THERMAL RADIATION Stefan Boltzmann's law Relationship between the energy luminosity R e and the spectral density of the energy luminosity of a black body Energy luminosity of a gray body Wien's displacement law (1st law) Dependence of the maximum spectral density of the energy luminosity of a black body on temperature (2nd law) Planck's formula
THERMAL RADIATION 1. The maximum spectral density of the solar energy luminosity occurs at wavelength = 0.48 microns. Assuming that the Sun radiates as a black body, determine: 1) the temperature of its surface; 2) the power emitted by its surface. According to Wien's displacement law, Power emitted by the surface of the Sun According to Stefan Boltzmann's law,
THERMAL RADIATION 2. Determine the amount of heat lost by 50 cm 2 from the surface of molten platinum in 1 minute, if the absorption capacity of platinum A T = 0.8. The melting point of platinum is 1770 °C. The amount of heat lost by platinum is equal to the energy emitted by its hot surface. According to Stefan Boltzmann's law,
THERMAL RADIATION 3. An electric furnace consumes power P = 500 W. The temperature of its inner surface with an open small hole with a diameter of d = 5.0 cm is 700 °C. How much of the power consumption is dissipated by the walls? The total power is determined by the sum of the Power released through the hole Power dissipated by the walls According to Stefan Boltzmann's law,
THERMAL RADIATION 4 A tungsten filament is heated in a vacuum with a current of force I = 1 A to a temperature T 1 = 1000 K. At what current strength will the filament be heated to a temperature T 2 = 3000 K? The absorption coefficients of tungsten and its resistivity corresponding to temperatures T 1, T 2 are equal to: a 1 = 0.115 and a 2 = 0.334; 1 = 25, Ohm m, 2 = 96, Ohm m The power emitted is equal to the power consumed from the electrical circuit in steady state Electric power released in the conductor According to Stefan Boltzmann's law,
THERMAL RADIATION 5. In the spectrum of the Sun, the maximum spectral density of energy luminosity occurs at a wavelength of .0 = 0.47 microns. Assuming that the Sun emits as a completely black body, find the intensity of solar radiation (i.e., radiation flux density) near the Earth outside its atmosphere. Luminous intensity (radiation intensity) Luminous flux According to the laws of Stefan Boltzmann and Wien
THERMAL RADIATION 6. Wavelength 0, which accounts for the maximum energy in the black body radiation spectrum, is 0.58 microns. Determine the maximum spectral density of energy luminosity (r, T) max, calculated for the wavelength interval = 1 nm, near 0. The maximum spectral density of energy luminosity is proportional to the fifth power of temperature and is expressed by Wien’s 2nd law. Temperature T is expressed from Wien’s displacement law value C is given in SI units, in which the unit wavelength interval = 1 m. According to the conditions of the problem, it is necessary to calculate the spectral luminosity density calculated for the wavelength interval of 1 nm, so we write out the value of C in SI units and recalculate it for a given wavelength interval:
THERMAL RADIATION 7. A study of the solar radiation spectrum shows that the maximum spectral density of energy luminosity corresponds to a wavelength = 500 nm. Taking the Sun to be a black body, determine: 1) the energetic luminosity R e of the Sun; 2) energy flow F e emitted by the Sun; 3) the mass of electromagnetic waves (of all lengths) emitted by the Sun in 1 s. 1. According to the laws of Stefan Boltzmann and Wien 2. Luminous flux 3. The mass of electromagnetic waves (all lengths) emitted by the Sun during the time t = 1 s, we determine by applying the law of proportionality of mass and energy E = ms 2. The energy of electromagnetic waves emitted during time t, is equal to the product of energy flow Ф e ((radiation power) by time: E=Ф e t. Therefore, Ф e =ms 2, whence m=Ф e/s 2.
d Φ e (\displaystyle d\Phi _(e)), emitted by a small area of the surface of the radiation source, to its area d S (\displaystyle dS) : M e = d Φ e d S .(\displaystyle M_(e)=(\frac (d\Phi _(e))(dS)).)
It is also said that energetic luminosity is the surface density of the emitted radiation flux.
