fundamental concepts, I understand. But what do you think anyway?

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Let me answer your question.

Here is what Wikipedia says:
The publication of the work by Eagleworks has led to EmDrive being sometimes described as "tested by NASA", although the agency's official position is different: "This is a small project that has not yet led to practical results."

But according to the text, it is obvious that there is interest in this device and the creators were able to attract attention. Otherwise, no one would have allocated money. What is there.
I suggest you wait a bit and see the final results. This will save you time and effort. But it’s not worth hoping for miracles and dreaming about how well-established knowledge and experience will collapse)))
It is better to build something new than to try to break what our ancestors did.
In simple terms, if their device works, then there will be a person who will calmly describe everything within the framework of existing theories.

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• • I understand your feelings well. Among my friends, programmers who have developed thinking but no experience with the theory of physics, there are a lot of such moods. Dig up a video on YouTube, find some grandfather in the garage who built a perpetual motion machine, etc. their favorite pastime.
    It is always fun and a good reason to get together in nature and fry barbecue.
    And for me, this is an opportunity to once again test my own knowledge and gaps. (Everyone has them. Some are really shy and disguise them.)

    The essence of your question lies in the foundations of physics. If you clearly reach the basics of the theory of physics, then you will understand a simple thing.
    As soon as the unique effect of emDrive is proven, and it is clear that this is not a disguised set of already known effects, then any competent physicist will come up with an explanation.
    But the proof of the experiment must be strict and in all procedures debugged for centuries. There are no obstacles here. You just need to follow the clear procedures adopted in the scientific world.

    The world of real physics is a lot of money. And they are given only for a specific result. No one likes to waste time and fall into empty shells. The punishment for mistakes is very severe. Before my eyes, people simply died in a few months when their hopes collapsed. And I'm silent about how much it just goes crazy obsessing over its ideas in an attempt to "help all of humanity."
    This is not normal.

    All physics is built on the simplest few ideas. Until you understand it thoroughly, it is better not to fight windmills.

    One of the postulates of the foundations of the theory of physics is the following: we can divide space and time to infinity.
    And then the math kicks in. You will also need a coin and a pencil.
    On the same paper with this idea, you can derive the Maxwell distribution. And predict the random distribution of balls in the standard experiment and go for a walk up the measurements.
    If you calmly do such an exercise, then you understand what you are doing.
    In other words, before doing somersaults on the horizontal bar, you need to calmly and without hesitation pull yourself up by any means.

    In the theory of physics there is a point from which everything is built. You should be able to build all the basic formulas and theories from this point.
    As soon as you run along the main paths and paths several times, you will become an honest and real inhabitant of this world.

    And just then you will understand that the language of physics can describe any phenomena.

    My linguist friend sees physics as a language for describing the real world. He doesn't even believe in the electron))) And that's his right...

    And familiar mathematicians say that physics is mathematics to which they added a drop of time (dt)

    Start with the very basics. Everything is clear and beautiful here)))

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"Thirdly, there is another force of attraction - gravitational. It does not depend on temperature, but grows with body weight."

I wouldn't be so sure that gravity doesn't depend on temperature. With temperature, the dynamics of particles grows, which means that the mass (at least relativistic) grows, which means that gravitation grows.
Generally speaking, taking into account [actually] the dynamic nature of gravitational forces, this fact itself links the gravitational force with temperature, as a dynamic characteristic of mechanical systems. But this is a topic for a separate discussion, or rather theory. ;)

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As far as I understand, in the "sound" field this effect is even easier to implement if the dipole is replaced by a membrane (for example, a soap bubble) with a resonance at a frequency higher than that to which the sound generator is tuned. Still, it’s somehow easier to put a kilowatt of energy into sound than into EM radiation))

It would be funny: soap bubbles are attracted to the speaker ...

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• Sound and music is generally a convenient thing for the study of waves. This is my hobby.
  If anyone is interested, here are my attempts to apply quantum physics and Schumann resonance in creativity.
  https://soundcloud.com/dmvkmusic

  This is 3D music, so you need to listen to it only in headphones or on good speakers.

  I have speakers and a whole studio and even soap bubbles.
  I will check your idea
  Thank you!

  Let's do more!)))

