The energy that a body loses due to thermal radiation is characterized by the following quantities.
Radiation flux (F) - energy emitted per unit time from the entire surface of the body.
In fact, this is the power of thermal radiation. The dimension of the radiation flux is [J/s = W].
Energy luminosity (Re) - energy of thermal radiation emitted per unit time from a unit surface of a heated body:
In the SI system, energetic luminosity is measured - [W/m 2 ].
The radiation flux and energetic luminosity depend on the structure of the substance and its temperature: Ф = Ф(Т),
The distribution of energetic luminosity over the spectrum of thermal radiation characterizes it spectral density. Let us denote the energy of thermal radiation emitted by a single surface in 1 s in a narrow range of wavelengths from λ before λ + d λ, via dRe.
Spectral luminosity density (r) or emissivity The ratio of energetic luminosity in a narrow part of the spectrum (dRe) to the width of this part (dλ) is called:
Approximate form of spectral density and energetic luminosity (dRe) in the wavelength range from λ before λ + d λ, shown in Fig. 13.1.
Rice. 13.1. Spectral density of energetic luminosity
The dependence of the spectral density of energetic luminosity on wavelength is called body radiation spectrum. Knowledge of this dependence allows one to calculate the energetic luminosity of a body in any wavelength range. The formula for calculating the energetic luminosity of a body in a range of wavelengths is:
The total luminosity is:
Bodies not only emit, but also absorb thermal radiation. The ability of a body to absorb radiation energy depends on its substance, temperature and wavelength of the radiation. The absorption capacity of the body is characterized by monochromatic absorption coefficient α.
Let a stream fall on the surface of the body monochromatic radiation Φ λ with wavelength λ. Part of this flow is reflected, and part is absorbed by the body. Let us denote the magnitude of the absorbed flux Φ λ abs.
Monochromatic absorption coefficient α λ is the ratio of the radiation flux absorbed by a given body to the magnitude of the incident monochromatic flux:
Monochromatic absorption coefficient is a dimensionless quantity. Its values lie between zero and one: 0 ≤ α ≤ 1.
Function α = α(λ,Τ) , expressing the dependence of the monochromatic absorption coefficient on wavelength and temperature, is called absorption capacity bodies. Its appearance can be quite complex. The simplest types of absorption are discussed below.
Pure black body is a body whose absorption coefficient is equal to unity for all wavelengths: α = 1.
Gray body is a body for which the absorption coefficient does not depend on the wavelength: α = const< 1.
Absolutely white body is a body whose absorption coefficient is zero for all wavelengths: α = 0.
Kirchhoff's law
Kirchhoff's law- the ratio of the emissivity of a body to its absorption capacity is the same for all bodies and is equal to the spectral density of the energy luminosity of an absolutely black body:
= /
Corollary of the law:
1. If a body at a given temperature does not absorb any radiation, then it does not emit it. Indeed, if for a certain wavelength the absorption coefficient α = 0, then r = α∙ε(λT) = 0
1. At the same temperature black body radiates more than any other. Indeed, for all bodies except black,α < 1, поэтому для них r = α∙ε(λT) < ε
2. If for a certain body we experimentally determine the dependence of the monochromatic absorption coefficient on wavelength and temperature - α = r = α(λT), then we can calculate the spectrum of its radiation.
§ 4 Energy luminosity. Stefan-Boltzmann law.
Wien's displacement law
RE(integrated energy luminosity) - energy luminosity determines the amount of energy emitted from a unit surface per unit time over the entire frequency range from 0 to ∞ at a given temperature T.
Connection energetic luminosity and emissivity
[ R E ] = J/(m 2 s) = W/m 2
Law of J. Stefan (Austrian scientist) and L. Boltzmann (German scientist)
Where
σ = 5.67·10 -8 W/(m 2 · K 4) - Steph-on-Boltzmann constant.
The energetic luminosity of a black body is proportional to the fourth power of thermodynamic temperature.
Stefan-Boltzmann law, defining the dependenceREon temperature does not provide an answer regarding the spectral composition of black body radiation. From experimental dependence curvesrλ ,T from λ at different T it follows that the energy distribution in the spectrum of an absolutely black body is uneven. All curves have a maximum, which, with increasing T shifts towards shorter wavelengths. Area limited by the dependence curverλ ,T from λ, is equal RE(this follows from the geometric meaning of the integral) and is proportional T 4 .
Wien's displacement law (1864 - 1928): Length, waves (λ max), which accounts for the maximum emissivity of the a.ch.t. at a given temperature, inversely proportional to temperature T.
b= 2.9·10 -3 m·K - Wien's constant.
The Wien shift occurs because as temperature increases, the maximum emissivity shifts toward shorter wavelengths.
§ 5 Rayleigh-Jeans formula, Wien formula and ultraviolet catastrophe
The Stefan-Boltzmann law allows us to determine the energetic luminosityREa.ch.t. according to its temperature. Wien's displacement law relates body temperature to the wavelength at which maximum emissivity occurs. But neither one nor the other law solves the main problem of how great the radiation emission ability is for each λ in the spectrum of the a.ch.t. at a temperature T. To do this, you need to establish a functional dependencerλ ,T from λ and T.
Based on the idea of the continuous nature of the emission of electromagnetic waves in the law of uniform distribution of energies over degrees of freedom, two formulas were obtained for the emissivity of the AC:
- Wine formula
Where A, b = const.
- Rayleigh-Jeans formula
k =1.38·10 -23 J/K - Boltzmann's constant.
Experimental testing has shown that for a given temperature, Wien's formula is correct for short waves and gives sharp discrepancies with experiment in the region of long waves. The Rayleigh-Jeans formula turned out to be true for long waves and not applicable for short ones.
The study of thermal radiation using the Rayleigh-Jeans formula showed that, within the framework of classical physics, it is impossible to solve the question of the function characterizing the emissivity of the AC. This unsuccessful attempt to explain the laws of radiation of a.ch.t. Using the apparatus of classical physics, it was called the “ultraviolet catastrophe.”