The emitted radiation can arise in the surface itself, then they speak of a self-luminous surface. Another option is observed when the surface is illuminated from the outside. In such cases, some part of the incident flux necessarily returns back as a result of scattering and reflection. Then the expression for energetic luminosity has the form:
M e = (ρ + σ) ⋅ E e , (\displaystyle M_(e)=(\rho +\sigma)\cdot E_(e),)Where ρ (\displaystyle \rho ) And σ (\displaystyle \sigma )- reflection coefficient and scattering coefficient of the surface, respectively, and - its irradiance.
Other names of energetic luminosity, sometimes used in the literature, but not provided for by GOST: - emissivity And integrated emissivity.
Spectral density of energetic luminosity
Spectral density of energetic luminosity M e , λ (λ) (\displaystyle M_(e,\lambda )(\lambda))- ratio of the magnitude of energetic luminosity d M e (λ) , (\displaystyle dM_(e)(\lambda),) falling on a small spectral interval d λ , (\displaystyle d\lambda ,), concluded between λ (\displaystyle \lambda) And λ + d λ (\displaystyle \lambda +d\lambda ), to the width of this interval:
M e , λ (λ) = d M e (λ) d λ .(\displaystyle M_(e,\lambda )(\lambda)=(\frac (dM_(e)(\lambda))(d\lambda )).)
The SI unit is W m−3. Since wavelengths of optical radiation are usually measured in nanometers, in practice W m −2 nm −1 is often used. Sometimes in literature M e , λ (\displaystyle M_(e,\lambda )) are called.
spectral emissivity
Light analogueWhere M v = K m ⋅ ∫ 380 n m 780 n m M e , λ (λ) V (λ) d λ , (\displaystyle M_(v)=K_(m)\cdot \int \limits _(380~nm)^ (780~nm)M_(e,\lambda )(\lambda)V(\lambda)d\lambda ,) K m (\displaystyle K_(m))
- maximum luminous radiation efficiency equal to 683 lm / W in the SI system. Its numerical value follows directly from the definition of candela.
Information about other basic energy photometric quantities and their light analogues is given in the table. Designations of quantities are given according to GOST 26148-84.| Energy photometric SI quantities | Name (synonym) | Quantity designation | Definition | SI units notation |
|---|---|---|---|---|
| Light magnitude | Radiation energy (radiant energy) Q e (\displaystyle Q_(e)) or | W (\displaystyle W) | Energy transferred by radiation | J |
| Light energy | Radiation flux (radiant flux)Φ (\displaystyle \Phi ) P (\displaystyle P) | Φ e = d Q e d t (\displaystyle \Phi _(e)=(\frac (dQ_(e))(dt))) | W | Light flow |
| Radiation intensity (light energy intensity) | I e (\displaystyle I_(e)) | I e = d Φ e d Ω (\displaystyle I_(e)=(\frac (d\Phi _(e))(d\Omega ))) | W sr −1 | The power of light |
| Volumetric radiation energy density | U e (\displaystyle U_(e)) | U e = d Q e d V (\displaystyle U_(e)=(\frac (dQ_(e))(dV))) | J m −3 | Volumetric density of light energy |
| Energy brightness | L e (\displaystyle L_(e)) | L e = d 2 Φ e d Ω d S 1 cos ε (\displaystyle L_(e)=(\frac (d^(2)\Phi _(e))(d\Omega \,dS_(1)\, \cos \varepsilon ))) | W m−2 sr−1 | Brightness |
| Integral energy brightness | Λ e (\displaystyle \Lambda _(e)) | Λ e = ∫ 0 t L e (t ′) d t ′ (\displaystyle \Lambda _(e)=\int _(0)^(t)L_(e)(t")dt") | J m −2 sr −1 | Integral brightness |
| Irradiance (irradiance) | E e (\displaystyle E_(e)) | E e = d Φ e d S 2 (\displaystyle E_(e)=(\frac (d\Phi _(e))(dS_(2)))) | W m−2 |
Spectral density of energy luminosity (brightness) is a function showing the distribution of energy luminosity (brightness) across the radiation spectrum.