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"And since the atom seeks to lower its interaction energy as much as possible, it is energetically advantageous for it to approach the ball - after all, the decrease in energy is most significant there!"
Some kind of crap, not an explanation, what the atom wants there, something is beneficial to him. And arbitrarily, at will, moves where he wants.
What a pity that there are no physicists now able to explain.
Not to mention that the impact of energy on the explanation lowers the energy level of the object. The second law of thermodynamics seems to be convulsing hysterically. Sorry.

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Unfortunately, it was not possible to obtain an exhaustive answer on the question of potential energy in the course of the discussion. Therefore, I tried to figure it out myself (which took time). That's what came out of it.

Many answers were found in the presentation of the lecture of the remarkable Russian physicist Dmitry Dyakonov “Quarks and where does the mass come from.” http://polit.ru/article/2010/09/16/quarks/. Dmitry Dyakonov had one of the highest citation ratings, I think he is among the great physicists.

What is surprising, when compared with the lecture, I did not lie in my assumptions when I wrote about the nature of potential energy.

Here is what Dmitry Dyakonov said.

“Now I want to plunge you into a deep thought. Look at slide 5. Everyone knows that a bird sits on a wire, there are 500 kilovolts in the wire, and at least henna is for her. Now, if the bird stretches out and grabs one wire with one paw, and the other with the other paw, it will not be good here. Why? Because, they say, that the electric potential itself has no physical meaning, we do not observe it, as we like to say. There is a more precise statement that the electric field strength is observed. Tension - who knows - is a potential gradient.

The principle - that it is not the value of the electric potential itself that is observable, but only its change in space and time - was discovered back in the 19th century. This principle applies to all fundamental interactions and is called “gradient invariance” or (another name) “gauge invariance”.

“I started my list with gravitational interaction. It turns out that it is also built on the principle of gauge invariance, only there is independence not from the “color”, not from the potential, but from something else. I'll try to explain why.
Imagine that somewhere there is a large mass. For example, the Sun. The sun is a big mass. What does it do? It seems to bend flat space, and the space becomes curved. Very visual. Now we place the Earth nearby, it begins to revolve around the Sun. In fact, the image is quite geometric: space is squeezed through and our planet Earth is spinning in this hole. Look at the slide - all the coordinate lines are distorted there. And that's what was the most important achievement of Einstein when he put forward the general theory of relativity. He said that all observable physical phenomena should not depend on what kind of grid we deign to apply and what clock we use.
Why I brought it here, because it is also a kind of “gauge invariance”.

Curvature is an observable thing, and in a mathematical sense, the strength of an electric field is also a kind of curvature. But we don’t see the potential, the bird sitting on one wire is alive.”

Based on this, we can conclude that potential energy should not be considered as a source of mass, since otherwise, the mass and physical processes will depend on the reporting system from which the observation is made.

This idea is reinforced by Dmitry Dyakonov's answer to the question about the mass of the electromagnetic field.

“Dmitry: Tell me, please, do force fields, for example, electric and gravitational fields, have mass?
Dmitry Dyakonov: If they do, then very little, and conventional wisdom is that they are massless.
Dmitry: I had in mind a little different. Let's say if we have a capacitor between the plates of which there is an electric field. Does this field have mass?
Dmitry Dyakonov: No.
Dmitry: Does it have energy?
Dmitry Dyakonov: Yes.
Dmitry: And mc??
Dmitry Dyakonov: Well, cook up a closed system for me, that is, including a capacitor, a battery, a hydroelectric power station, a source in the sun, and so on. That's when you concoct a closed system, then we will measure its mass, and I will say that E, which is mc? from this mass - this is the rest energy of this closed system. I make no other assertions.
Dmitry: That is, the energy of the field, in fact, is the energy of the battery, wires and plates?
Dmitry Dyakonov: Of course. You need to take a closed system, you can make a judgment about it.

So where does mass come from in our world?

Dmitry Dyakonov: “As you can see, the whole history of science has consisted in the fact that we were engaged in a wide variety of connected positions, and always the sum of the masses of the components was greater than the whole. And now we reach the last bound state - these are protons and neutrons, which are made of three quarks, and here, it turns out, the opposite is true! The proton mass is 940 MeV - see slide 9. And the mass of the constituent quarks, that is, two u and one d, add 4 + 4 + 7 and get only 15 MeV. This means that the sum of the constituent masses is not more than the whole, as usual, but less, and not just less, but 60 times less! That is, for the first time in the history of science, we meet with a bound state in which everything is the opposite in comparison with the usual one.