If you try to calculateREusing the Rayleigh-Jeans formula, then
- “ ultraviolet disaster”
§6 Quantum hypothesis and Planck's formula.
In 1900, M. Planck (a German scientist) put forward a hypothesis according to which the emission and absorption of energy does not occur continuously, but in certain small portions - quanta, and the energy of a quantum is proportional to the frequency of oscillations (Planck’s formula):
h = 6.625·10 -34 J·s - Planck’s constant or
Where
Since radiation occurs in portions, the energy of the oscillator (oscillating atom, electron) E takes only values that are multiples of an integer number of elementary portions of energy, that is, only discrete values
E = n E o = nhν .
The influence of light on the course of electrical processes was first studied by Hertz in 1887. He conducted experiments with an electric discharger and discovered that when irradiated with ultraviolet radiation, the discharge occurs at a significantly lower voltage.
In 1889-1895. A.G. Stoletov studied the effect of light on metals using the following scheme. Two electrodes: cathode K made of the metal under study and anode A (in Stoletov’s scheme - a metal mesh that transmits light) in a vacuum tube are connected to the battery so that with the help of resistance R you can change the value and sign of the voltage applied to them. When the zinc cathode was irradiated, a current flowed in the circuit, recorded by a milliammeter. By irradiating the cathode with light of various wavelengths, Stoletov established the following basic principles:
- Ultraviolet radiation has the most powerful effect;
- When exposed to light, negative charges are released from the cathode;
- The strength of the current generated by light is directly proportional to its intensity.
Lenard and Thomson in 1898 measured the specific charge ( e/ m), particles being torn out, and it turned out that it is equal to the specific charge of an electron, therefore, electrons are ejected from the cathode.
§ 2 External photoelectric effect. Three laws of external photoelectric effect
The external photoelectric effect is the emission of electrons by a substance under the influence of light. Electrons emitted from a substance during the external photoelectric effect are called photoelectrons, and the current they generate is called photocurrent.
Using Stoletov’s scheme, the following dependence of the photocurrent onapplied voltage at a constant luminous flux F(that is, the current-voltage characteristic was obtained):At some voltageUNphotocurrent reaches saturationI n - all electrons emitted by the cathode reach the anode, hence the saturation currentI n determined by the number of electrons emitted by the cathode per unit time under the influence of light. The number of released photoelectrons is proportional to the number of light quanta incident on the cathode surface. And the number of light quanta is determined by the luminous flux F, incident on the cathode. Number of photonsN, falling over timet to the surface is determined by the formula:
Where W- radiation energy received by the surface during time Δt,
Photon energy,
F e -luminous flux (radiation power).
1st law of external photoelectric effect (Stoletov’s law):
At a fixed frequency of incident light, the saturation photocurrent is proportional to the incident light flux:
Ius~ Ф, ν =const
Uh - holding voltage- the voltage at which not a single electron can reach the anode. Consequently, the law of conservation of energy in this case can be written: the energy of the emitted electrons is equal to the stopping energy of the electric field
therefore, we can find the maximum speed of emitted photoelectronsVmax
2nd law of photoelectric effect : maximum initial speedVmaxphoto-electrons does not depend on the intensity of the incident light (from F), and is determined only by its frequency ν
3rd law of photoelectric effect : for each substance there is "red border" photo effect, that is, the minimum frequency ν kp, depending on the chemical nature of the substance and the state of its surface, at which the external photoelectric effect is still possible.
The second and third laws of the photoelectric effect cannot be explained using the wave nature of light (or the classical electromagnetic theory of light). According to this theory, the ejection of conduction electrons from a metal is the result of their “swinging” by the electromagnetic field of a light wave. With increasing light intensity ( F) the energy transferred by the electron of the metal must increase, therefore, it must increaseVmax, and this contradicts the 2nd law of the photoelectric effect.
Since, according to the wave theory, the energy transmitted by the electromagnetic field is proportional to the intensity of light ( F), then any light; frequency, but with a sufficiently high intensity, it would have to pull electrons out of the metal, that is, the red limit of the photoelectric effect would not exist, which contradicts the 3rd law of the photoelectric effect. The external photoelectric effect is inertialess. But the wave theory cannot explain its inertialessness.
§ 3 Einstein's equation for the external photoelectric effect.
Work function
In 1905, A. Einstein explained the photoelectric effect based on quantum concepts. According to Einstein, light is not only emitted by quanta in accordance with Planck's hypothesis, but spreads in space and is absorbed by matter in separate portions - quanta with energy E 0 = hv. Quanta of electromagnetic radiation are called photons.
Einstein's equation (law of conservation of energy for external photo-effect):
Incident photon energy hv is spent on ejecting an electron from the metal, that is, on the work function And out, and to communicate kinetic energy to the emitted photoelectron.
The minimum energy that must be imparted to an electron in order to remove it from a solid into a vacuum is called work function.
Since the Ferm energy to E Fdepends on temperature and E F, also changes with temperature changes, then, consequently, And out depends on temperature.
In addition, the work function is very sensitive to surface cleanliness. Applying a film to the surface ( Sa, SG, Va) on WAnd outdecreases from 4.5 eV for pureW up to 1.5 ÷ 2 eV for impurityW.
Einstein's equation allows us to explain in c e three laws of external photoeffect,
1st law: each quantum is absorbed by only one electron. Therefore, the number of ejected photoelectrons should be proportional to the intensity ( F) Sveta
2nd law: Vmax~ ν, etc. And out does not depend on F, thenVmax does not depend on F
3rd law: As ν decreases, it decreasesVmax and for ν = ν 0 Vmax = 0, therefore,hν 0 = And out, therefore, i.e. There is a minimum frequency from which the external photoelectric effect is possible.