Meaning that:
Energetic luminosity is the surface flux density of energy emitted by a surface
Energy brightness is the amount of flux emitted per unit area per unit solid angle in a given direction
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.
Pure black body
Pure black body- this is a physical abstraction (model), which is understood as a body that completely absorbs all electromagnetic radiation incident on it
For a completely black body
Gray body
Gray body- this is a body whose absorption coefficient does not depend on frequency, but depends only on temperature
For gray body
Kirchhoff's law for thermal radiation
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 and chemical nature.
Temperature dependence of the spectral density of the energy luminosity of an absolutely black body
The dependence of the spectral radiation energy density L (T) of a black body on the temperature T in the microwave radiation range is established for the temperature range from 6300 to 100000 K.
Wien's displacement law gives the dependence of the wavelength at which the radiation flux of black body energy reaches its maximum on the temperature of the black body.
B=2.90* m*K
Stefan-Boltzmann law
Rayleigh-jeans formula
Planck's formula
constant bar
Photo effect- this is the emission of electrons by 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 frequency of light (or maximum wavelength λ 0) at which the photoelectric effect is still possible, and if , then the photoelectric effect no longer occurs.
Photon- an elementary particle, a quantum of electromagnetic radiation (in the narrow sense of light). It is a massless particle that can only exist by moving at the speed of light. The electric charge of a photon is also zero.
Einstein's equation for the external photoelectric effect
Photocell- an electronic device that converts photon energy into electrical energy. The first photocell based on the external photoelectric effect was created by Alexander Stoletov at the end of the 19th century.
energy, mass and momentum of the photon
Light pressure is the pressure produced by electromagnetic light waves incident on the surface of a body.
The pressure p exerted by the wave on the metal surface could be calculated as the ratio of the resultant Lorentz forces acting on free electrons in the surface layer of the metal to the surface area of the metal:
Quantum theory of light explains light pressure as a result of photons transferring their momentum to atoms or molecules of matter.
Compton effect(Compton effect) - the phenomenon of changing the wavelength of electromagnetic radiation due to elastic scattering by electrons
Compton wavelength
De Broglie's conjecture is that the French physicist Louis de Broglie put forward the idea of attributing wave properties to the electron. Drawing an analogy between a quantum, de Broglie suggested that the movement of an electron or any other particle with rest mass is associated with a wave process.
De Broglie's conjecture establishes that a moving particle with energy E and momentum p corresponds to a wave process whose frequency is equal to:
and wavelength:
where p is the momentum of the moving particle.
Davisson-Germer experiment- a physical experiment on electron diffraction conducted in 1927 by American scientists Clinton Davisson and Lester Germer.
A study was carried out on the reflection of electrons from a nickel single crystal. The setup included a single crystal of nickel, ground at an angle and mounted on a holder. A beam of monochromatic electrons was directed perpendicularly to the polished section plane. The electron speed was determined by the voltage on the electron gun:
A Faraday cup was installed at an angle to the incident electron beam, connected to a sensitive galvanometer. Based on the readings of the galvanometer, the intensity of the electron beam reflected from the crystal was determined. The entire installation was in vacuum.
In the experiments, the intensity of the electron beam scattered by the crystal was measured depending on the scattering angle, the azimuthal angle, and the speed of the electrons in the beam.
Experiments have shown that there is a pronounced selectivity in electron scattering. At different angles and velocities, intensity maxima and minima are observed in the reflected rays. Maximum condition:
Here is the interplanar distance.
Thus, electron diffraction was observed on the crystal lattice of a single crystal. The experiment was a brilliant confirmation of the existence of wave properties in microparticles.
Wave function, or psi function is a complex-valued function used in quantum mechanics to describe the pure state of a system. Is the coefficient of expansion of the state vector over a basis (usually a coordinate one):
where is the coordinate basis vector, and is the wave function in coordinate representation.
The physical meaning of the wave function is that, according to the Copenhagen interpretation of quantum mechanics, the probability density of finding a particle at a given point in space at a given moment in time is considered equal to the square of the absolute value of the wave function of this state in coordinate representation.