It turns out that empty space, vacuum, lives a very complex and very rich life, which is depicted here. In this case, this is not a caricature, but a real computer simulation of the real quantum chromodynamics, and there is an author, my colleague Derick Leinweber, who kindly provided me this picture for demonstrations. Moreover, what is remarkable, the presence of matter has almost no effect on the vacuum fluctuations of the field. It's a gluon field that keeps fluctuating in this weird way all the time.
And now let's let quarks in, see slide 13. What will happen to them? A rather interesting thing is happening. Here, too, the thought is not superficial, try to delve into it. Imagine two quarks, or a quark and an antiquark, that happen to be in the vicinity of such a large fluctuation at the same time. The fluctuation induces a certain correlation between them. And correlation means that they interact.
Here I can just give an everyday image. You drain the water from the bath, a funnel is formed there, where two matches fall, they are tightened by this funnel, and both of them spin in the same way. That is, the behavior of the two matches is correlated. And you can say that the funnel caused the interaction between the matches. That is, external influence induces interaction between objects that fall under this influence. Or, say, you are walking along Myasnitskaya and it starts to rain. And for some reason, suddenly everyone raises some object above their heads. This is a correlated behavior, it turns out that people interact, but they do not directly interact, and the interaction brought an external influence, in this case, rain.
Everyone has probably heard about superconductivity, and if there are physicists in the hall, they will explain that the mechanism of superconductivity is the condensation of the so-called Cooper pairs of electrons in a superconductor. A similar phenomenon occurs here, only the quantum condensate is formed not by electrons, but by pairs of quarks and antiquarks.

What happens if a quark enters such a medium? The quark flies, it can knock out one quark, which has already organized into such a pair, this one flies further, randomly falls into the next one, and so on, see slide 14. That is, the quark travels in a complex way through this medium. And that's what gives it mass. I can explain it in different languages, but, unfortunately, it will not get better.

The mathematical model of this phenomenon, which bears the beautiful name “spontaneous chiral symmetry breaking”, was first proposed back in 1961 simultaneously by our domestic scientists Vaks and Larkin and the remarkable Japanese scientist Nambu, who lived all his life in America and in 2008, in a very old age, received the Nobel Prize for this work.

The lecture had slide 14 showing how quarks travel. Based on this slide, it follows that the mass is formed due to the energy of the quarks, and not the gluon field. And this mass is dynamic - arising as a result of energy flows (movement of quarks), under the conditions of "spontaneous violation of chiral symmetry".

All that I have written here is very brief excerpts from Dmitry Dyakonov's lecture. It is better to read this lecture http://polit.ru/article/2010/09/16/quarks/ in full. There are beautiful slides explaining the meaning.

I will explain why during the discussion in this thread I asked questions on potential energy. In the answers, I wanted to read about the same as what is written in the presentation of Dmitry Dyakonov's lecture, in order to further rely on these statements and continue the discussion. However, unfortunately, the discussion did not take place.

This is necessary to strengthen the position of the hypothesis of the evolution of matter. According to the hypothesis, the mass in our universe arises as a result of the structuring of matter. Structurization is the formation of order against the background of chaos. Everything that is written in the presentation of Dmitry Dyakonov's lecture, in my opinion, supports this hypothesis.

Structurization of matter can go in several stages. Transitions between stages are accompanied by revolutionary changes in the properties of matter. These changes in physics are called phase transitions. At present, it is generally accepted that there were several phase transitions (Dmitry Dyakonov also wrote about this). The last of the phase transitions could have had the observable phenomena that cosmologists present as evidence for the standard cosmological theory. Therefore, the observations do not contradict this hypothesis.

There is another interesting aspect here. To make calculations related to the effect, it is not necessary to measure the potential at all. In order to calculate the force that acts on the hair and their additional energy, it is necessary to measure the electrical charge (number of electrons) that has gone into the boy's body, as well as to know the geometric characteristics of the boy's body, including the characteristics of his hair, the size and location of the surrounding electrically conductive bodies.

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• If the boy is inside the Faraday cage, then as far as I understand, even with email. contact with her, he will never receive email on his surface. charge.
  When a cell is connected to a charged ball, the entire charge will be distributed over the surface of the cell. There will be no e-mail inside it. stat. fields, no charge. The potential on the boy's surface will also be zero and his hair will remain in place. I think even if he takes the grounded wire in his hands, he will not get anything from it. No charge, no potential difference, no current.