Energy luminosity of the body- - a physical quantity that is a function of temperature and is numerically equal to the energy emitted by a body per unit time from a unit surface area in all directions and across the entire frequency spectrum. J/s m²=W/m²
Spectral density of energetic luminosity- a function of frequency and temperature characterizing the distribution of radiation energy over the entire spectrum of frequencies (or wavelengths). , A similar function can be written in terms of wavelength
It can be proven that the spectral density of energy luminosity, expressed in terms of frequency and wavelength, are related by the relation:
Absolutely black body- a physical idealization used in thermodynamics, a body that absorbs all electromagnetic radiation incident on it in all ranges and does not reflect anything. Despite the name, a completely black body can itself emit electromagnetic radiation of any frequency and visually have color. The radiation spectrum of an absolutely black body is determined only by its temperature.
The importance of an absolutely black body in the question of the spectrum of thermal radiation of any (gray and colored) bodies in general, in addition to the fact that it represents the simplest non-trivial case, also lies in the fact that the question of the spectrum of equilibrium thermal radiation of bodies of any color and reflection coefficient is reduced by the methods of classical thermodynamics to the question of the radiation of an absolutely black body (and historically this was already done by the end of the 19th century, when the problem of radiation of an absolutely black body came to the fore).
Absolutely black bodies do not exist in nature, so in physics a model is used for experiments. It is a closed cavity with a small hole. Light entering through this hole will be completely absorbed after repeated reflections, and the hole will appear completely black from the outside. But when this cavity is heated, it will develop its own visible radiation. Since the radiation emitted by the inner walls of the cavity, before it leaves (after all, the hole is very small), in the overwhelming majority of cases will undergo a huge amount of new absorption and radiation, we can say with confidence that the radiation inside the cavity is in thermodynamic equilibrium with the walls. (In fact, the hole is not important for this model at all, it is only needed to emphasize the fundamental observability of the radiation located inside; the hole can, for example, be completely closed, and quickly opened only when equilibrium has already been established and the measurement is being carried out).
2. Kirchhoff's radiation law- a physical law established by the German physicist Kirchhoff in 1859. In its modern formulation, the law reads as follows: The ratio of the emissivity of any body to its absorption capacity is the same for all bodies at a given temperature for a given frequency and does not depend on their shape, chemical composition, etc.
It is known that when electromagnetic radiation falls on a certain body, part of it is reflected, part is absorbed, and part can be transmitted. The fraction of radiation absorbed at a given frequency is called absorption capacity body. On the other hand, every heated body emits energy according to some law called emissivity of the body.
The values of and can vary greatly when moving from one body to another, however, according to Kirchhoff’s law of radiation, the ratio of emissive and absorption abilities does not depend on the nature of the body and is a universal function of frequency (wavelength) and temperature:
By definition, an absolutely black body absorbs all radiation incident on it, that is, for it. Therefore, the function coincides with the emissivity of an absolutely black body, described by the Stefan-Boltzmann law, as a result of which the emissivity of any body can be found based only on its absorption capacity.
Stefan-Boltzmann law- the law of black body radiation. Determines the dependence of the radiation power of an absolutely black body on its temperature. Statement of the law: The radiation power of an absolutely black body is directly proportional to the surface area and the fourth power of the body temperature: P = Sεσ T 4, where ε is the degree of emissivity (for all substances ε< 1, для абсолютно черного тела ε = 1).
Using Planck's law for radiation, the constant σ can be defined as where is Planck's constant, k- Boltzmann constant, c- speed of light.
Numerical value J s −1 m −2 K −4.
The German physicist W. Wien (1864-1928), relying on the laws of thermo- and electrodynamics, established the dependence of the wavelength l max corresponding to the maximum of the function r l , T , on temperature T. According to Wien's displacement law,l max =b/T
i.e. wavelength l max corresponding to the maximum value of the spectral density of energy luminosity r l , T black body, is inversely proportional to its thermodynamic temperature, b- Wien's constant: its experimental value is 2.9 10 -3 m K. Expression (199.2) is therefore called the law offsets The fault is that it shows a shift in the position of the maximum of the function r l , T as the temperature increases into the region of short wavelengths. Wien's law explains why, as the temperature of heated bodies decreases, long-wave radiation increasingly dominates in their spectrum (for example, the transition of white heat to red heat when a metal cools).
Despite the fact that the Stefan-Boltzmann and Wien laws play an important role in the theory of thermal radiation, they are particular laws, since they do not give a general picture of the frequency distribution of energy at different temperatures.
3. Let the walls of this cavity completely reflect the light falling on them. Let's place some body in the cavity that will emit light energy. An electromagnetic field will arise inside the cavity and, ultimately, it will be filled with radiation that is in a state of thermal equilibrium with the body. Equilibrium will also occur in the case when in some way the exchange of heat of the body under study with its surrounding environment is completely eliminated (for example, we will carry out this mental experiment in a vacuum, when there are no phenomena of thermal conductivity and convection). Only through the processes of emission and absorption of light will equilibrium be achieved: the radiating body will have a temperature equal to the temperature of electromagnetic radiation isotropically filling the space inside the cavity, and each selected part of the surface of the body will emit as much energy per unit time as it absorbs. In this case, equilibrium must occur regardless of the properties of the body placed inside a closed cavity, which, however, influence the time it takes to establish equilibrium. The energy density of the electromagnetic field in the cavity, as will be shown below, in a state of equilibrium is determined only by temperature.
To characterize equilibrium thermal radiation, not only the volumetric energy density is important, but also the distribution of this energy over the spectrum. Therefore, we will characterize the equilibrium radiation isotropically filling the space inside the cavity using the function u ω - spectral radiation density, i.e., the average energy per unit volume of the electromagnetic field, distributed in the frequency interval from ω to ω + δω and related to the value of this interval. Obviously the meaning uω should depend significantly on temperature, so we denote it u(ω, T). Total Energy Density U(T) associated with u(ω, T) formula.