Heisenberg Uncertainty Principle(or Heisenberg) in quantum mechanics - a fundamental inequality (uncertainty relation) that sets the limit of accuracy for the simultaneous determination of a pair of physical observables characterizing a quantum system (see physical quantity), described by non-commuting operators (for example, coordinates and momentum, current and voltage, electric and magnetic field). The uncertainty relation [* 1] sets a lower limit for the product of the standard deviations of a pair of quantum observables. The uncertainty principle, discovered by Werner Heisenberg in 1927, is one of the cornerstones of quantum mechanics.
Quantity designation If there are several (many) identical copies of the system in a given state, then the measured values of the coordinate and momentum will obey a certain probability distribution - this is a fundamental postulate of quantum mechanics. By measuring the value of the standard deviation of the coordinate and the standard deviation of the impulse, we will find that:
Schrödinger equation
Potential well– a region of space where there is a local minimum of the potential energy of a particle.
Tunnel effect, tunneling- overcoming a potential barrier by a microparticle in the case when its total energy (which remains unchanged during tunneling) is less than the height of the barrier. The tunnel effect is a phenomenon of exclusively quantum nature, impossible and even completely contradictory to classical mechanics. An analogue of the tunnel effect in wave optics can be the penetration of a light wave into a reflecting medium (at distances on the order of the light wavelength) under conditions where, from the point of view of geometric optics, total internal reflection occurs. The phenomenon of tunneling underlies many important processes in atomic and molecular physics, in the physics of the atomic nucleus, solid state, etc.
Harmonic oscillator in quantum mechanics, it is a quantum analogue of a simple harmonic oscillator; in this case, it is not the forces acting on the particle that are considered, but the Hamiltonian, that is, the total energy of the harmonic oscillator, and the potential energy is assumed to depend quadratically on the coordinates. Taking into account the following terms in the expansion of potential energy along a coordinate leads to the concept of an anharmonic oscillator.
The study of the structure of atoms has shown that atoms consist of a positively charged nucleus, in which almost all the mass is concentrated. h of the atom, and negatively charged electrons moving around the nucleus.
Bohr-Rutherford planetary model of the atom. In 1911, Ernest Rutherford, after conducting a series of experiments, came to the conclusion that the atom is a kind of planetary system in which electrons move in orbits around a heavy, positively charged nucleus located in the center of the atom (“Rutherford’s atom model”). However, such a description of the atom came into conflict with classical electrodynamics. The fact is that, according to classical electrodynamics, an electron, when moving with centripetal acceleration, should emit electromagnetic waves and, therefore, lose energy. Calculations showed that the time it takes for an electron in such an atom to fall onto the nucleus is absolutely insignificant. To explain the stability of atoms, Niels Bohr had to introduce postulates that boiled down to the fact that an electron in an atom, being in some special energy states, does not emit energy (“Bohr-Rutherford model of the atom”). Bohr's postulates showed that classical mechanics is inapplicable to describe the atom. Further study of atomic radiation led to the creation of quantum mechanics, which made it possible to explain the vast majority of observed facts.
Emission spectra of atoms usually obtained at a high temperature of a light source (plasma, arc or spark), at which the substance evaporates, its molecules split into individual atoms and the atoms are excited to glow. Atomic analysis can be either emission - the study of emission spectra, or absorption - the study of absorption spectra.
The emission spectrum of an atom is a set of spectral lines. The spectral line appears as a result of monochromatic light radiation during the transition of an electron from one electronic sublevel allowed by Bohr's postulate to another sublevel of different levels. This radiation is characterized by wavelength K, frequency v or wave number co.
The emission spectrum of an atom is a set of spectral lines. The spectral line appears as a result of monochromatic light radiation during the transition of an electron from one electronic sublevel allowed by Bohr's postulate to another sublevel of different levels.