  Those. in short, by placing the boy in a cage, you thereby reset his email. potential. The potential will be invisible, because. it is simply not there. :-)

  The potential difference effect can also be observed. To do this, it is enough to put another ball next to the boy, connected to another source or simply grounded. As soon as the boy touches both balls at once, he will feel for himself what the potential difference is (children, do not do this!).

  Email potential is observed not only through the hair. There is another beautiful effect - St. Elmo's fires or simply - corona discharge: http://molniezashitadoma.ru/ogon%20elma.jpg

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> a beautiful effect with the boy's hair is not associated with the potential of the electric field, but with the potential difference between the boy's body and the environment (in other words, with the strength of the electric field)

Email tension. Art. field is not a potential difference at all. ;-)
This is the main characteristic of e. Art. field, which characterizes each of its points: https://ru.wikipedia.org/wiki/Electric_field_strength
_______________

As for Dmitry Dyakonov, his statements seem strange to me, to put it mildly... Perhaps he was too carried away by his "quarks" and noticeably broke away from the real world. :-)

And how old was Bohr when he saved physics from the fall of an electron onto a nucleus by his assertion that the fall proceeds in leaps and bounds? Because orbits can be divided into pure and impure!
So it turned out and share!
How old was Maxwell when he invented the electromagnetic field?
And many people do understand what polarization is!
Sometimes it seems to me that we were hammered in a lot of respect at too early an age.
I would be very grateful to Igor Ivanov if he made a digression into the age of the great discoverers.
Sometimes it still seems to me that physics is afraid of clear formulations.
Or dodging?
....................
Not criticism, but balance.
Ege?

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I believe that Avogadro's law holds true for all atoms (all chemical elements) without exception.
And I DO NOT KNOW what the weight of one atom is.
In the experiment that is described, no parallel is drawn with the conditions of the "tests according to Avogadro". But there were different atoms?
There is a possibility that we are trying to understand something completely different from what the experimenters wanted to find out.
........................
And how old are they, by the way?

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The task of the movement of the planet Earth relative to the Sun is the task of three magnets. Two magnets with the same polarity directed at each other - this is the Earth in its plane relative to the axis of the Sun. The Sun is the third magnet, spinning the Earth and other planets about their axes in proportion to their masses. The elliptical orbit of the Earth indicates that there is some other force acting from the "winter" chord of the ellipse. Cold small bodies of space also do not move freely in space, they have an acquired acceleration. This study can only confirm that planetary gravitational force is due to sufficiently heated planetary bases. That is, any planet in the solar system is hot inside.
Why the Earth and other planets are not attracted to the Sun closely? The system is dynamic, not static, the axes of the planets are parallel, so you get a lot of tops. And the planets cannot have a change of poles, since this is tantamount to leaving the orbit.

• • Do you think that it is possible for a body with a magnetic field and a satellite to move by inertia for an infinitely long time? In this case, the Earth should have two moons, located symmetrically. The behavior of the gyroscope explains the moment of inertia, and the equilibrium distribution of mass about the axis of rotation. If the disc of the top is unbalanced relative to the axis, then it begins to describe the spiral with the axis. This also applies to the Earth, it has one satellite, which would have to bring it from orbit and carry it into space, if its movement relative to the Sun was explained only by the mechanical moment of inertia. Here the magnetism from the side of the Sun is so strong that it is able to compensate for the influence of the Moon on the Earth.
    Nothing else but magnetism can explain the orderly movement of the planets and their satellites of the Solar System. We in the form of the Sun have, as it were, a stator, being a rotor, but at the same time we are a stator for the Moon.

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    • Magnetic and electric fields are shielded, Ambrose. More precisely - shunted. But now it doesn't matter.):
      How do you imagine a spring balance with a kilogram weight after covering it with a magnetic screen? The arrow will run from right to left?
      It seemed to me that the gyroscope is a wonderful subject for the development of thinking. Even the Chinese think so.
      Just think about it. The gyroscope can be freely moved along any of the three Cartesian axes! If you do not notice the inclination of the own axis of the gyroscope in its binding to some imaginary base.
      For example, you can move your mind's eye away from the spinning top until it becomes so small for the observer that no thoughts will arise to draw the axis of rotation through this "point".
      By the way, Ambrose, have you ever thought about the axes of rotation of infinitely small points?
      ............
      And so, this exceptional property of the gyroscope prompted scientists to look for the specific nature of ITS inertia only for the gyroscope!
      Perhaps this was the first step of "science" back into the future of metaphysics. The first step that did not cause immune rejection by society. (Men have never seen such sadness)
      ....................
      Some years have passed.
      One genius suggested that the nature of the inertia of a material body is not inside the body, but in the space surrounding this body.
      This conclusion was as simple as it was stunning.
      Moreover, as a model for studying the nature of inertia, the gyroscope turned out to be the most convenient tool. Indeed, in laboratory settings, it is easily accessible for observation! Unlike, for example, the flow of shells. Even if this flow is limited by a steel pipe.
      Can you imagine what a giant step science has taken?
      .................
      Well, yes.
      And I don't represent.
      Think Ambrose.
      Think.