Strictly speaking, the concept of temperature is applicable only for equilibrium thermal radiation. Under equilibrium conditions, the temperature must remain constant. However, the concept of temperature is often also used to characterize incandescent bodies that are not in equilibrium with radiation. Moreover, with a slow change in the parameters of the system, at any given period of time it is possible to characterize its temperature, which will change slowly. So, for example, if there is no influx of heat and the radiation is due to a decrease in the energy of the luminous body, then its temperature will also decrease.
Let us establish a connection between the emissivity of a completely black body and the spectral density of equilibrium radiation. To do this, we calculate the energy flow incident on a single area located inside a closed cavity filled with electromagnetic energy of average density U ω . Let radiation fall on a unit area in the direction determined by the angles θ and ϕ (Fig. 6a) within the solid angle dΩ:
Since equilibrium radiation is isotropic, a fraction propagating in a given solid angle is equal to the total energy filling the cavity. Flow of electromagnetic energy passing through a unit area per unit time
Replacing dΩ expression and integrating over ϕ within the limits (0, 2π) and over θ within the limits (0, π/2), we obtain the total energy flux incident on a unit area:
Obviously, under equilibrium conditions it is necessary to equate expression (13) of the emissivity of an absolutely black body rω, characterizing the energy flux emitted by the platform in a unit frequency interval near ω:
Thus, it is shown that the emissivity of a completely black body, up to a factor of c/4, coincides with the spectral density of equilibrium radiation. Equality (14) must be satisfied for each spectral component of the radiation, therefore it follows that f(ω, T)= u(ω, T) (15)
In conclusion, we point out that the radiation of an absolute black body (for example, light emitted by a small hole in a cavity) will no longer be in equilibrium. In particular, this radiation is not isotropic, since it does not propagate in all directions. But the energy distribution over the spectrum for such radiation will coincide with the spectral density of equilibrium radiation isotropically filling the space inside the cavity. This allows us to use relation (14), which is valid at any temperature. No other light source has a similar energy distribution across the spectrum. For example, an electric discharge in gases or a glow under the influence of chemical reactions have spectra that are significantly different from the glow of an absolutely black body. The distribution of energy across the spectrum of incandescent bodies also differs markedly from the glow of an absolutely black body, which was higher by comparing the spectra of a common light source (incandescent lamps with a tungsten filament) and an absolutely black body.
4. Based on the law of equidistribution of energy over degrees of freedom: for each electromagnetic oscillation there is, on average, an energy that is the sum of two parts kT. One half is contributed by the electrical component of the wave, and the second by the magnetic component. By itself, equilibrium radiation in a cavity can be represented as a system of standing waves. The number of standing waves in three-dimensional space is given by:
In our case, the speed v should be set equal c, moreover, two electromagnetic waves with the same frequency, but with mutually perpendicular polarizations, can move in the same direction, then (1) in addition should be multiplied by two:
So, Rayleigh and Jeans, energy was assigned to each vibration. Multiplying (2) by , we obtain the energy density that falls on the frequency interval dω:
Knowing the relationship between the emissivity of a completely black body f(ω, T) with equilibrium density of thermal radiation energy, for f(ω, T) we find: Expressions (3) and (4) are called Rayleigh-Jeans formula.
Formulas (3) and (4) agree satisfactorily with experimental data only for long wavelengths; at shorter wavelengths the agreement with experiment sharply diverges. Moreover, integration (3) over ω in the range from 0 to for the equilibrium energy density u(T) gives an infinitely large value. This result, called ultraviolet disaster, obviously contradicts experiment: the equilibrium between radiation and the radiating body must be established at finite values u(T).
Ultraviolet disaster- a physical term describing the paradox of classical physics, which consists in the fact that the total power of thermal radiation of any heated body must be infinite. The paradox got its name due to the fact that the spectral power density of the radiation should have increased indefinitely as the wavelength shortened. In essence, this paradox showed, if not the internal inconsistency of classical physics, then at least an extremely sharp (absurd) discrepancy with elementary observations and experiment.
5. Planck's hypothesis- a hypothesis put forward on December 14, 1900 by Max Planck and which states that during thermal radiation energy is emitted and absorbed not continuously, but in separate quanta (portions). Each such quantum portion has energy , proportional to frequency ν radiation:
Where h or - the proportionality coefficient, later called Planck's constant. Based on this hypothesis, he proposed a theoretical derivation of the relationship between the temperature of a body and the radiation emitted by this body - Planck's formula.
Planck's formula- expression for the spectral power density of black body radiation, which was obtained by Max Planck. For radiation energy density u(ω, T):
Planck's formula was obtained after it became clear that the Rayleigh-Jeans formula satisfactorily describes radiation only in the long-wave region. To derive the formula, Planck in 1900 made the assumption that electromagnetic radiation is emitted in the form of individual portions of energy (quanta), the magnitude of which is related to the frequency of the radiation by the expression:
The proportionality coefficient was subsequently called Planck's constant, = 1.054 · 10 −27 erg s.
To explain the properties of thermal radiation, it was necessary to introduce the concept of the emission of electromagnetic radiation in portions (quanta). The quantum nature of radiation is also confirmed by the existence of a short-wavelength limit in the bremsstrahlung X-ray spectrum.
X-ray radiation occurs when solid targets are bombarded by fast electrons. Here the anode is made of W, Mo, Cu, Pt - heavy refractory or high thermal conductivity metals. Only 1–3% of the electron energy is used for radiation, the rest is released at the anode in the form of heat, so the anodes are cooled with water. Once in the anode substance, the electrons experience strong inhibition and become a source of electromagnetic waves (X-rays).
The initial speed of an electron when it hits the anode is determined by the formula:
Where U– accelerating voltage.