Bohr model of the atom (Bohr Model)- a semi-classical model of the atom proposed by Niels Bohr in 1913. He took as a basis the planetary model of the atom put forward by Rutherford. However, from the point of view of classical electrodynamics, an electron in Rutherford's model, moving around the nucleus, should emit continuously, and very quickly, having lost energy, fall onto the nucleus. To overcome this problem, Bohr introduced an assumption, the essence of which is that electrons in an atom can only move in certain (stationary) orbits, in which they do not emit, and emission or absorption occurs only at the moment of transition from one orbit to another. Moreover, only those orbits are stationary when moving along which the angular momentum of the electron is equal to an integer number of Planck’s constants: .
Using this assumption and the laws of classical mechanics, namely the equality of the attractive force of an electron from the side of the nucleus and the centrifugal force acting on a rotating electron, he obtained the following values for the radius of a stationary orbit and the energy of the electron located in this orbit:
Here is the mass of the electron, Z is the number of protons in the nucleus, is the dielectric constant, e is the charge of the electron.
It is precisely this expression for energy that can be obtained by applying the Schrödinger equation, solving the problem of the motion of an electron in a central Coulomb field.
The radius of the first orbit in the hydrogen atom R 0 =5.2917720859(36)·10 −11 m, now called the Bohr radius, or atomic unit of length and is widely used in modern physics. The energy of the first orbit, eV, is the ionization energy of the hydrogen atom.
Bohr's postulates
§ An atom can only be in special stationary, or quantum, states, each of which has a specific energy. In a stationary state, an atom does not emit electromagnetic waves.
§ An electron in an atom, without losing energy, moves along certain discrete circular orbits, for which the angular momentum is quantized: , where are natural numbers, and is Planck’s constant. The presence of an electron in the orbit determines the energy of these stationary states.
§ When an electron moves from an orbit (energy level) to an orbit, a quantum of energy is emitted or absorbed, where are the energy levels between which the transition occurs. When moving from an upper level to a lower one, energy is emitted; when moving from a lower to an upper level, it is absorbed.
Using these postulates and the laws of classical mechanics, Bohr proposed a model of the atom, now called the Bohr model of the atom. Subsequently, Sommerfeld expanded Bohr's theory to the case of elliptical orbits. It is called the Bohr-Sommerfeld model.
Frank and Hertz experiments
experience has shown that electrons transfer their energy to mercury atoms in portions , and 4.86 eV is the smallest possible portion that can be absorbed by a mercury atom in the ground energy state
Balmer formula
To describe the wavelengths λ of the four visible lines of the hydrogen spectrum, I. Balmer proposed the formula
where n = 3, 4, 5, 6; b = 3645.6 Å.
Currently, a special case of the Rydberg formula is used for the Balmer series:
where λ is the wavelength,
R≈ 1.0974 10 7 m −1 - Rydberg constant,
n- the main quantum number of the initial level is a natural number greater than or equal to 3.
Hydrogen-like atom- an atom containing one and only one electron in its electron shell.
X-ray radiation- electromagnetic waves, the energy of photons of which lies on the scale of electromagnetic waves between ultraviolet radiation and gamma radiation, which corresponds to wavelengths from 10 −2 to 10 3 Å (from 10 −12 to 10 −7 m)
X-ray tube- an electric vacuum device designed to generate X-ray radiation.
Bremsstrahlung- electromagnetic radiation emitted by a charged particle when it is scattered (braked) in an electric field. Sometimes the concept of “bremsstrahlung” also includes the radiation of relativistic charged particles moving in macroscopic magnetic fields (in accelerators, in outer space), and is called magnetobremsstrahlung; however, the more commonly used term in this case is “synchrotron radiation.”
CHARACTERISTIC EMISSION- X-ray line spectrum radiation. Characteristic of the atoms of each element.
Chemical bond- the phenomenon of interaction of atoms, caused by the overlap of electron clouds of bonding particles, which is accompanied by a decrease in the total energy of the system.
molecular spectrum- emission (absorption) spectrum arising during quantum transitions between energy levels of molecules
Energy level- eigenvalues of the energy of quantum systems, that is, systems consisting of microparticles (electrons, protons and other elementary particles) and subject to the laws of quantum mechanics.