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      • "One genius suggested that the nature of the inertia of a material body is not inside the body, but in the space surrounding this body."
        Interestingly, you are not writing about the principle of mach?

        But I'm talking about mine. What I wrote here (post dated 20.09.2017 08:05) refers to "spatial symmetry". (Do not look for this term on the Internet in the sense that I use it). There in the post there was a speech about the 4D case of spatial symmetry. (The fourth spatial coordinate is directed outward from the point.) In general, the directions of spatial symmetry are not equal. And this can be shown using a top (gyroscope), for one coordinate. Let's take a number line. There is a direction of the numerical axis in the positive direction. And there is in the negative. So - these directions are not equal. If we move in the negative direction, then on this axis we will not meet real numbers that are equal to the square root of the coordinate of this axis. The negative axis is sparse. In space, it is impossible to explicitly distinguish where the positive direction is, and where the negative direction is. However, you can separate them using a top. The top, when moving in the direction along the axis of the top, forms a screw. Right and left. The direction of the right screw will be taken as a positive direction, and the left one as a negative one. In this case, the positive and negative directions can be separated. So, in nature there are processes that feel the difference between movement in the positive and negative directions - or, in other words, feel the sparseness of the negative axis.

        Here http://old.site/nauchno-populyarnaya_biblioteka/43375 0/Mnogo_vselennykh_iz_nichego in a comment to the article "Many universes from nothing" by the wonderful science fiction writer Pavel Amnuel, I wrote a point of view on the movement of the mother in our universe using "spatial symmetry". This comment is a continuation of the post from 09/20/2017 08:05. There it is just on the topic of the article under discussion. I would like to know your opinion.

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        • Unfortunately, I have not yet found your second comment on the article based on Amnuel. But only from 02.09.17. Maybe I'm just not that deterministic?):
          There was a mention of Planck (as a spacecraft ... a man and a steamer ...)
          Generally interesting. When I realized that he simply calculated the constant of his name by dividing the known result by the Rayleigh formula, I almost burst with anger. Even in the bursa, I also chipped off something similar. It turns out that not too many people can see the relationship of formulas without bothering to accurately model them. ... How else to spread it on bread?
          ):
          There was an interesting story there. People invented the abstraction of a completely black body, which does not exist in nature.
          So take it, and find it!
          So what?
          Have scientists called space the firmament of heaven?
          - Figushki! Yes?
          And they simply added matter to it, kneading it with energy.
          Well, anyway.

          Even in that article, the possibility of a "collision of universes" is suggested.
          It is easier.
          -----------
          Now I will start with the second "if", and the first will be mentioned later.
          Can?
          If we can distinguish two (several, as many as you like) universes, then each of them must have a feature that phenomenologically allows such a selection.
          Scientists once tried to enumerate such signs in so-called "set theory".
          We will act a little more simply. - Obviously, it is phenomenologically (from the point of view of the convenience of describing the "collision") that we can describe each of the universes simply as a "shell before the collision."
          IF this is so, then our mind can operate
          COLLISION OF SHELLS.
          And if this is not so, then the mind that allowed the collision of the universes is still mature, but not enough.

          IF two (several) shells collide, then...
          and now the first if will go:
          IF the space of the initial and resulting shells is THREE DIMENSIONAL, then, in particular, a plane is formed.
          For example, the plane of the ecliptic.
          Which we were honored to observe.
          Everything else is of less importance to me.

          Already it turns out long, and still did not answer a direct question. So I apologize in advance.

          No, I meant the basic position of GR.
          I first learned about Mach and his world center from my father. Still at school. By the way, I agree with you. - The idea formulated by Einstein "was in the atmosphere", created, in many respects, precisely by the works of Mach. It is a pity that this is not included in the school curriculum.

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