>Noticeable emission is observed only with a sharp deceleration of fast electrons, starting from U~ 50 kV, while ( With– speed of light). In induction electron accelerators - betatrons, electrons acquire energy up to 50 MeV, = 0.99995 With. By directing such electrons to a solid target, we obtain X-ray radiation with a short wavelength. This radiation has great penetrating power. According to classical electrodynamics, when an electron decelerates, radiation of all wavelengths from zero to infinity should arise. The wavelength at which the maximum radiation power occurs should decrease as the electron speed increases. However, there is a fundamental difference from the classical theory: zero power distributions do not go to the origin of coordinates, but break off at finite values - this is short wavelength end of the X-ray spectrum.
It has been experimentally established that
The existence of the short-wave boundary directly follows from the quantum nature of radiation. Indeed, if radiation occurs due to the energy lost by the electron during braking, then the energy of the quantum cannot exceed the energy of the electron eU, i.e. , from here or .
In this experiment we can determine Planck's constant h. Of all the methods for determining Planck's constant, the method based on measuring the short-wavelength boundary of the X-ray bremsstrahlung spectrum is the most accurate.
7. Photo effect- this is the emission of electrons from a substance under the influence of light (and, generally speaking, any electromagnetic radiation). In condensed substances (solid and liquid) there is an external and internal photoelectric effect.
Laws of the photoelectric effect:
Formulation 1st law of photoelectric effect: the number of electrons emitted by light from the surface of a metal per unit time at a given frequency is directly proportional to the light flux illuminating the metal.
According to 2nd law of photoelectric effect, the maximum kinetic energy of electrons ejected by light increases linearly with the frequency of light and does not depend on its intensity.
3rd law of photoelectric effect: for each substance there is a red limit of the photoelectric effect, that is, the minimum light frequency ν 0 (or maximum wavelength λ 0), at which the photoelectric effect is still possible, and if ν 0, then the photoelectric effect no longer occurs.
The theoretical explanation of these laws was given in 1905 by Einstein. According to it, electromagnetic radiation is a stream of individual quanta (photons) with energy hν each, where h is Planck’s constant. With the photoelectric effect, part of the incident electromagnetic radiation is reflected from the metal surface, and part penetrates into the surface layer of the metal and is absorbed there. Having absorbed a photon, the electron receives energy from it and, performing a work function, leaves the metal: hν = A out + W e, Where W e- the maximum kinetic energy that an electron can have when leaving the metal.
From the law of conservation of energy, when representing light in the form of particles (photons), Einstein’s formula for the photoelectric effect follows: hν = A out + Ek
Where A out- so-called work function (the minimum energy required to remove an electron from a substance), Ek is the kinetic energy of the emitted electron (depending on the speed, either the kinetic energy of a relativistic particle can be calculated or not), ν is the frequency of the incident photon with energy hν, h- Planck's constant.
Work function- the difference between the minimum energy (usually measured in electron volts) that must be imparted to an electron for its “direct” removal from the volume of a solid body, and the Fermi energy.
“Red” border of the photo effect- minimum frequency or maximum wavelength λ max light, at which the external photoelectric effect is still possible, that is, the initial kinetic energy of photoelectrons is greater than zero. The frequency depends only on the output function A out electron: , where A out- work function for a specific photocathode, h is Planck's constant, and With- speed of light. Work function A out depends on the material of the photocathode and the condition of its surface. The emission of photoelectrons begins as soon as light of frequency or wavelength λ is incident on the photocathode.
Thermal radiation are called electromagnetic waves emitted by atoms, which are excited due to the energy of their thermal motion. If radiation is in equilibrium with matter, it is called equilibrium thermal radiation.
All bodies at a temperature T > 0 K emit electromagnetic waves. Rarefied monatomic gases give line emission spectra, polyatomic gases and liquids give striped spectra, i.e. regions with an almost continuous set of wavelengths. Solids emit continuous spectra consisting of all possible wavelengths. The human eye sees radiation in a limited range of wavelengths from approximately 400 to 700 nm. For a person to be able to see body radiation, the body temperature must be at least 700 o C.
Thermal radiation is characterized by the following quantities:
W- radiation energy (in J);
(J/(s.m 2) - energetic luminosity (D.S.- radiating area
surface). Energetic luminosity R- within the meaning of -
is the energy emitted per unit area per unit
time for all wavelengths l from 0 to .
In addition to these characteristics, called integral, they also use spectral characteristics, which take into account the amount of emitted energy per unit wavelength interval or unit interval
absorptivity (absorption coefficient) is the ratio of the absorbed light flux to the incident flux, taken in a small range of wavelengths near a given wavelength.
The spectral density of energy luminosity is numerically equal to the radiation power per unit surface area of this body in a frequency interval of unit width.
Thermal radiation and its nature. Ultraviolet disaster. Thermal radiation distribution curve. Planck's hypothesis.
THERMAL RADIATION (temperature radiation) - el-magn. radiation emitted by a substance and arising due to its internal. energy (unlike, for example, luminescence, which is excited by external energy sources). T. and. has a continuous spectrum, the position of the maximum of which depends on the temperature of the substance. As it increases, the total energy of emitted radiation increases, and the maximum moves to the region of short wavelengths. T. and. emits, for example, the surface of hot metal, the earth's atmosphere, etc.
T. and. arises under conditions of detailed equilibrium in a substance (see Detailed equilibrium principle) for all non-radiants. processes, i.e. for decomp. types of particle collisions in gases and plasmas, for the exchange of electronic and vibrational energies. movements in solids, etc. The equilibrium state of matter at each point in space is the state of local thermodynamic. equilibrium (LTE) - in this case it is characterized by the value of the temperature, on which the temperature depends. at this point.
In the general case of systems of bodies, for which only LTE and decomposition are carried out. cut points have different temperatures, T. and. is not in thermodynamic state. equilibrium with matter. Hotter bodies emit more than they absorb, and colder ones do the opposite. There is a transfer of radiation from hotter bodies to colder ones. To maintain a stationary state, in which the temperature distribution in the system is maintained, it is necessary to compensate for the loss of thermal energy with a radiating hotter body and remove it from the colder body.