Quantum number n – The main thing . It determines the energy of the electron in the hydrogen atom and one-electron systems (He +, Li 2+, etc.). In this case, the electron energy
Where n takes values from 1 to ∞. The less n, the greater the energy of interaction between the electron and the nucleus. At n= 1 hydrogen atom is in the ground state, at n> 1 – excited.
Selection rules in spectroscopy, they call restrictions and prohibitions on transitions between levels of a quantum mechanical system with the absorption or emission of a photon, imposed by conservation laws and symmetry.
Multi-electron atoms atoms with two or more electrons are called.
Zeeman effect- splitting of lines of atomic spectra in a magnetic field.
Discovered in 1896 by Zeeman for sodium emission lines.
The essence of the phenomenon of electron paramagnetic resonance is the resonant absorption of electromagnetic radiation by unpaired electrons. An electron has a spin and an associated magnetic moment.
The energy that a body loses due to thermal radiation is characterized by the following quantities.
Radiation flux (F) - energy emitted per unit time from the entire surface of the body.
In fact, this is the power of thermal radiation. The dimension of the radiation flux is [J/s = W].
Energy luminosity (Re) - energy of thermal radiation emitted per unit time from a unit surface of a heated body:
In the SI system, energetic luminosity is measured - [W/m 2 ].
The radiation flux and energetic luminosity depend on the structure of the substance and its temperature: Ф = Ф(Т),
The distribution of energetic luminosity over the spectrum of thermal radiation characterizes it spectral density. Let us denote the energy of thermal radiation emitted by a single surface in 1 s in a narrow range of wavelengths from λ before λ +d λ, via dRe.
Spectral luminosity density (r) or emissivity The ratio of energetic luminosity in a narrow part of the spectrum (dRe) to the width of this part (dλ) is called:
Approximate form of spectral density and energetic luminosity (dRe) in the wavelength range from λ before λ +d λ, shown in Fig. 13.1.
Rice. 13.1. Spectral density of energetic luminosity
The dependence of the spectral density of energetic luminosity on wavelength is called body radiation spectrum. Knowledge of this dependence allows one to calculate the energetic luminosity of a body in any wavelength range. The formula for calculating the energetic luminosity of a body in a range of wavelengths is:
The total luminosity is:
Bodies not only emit, but also absorb thermal radiation. The ability of a body to absorb radiation energy depends on its substance, temperature and wavelength of the radiation. The absorption capacity of the body is characterized by monochromatic absorption coefficient α.
Let a stream fall on the surface of the body monochromatic radiation Φ λ with wavelength λ. Part of this flow is reflected, and part is absorbed by the body. Let us denote the magnitude of the absorbed flux Φ λ abs.
Monochromatic absorption coefficient α λ is the ratio of the radiation flux absorbed by a given body to the magnitude of the incident monochromatic flux:
Monochromatic absorption coefficient is a dimensionless quantity. Its values lie between zero and one: 0 ≤ α ≤ 1.
Function α = α(λ,Τ) , expressing the dependence of the monochromatic absorption coefficient on wavelength and temperature, is called absorption capacity bodies. Its appearance can be quite complex. The simplest types of absorption are discussed below.
Pure black body is a body whose absorption coefficient is equal to unity for all wavelengths: α = 1.
Gray body is a body for which the absorption coefficient does not depend on the wavelength: α = const< 1.
Absolutely white body is a body whose absorption coefficient is zero for all wavelengths: α = 0.
Kirchhoff's law
Kirchhoff's law- the ratio of the emissivity of a body to its absorption capacity is the same for all bodies and is equal to the spectral density of the energy luminosity of an absolutely black body:
= /
Corollary of the law:
1. If a body at a given temperature does not absorb any radiation, then it does not emit it. Indeed, if for a certain wavelength the absorption coefficient α = 0, then r = α∙ε(λT) = 0
1. At the same temperature black body radiates more than any other. Indeed, for all bodies except black,α < 1, поэтому для них r = α∙ε(λT) < ε
2. If for a certain body we experimentally determine the dependence of the monochromatic absorption coefficient on wavelength and temperature - α = r = α(λT), then we can calculate the spectrum of its radiation.
Thermal radiation 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 matter (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 bodies do the opposite. Radiation is transferred 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.