At full thermodynamic In equilibrium, all parts of a system of bodies have the same temperature and the energy of the thermal energy emitted by each body is compensated by the energy of the thermal energy absorbed by this body. other phones In this case, detailed equilibrium also takes place for radiators. transitions, T. and. is in thermodynamic equilibrium with the substance and called radiation is equilibrium (the radiation of an absolutely black body is equilibrium). The spectrum of equilibrium radiation does not depend on the nature of the substance and is determined by Planck’s law of radiation.
For T. and. For non-black bodies, Kirchhoff's law of radiation is valid, connecting them to emit. and absorb. abilities with emit. the ability of a completely black body.
In the presence of LTE, applying the laws of radiation of Kirchhoff and Planck to the emission and absorption of T. and. in gases and plasmas, it is possible to study the processes of radiation transfer. This consideration is widely used in astrophysics, in particular in the theory of stellar atmospheres.
Ultraviolet disaster- a physical term describing the paradox of classical physics, which consists in the fact that the total power of thermal radiation of any heated body must be infinite. The paradox got its name due to the fact that the spectral energy density of the radiation should have increased indefinitely as the wavelength shortened.
In essence, this paradox showed, if not the internal inconsistency of classical physics, then at least an extremely sharp (absurd) discrepancy with elementary observations and experiment.
Since this does not agree with experimental observation, at the end of the 19th century difficulties arose in describing the photometric characteristics of bodies.
The problem was solved by Max Planck's quantum theory of radiation in 1900.
Planck's hypothesis is a hypothesis put forward on December 14, 1900 by Max Planck, which states that during thermal radiation energy is emitted and absorbed not continuously, but in separate quanta (portions). Each such quantum portion has an energy proportional to the frequency ν of radiation:
where h or is the proportionality coefficient, later called Planck’s constant. Based on this hypothesis, he proposed a theoretical derivation of the relationship between the temperature of a body and the radiation emitted by this body - Planck's formula.
Planck's hypothesis was later confirmed experimentally.
So what is thermal radiation?
Thermal radiation is electromagnetic radiation that arises due to the energy of the rotational and vibrational motion of atoms and molecules within a substance. Thermal radiation is characteristic of all bodies that have a temperature above absolute zero.
Thermal radiation of the human body belongs to the infrared range of electromagnetic waves. Such radiation was first discovered by the English astronomer William Herschel. In 1865, the English physicist J. Maxwell proved that infrared radiation is of an electromagnetic nature and consists of waves with a length of 760 nm up to 1-2 mm. Most often, the entire range of IR radiation is divided into areas: near (750 nm-2.500nm), average (2.500 nm - 50.000nm) and long-range (50,000 nm-2.000.000nm).
Let's consider the case when body A is located in cavity B, which is limited by an ideal reflective (impenetrable to radiation) shell C (Fig. 1). As a result of multiple reflection from the inner surface of the shell, the radiation will be stored within the mirror cavity and partially absorbed by body A. Under such conditions, the system cavity B - body A will not lose energy, but there will only be a continuous exchange of energy between body A and the radiation that fills cavity B.
Fig.1. Multiple reflection of thermal waves from the mirror walls of cavity B
If the energy distribution remains unchanged for each wavelength, then the state of such a system will be equilibrium, and the radiation will also be equilibrium. The only type of equilibrium radiation is thermal. If for some reason the equilibrium between radiation and the body shifts, then thermodynamic processes begin to occur that will return the system to a state of equilibrium. If body A begins to emit more than it absorbs, then the body begins to lose internal energy and the body temperature (as a measure of internal energy) will begin to fall, which will reduce the amount of energy emitted. The body's temperature will drop until the amount of energy emitted equals the amount of energy absorbed by the body. Thus, an equilibrium state will occur.
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 equally probable), unpolarized (the directions and values of the electric and magnetic field strength vectors at all points of the cavity change chaotically).
The main quantitative characteristics of thermal radiation are:
- energetic luminosity is the amount of energy of electromagnetic radiation in the entire range of wavelengths of thermal radiation that is emitted by a body in all directions from a unit surface area per unit time: R = E/(S t), [J/(m 2 s)] = [W /m 2 ] 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.
- spectral luminosity density - energetic luminosity of a body for given wavelengths (λ + dλ) at a given temperature (T + dT): R λ,T = f(λ, T).
The energetic luminosity of a body within certain wavelengths is calculated by integrating R λ,T = f(λ, T) for T = const:
- absorption coefficient
- the ratio of the energy absorbed by the body to the incident energy. So, if radiation from a flux dФ inc falls on a body, then one part of it is reflected from the surface of the body - dФ neg, the other part passes into the body and partially turns into heat dФ abs, and the third part, after several internal reflections, passes through the body outwards dФ inc : α = dФ abs./dФ down.
The absorption coefficient α depends on the nature of the absorbing body, the wavelength of the absorbed radiation, the temperature and state of the surface of the body.
- monochromatic absorption coefficient- absorption coefficient of thermal radiation of a given wavelength at a given temperature: α λ,T = f(λ,T)
Among the bodies there are bodies that can absorb all thermal radiation of any wavelength that falls on them. Such ideally 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 cavity opening with a heat-proof shell. The hole diameter is no more than 0.1 of the cavity diameter. At a constant temperature, some energy is emitted from the hole, corresponding to the energetic luminosity of a completely black body. But the black hole is an idealization. But the laws of thermal radiation of the black body help to get closer to real patterns.
2. Laws of thermal radiation
1. Kirchhoff's law. Thermal radiation is equilibrium - the amount of energy emitted by a body is how much it is absorbed by it. For three bodies located in a closed cavity we can write:
The indicated relationship will also be true when one of the bodies is AC:
Because for the black body α λT .
This is Kirchhoff's law: the ratio of the spectral density of the energetic 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 to the spectral density of energetic luminosity at the same temperature and wavelength.
Corollaries from Kirchhoff's law:
1. The spectral energetic luminosity of the black body is a universal function of wavelength and body temperature.
2. The spectral energy luminosity of the black body is the greatest.
3. The spectral energy luminosity of an arbitrary body is equal to the product of its absorption coefficient and the spectral energy luminosity of an absolutely black body.
4. Any body at a given temperature emits waves of the same wavelength that it emits at a given temperature.
A systematic study of the spectra of a number of elements allowed Kirchhoff and Bunsen to establish an unambiguous connection between the absorption and emission spectra of gases and the individuality of the corresponding atoms. So it was proposed spectral analysis, with which you can identify substances whose concentration is 0.1 nm.
Distribution of spectral density of energy luminosity for an absolutely black body, a gray body, an arbitrary body. The last curve has several maxima and minima, which indicates the selectivity of emission and absorption of such bodies.
2. Stefan-Boltzmann law.
In 1879, Austrian scientists Joseph Stefan (experimentally for an arbitrary body) and Ludwig Boltzmann (theoretically for a black body) established that the total energetic luminosity over the entire wavelength range is proportional to the fourth power of the absolute temperature of the body:
3. Wine's Law.
German physicist Wilhelm Wien in 1893 formulated a law that determines the position of the maximum spectral density of the energetic luminosity of a body in the radiation spectrum of the 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 the black body, is inversely proportional to its absolute temperature T: λ max = в/t, where в = 2.9*10 -3 m·K is Wien’s constant.
Thus, with increasing temperature, not only the total radiation energy changes, but also the very shape of the distribution curve of the spectral density of energy luminosity. With increasing temperature, the maximum spectral density shifts towards shorter wavelengths. Therefore, Wien's law is called the law of displacement.
Wine's Law Applies in optical pyrometry- a method for determining temperature from the radiation spectrum of highly heated bodies that are distant from the observer. It was this method that first determined the temperature of the Sun (for 470 nm T = 6160 K).
The presented laws did not allow us to theoretically find equations for the distribution of the spectral density of energetic luminosity over wavelengths. The works of Rayleigh and Jeans, in which scientists studied the spectral composition of the black body radiation based on the laws of classical physics, led to fundamental difficulties called the ultraviolet catastrophe. In the range of UV waves, the energetic luminosity of the black body 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 the 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 Planck's constant.
Guided by ideas about the quantum radiation of the black body, he obtained an equation for the spectral density of the energy luminosity of the black body:
This formula is in accordance with experimental data over the entire wavelength range at all temperatures.
The sun is the main source of thermal radiation in nature. Solar radiation occupies a wide range of wavelengths: from 0.1 nm to 10 m or more. 99% of solar energy occurs in the range from 280 to 6000 nm. Per unit area of the Earth's surface, in the mountains there is from 800 to 1000 W/m2. One two-billionth part of the heat reaches the earth's surface - 9.23 J/cm2. For the range of thermal radiation from 6000 to 500000 nm accounts for 0.4% of the sun's energy. In the Earth's atmosphere, most of the infrared radiation is absorbed by molecules of water, oxygen, nitrogen, and carbon dioxide. The radio range is also mostly absorbed by the atmosphere.
The amount of energy that the sun's rays bring per 1 s to an area of 1 sq.m, located outside the earth's atmosphere at an altitude of 82 km perpendicular to the sun's rays is called the solar constant. It is equal to 1.4 * 10 3 W/m 2.
The spectral distribution of the normal flux density of solar radiation coincides with that for the black body at a temperature of 6000 degrees. Therefore, the Sun relative to thermal radiation is a black body.
3. Radiation from real bodies and the human body
Thermal radiation from the surface of the human body plays a large 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 have a dominant role (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 lethal environment for naked person, and after 2-4 hours fainting and death occurs due to hypothermia of the brain). The share of radiation in the total heat transfer can range from 75 to 25%. Under normal conditions, about 50% at physiological rest.
Thermal radiation, which plays a role in the life of living organisms, is divided into short wavelengths (from 0.3 to 3 µm) and long wavelength (from 5 to 100 µm). The source of short-wave radiation is the Sun and open flame, and living organisms are exclusively recipients of such radiation. Long-wave radiation is both emitted and absorbed by living organisms.
The value of the absorption coefficient depends on the ratio of the temperatures of the medium and the body, the area of their interaction, the orientation of these areas, and for short-wave radiation - on the color of the surface. Thus, in blacks only 18% of short-wave radiation is reflected, while in people of the white race it is about 40% (most likely, the skin color of blacks in evolution had nothing to do with heat transfer). For long-wave radiation, the absorption coefficient is close to 1.
Calculating heat transfer by radiation is a very difficult task. The Stefan-Boltzmann law cannot be used for real bodies, since they have a more complex dependence of energetic luminosity on temperature. It turns out that it depends on temperature, the nature of the body, the shape of the body and the state of its surface. With a change in temperature, the coefficient σ and the temperature exponent change. The surface of the human body has a complex configuration, the person wears clothes that change the radiation, and the process is affected by the posture in which the person is.
For a gray body, the radiation power in the entire range is determined by the formula: P = α d.t. σ·T 4 ·S Considering, with certain approximations, real bodies (human skin, clothing fabrics) to be close to gray bodies, we can find a formula for calculating the radiation power of real bodies at a certain temperature: P = α·σ·T 4 ·S Under different conditions temperatures of the radiating body and the environment: P = α·σ·(T 1 4 - T 2 4)·S
There are features of the spectral density of the energy luminosity of real bodies: at 310 TO, which corresponds to the average human body temperature, the maximum thermal radiation occurs at 9700 nm. Any change in body temperature leads to a change in the power of thermal radiation from the surface of the body (0.1 degrees is enough). Therefore, the study of skin areas connected through the central nervous system to certain organs helps to identify diseases, as a result of which the temperature changes quite significantly ( thermography of the Zakharyin-Ged zones).
An interesting method of non-contact massage with the human biofield (Juna Davitashvili). Palm thermal radiation power 0.1 W, and the thermal sensitivity of the skin is 0.0001 W/cm 2 . If you act on the above-mentioned zones, you can reflexively stimulate the work of these organs.
4. Biological and therapeutic effects of heat and cold
The human body constantly emits and absorbs thermal radiation. This process depends on the temperature of the human body and the environment. The maximum infrared radiation of the human body is at 9300 nm.
With small and medium doses of IR irradiation, metabolic processes are enhanced and enzymatic reactions, regeneration and repair processes are accelerated.
As a result of the action of infrared rays and visible radiation, biologically active substances (bradykinin, kalidin, histamine, acetylcholine, mainly vasomotor substances, which play a role in the implementation and regulation of local blood flow) are formed in tissues.
As a result of the action of infrared rays, thermoreceptors in the skin are activated, information from which is sent to the hypothalamus, as a result of which the blood vessels of the skin dilate, the volume of blood circulating in them increases, and sweating increases.
The depth of penetration of infrared rays depends on the wavelength, skin moisture, its filling with blood, the degree of pigmentation, etc.
Red erythema appears on human skin under the influence of infrared rays.
It is used in clinical practice to influence local and general hemodynamics, increase sweating, relax muscles, reduce pain, accelerate the resorption of hematomas, infiltrates, etc.
Under conditions of hyperthermia, the antitumor effect of radiation therapy—thermoradiotherapy—is enhanced.
The main indications for the use of IR therapy: acute non-purulent inflammatory processes, burns and frostbite, chronic inflammatory processes, ulcers, contractures, adhesions, injuries of joints, ligaments and muscles, myositis, myalgia, neuralgia. Main contraindications: tumors, purulent inflammations, bleeding, circulatory failure.
Cold is used to stop bleeding, relieve pain, and treat certain skin diseases. Hardening leads to longevity.
Under the influence of cold, heart rate and blood pressure decrease, and reflex reactions are inhibited.
In certain doses, cold stimulates the healing of burns, purulent wounds, trophic ulcers, erosions, and conjunctivitis.
Cryobiology- studies the processes that occur in cells, tissues, organs and the body under the influence of low, non-physiological temperatures.
Used in medicine cryotherapy And hyperthermia. Cryotherapy includes methods based on dosed cooling of tissues and organs. Cryosurgery (part of cryotherapy) uses local freezing of tissues for the purpose of their removal (part of the tonsil. If all - cryotonsillectomy. Tumors can be removed, for example, skin, cervix, etc.) Cryoextraction based on cryoadhesion (adhesion of wet bodies to a frozen scalpel ) - separation of a part from an organ.
With hyperthermia, it is possible to preserve the functions of organs in vivo for some time. Hypothermia with the help of anesthesia is used to preserve organ function in the absence of blood supply, since tissue metabolism slows down. Tissues become resistant to hypoxia. Cold anesthesia is used.
The effect of heat is carried out using incandescent lamps (Minin lamp, Solux, light-thermal bath, IR ray lamp) using physical media that have high heat capacity, poor thermal conductivity and good heat-retaining ability: mud, paraffin, ozokerite, naphthalene, etc.
5. Physical foundations of thermography. Thermal imagers
Thermography, or thermal imaging, is a functional diagnostic method based on recording infrared radiation from the human body.
There are 2 types of thermography:
- contact cholesteric thermography: The method uses the optical properties of cholesteric liquid crystals (multicomponent mixtures of esters and other cholesterol derivatives). Such substances selectively reflect different wavelengths, which makes it possible to obtain images of the thermal field of the surface of the human body on films of these substances. A stream of white light is directed onto the film. Different wavelengths are reflected differently from the film depending on the temperature of the surface on which the cholesteric is applied.
Under the influence of temperature, cholesterics can change color from red to purple. As a result, a color image of the thermal field of the human body is formed, which is easy to decipher, knowing the temperature-color relationship. There are cholesterics that allow you to record a temperature difference of 0.1 degrees. Thus, it is possible to determine the boundaries of the inflammatory process, foci of inflammatory infiltration at different stages of its development.
In oncology, thermography makes it possible to identify metastatic nodes with a diameter of 1.5-2 mm in the mammary gland, skin, thyroid gland; in orthopedics and traumatology, assess the blood supply to each segment of the limb, for example, before amputation, anticipate the depth of the burn, etc.; in cardiology and angiology, identify disturbances in the normal functioning of the cardiovascular system, circulatory disorders due to vibration disease, inflammation and blockage of blood vessels; varicose veins, etc.; in neurosurgery, determine the location of lesions of nerve conduction, confirm the location of neuroparalysis caused by apoplexy; in obstetrics and gynecology, determine pregnancy, localization of the child's place; diagnose a wide range of inflammatory processes.
- Telethermography - is based on the conversion of infrared radiation from the human body into electrical signals that are recorded on the screen of a thermal imager or other recording device. The method is non-contact.
IR radiation is perceived by a system of mirrors, after which the IR rays are directed to the IR wave receiver, the main part of which is the detector (photoresistor, metal or semiconductor bolometer, thermoelement, photochemical indicator, electron-optical converter, piezoelectric detectors, etc.) .
Electrical signals from the receiver are transmitted to an amplifier, and then to a control device, which serves to move mirrors (scanning an object), heat up a TIS point light source (proportional to thermal radiation), and move photographic film. Each time the film is illuminated with TIS according to the body temperature at the study site.
After the control device, the signal can be transmitted to a computer system with a display. This allows you to store thermograms and process them using analytical programs. Additional capabilities are provided by color thermal imagers (colors similar in temperature are indicated in contrasting colors), and isotherms can be drawn.
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