Physics
Black Body Radiation
Black body radiation refers to the electromagnetic radiation emitted by a perfect absorber and emitter of radiation, known as a black body. It is characterized by a continuous spectrum of radiation that depends only on the body's temperature. This phenomenon played a crucial role in the development of quantum mechanics and the understanding of the behavior of light.
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11 Key excerpts on "Black Body Radiation"
eBook - ePubBlackbody Radiation
A History of Thermal Radiation Computational Aids and Numerical Methods
- Sean M. Stewart, R. Barry Johnson(Authors)
- 2016(Publication Date)
- CRC Press(Publisher)
The name given to the body is appropriate. 3 Provided a body is not hot enough so as to appear self-luminous, as no radiation is reflected by the body, it appears completely black. The complete absorption of radiation by a blackbody holds true for radiation at all wavelengths and for all angles of incident upon the body. For a blackbody in thermal equilibrium with its surroundings it means that all radiation received through absorption must be emitted if its temperature is to remain constant as there is no other mechanism available to the body to lose energy without a corresponding increase in its temperature. A blackbody therefore radiates more energy per unit time in any given wavelength interval and more total energy per unit time over all wavelengths than any other body at the same temperature and is independent of the nature (its size, shape, or material from which it is made) of the radiating body. The radiation from a blackbody is referred to as blackbody radiation. By the late nineteenth century, the problem of the blackbody had become one of finding a mathematical expression that could describe the amount of energy emitted within a given spectral range as a function of both wavelength and temperature. Not surprisingly it was Kirchhoff, having first proposed the blackbody problem, who made the first serious attempt at its solution. In the winter of 1859–60, following a simple yet brilliant line of physical reasoning based on the second law of thermodynamics, he postulated that the radiation emitted from a blackbody within a given wavelength interval is a universal function depending only on the temperature of the body [ 354, 355 ]. It was an important first step, and constitutes what today is known as Kirchhoff’s law of thermal radiation, but there was still a long way to go
eBook - PDFBlackbody Radiation
A History of Thermal Radiation Computational Aids and Numerical Methods
- Sean M. Stewart, R. Barry Johnson(Authors)
- 2016(Publication Date)
- CRC Press(Publisher)
The name given to the body is appropriate. 3 Provided a body is not hot enough so as to appear self-luminous, as no radiation is reflected by the body, it appears completely black. The complete absorption of radiation by a blackbody holds true for radiation at all wavelengths and for all angles of incident upon the body. For a blackbody in thermal equilibrium with its surroundings it means that all radiation received through absorption must be emitted if its temperature is to remain constant as there is no other mech- anism available to the body to lose energy without a corresponding increase in its temperature. A blackbody therefore radiates more energy per unit time in any given wavelength interval and more total energy per unit time over all wavelengths than any other body at the same temperature and is inde- pendent of the nature (its size, shape, or material from which it is made) of the radiating body. The radiation from a blackbody is referred to as black- body radiation. By the late nineteenth century, the problem of the blackbody had become one of finding a mathematical expression that could describe the amount of energy emitted within a given spectral range as a function of both wavelength and temperature. Not surprisingly it was Kirchhoff, having first proposed the blackbody problem, who made the first serious attempt at its solution. In the winter of 3 4 Blackbody radiation 1859–60, following a simple yet brilliant line of physical reasoning based on the second law of thermodynamics, he postulated that the radiation emitted from a blackbody within a given wavelength interval is a universal function depending only on the temperature of the body [354, 355]. It was an important first step, and constitutes what today is known as Kirchhoff ’s law of thermal radiation, but there was still a long way to go.
eBook - PDFStatistical and Thermal Physics
Fundamentals and Applications
- M.D. Sturge(Author)
- 2018(Publication Date)
- A K Peters/CRC Press(Publisher)
The problem of Black Body Radiation (that is, the electromagnetic radiation emitted by a hot surface), 201 202 10. Black Body Radiation and the Photon Gas Figure 10.1. (a) Cavity containing radiation, enclosed in an opaque heat bath. (b) Two cavities connected by a hole that is covered by a h lter. has been under active consideration since the middle of the nineteenth century. It was the inability of classical statistical mechanics to account for the black body spectrum (the emitted power at a given temperature as a function of frequency) that led Planck 1 in 1900 to introduce the concept of the quantum. On the other hand, in 1884 Boltzmann used thermodynamic reasoning to correctly predict the temperature dependence of the total radiation from a hot body, and we begin by discussing the thermodynamics of radiation, leaving the statistical treatment till later. Radiation, whether from a hot body, from a 4 uorescent gas, or from a laser, is not under normal circumstances in equilibrium; energy is 4 owing outwards, and must be replenished from some source if it is to continue. However, if we are to apply thermodynamics to the radiation from a hot body, we must h rst h nd some situation where radiation is being emitted and absorbed at the same average rate, so that the body is in equilibrium with the radiation. This h rst step in understanding was made by Kirch-ho , 2 who considered an enclosure (cavity) inside an opaque but thermally conducting solid body, which can be regarded as a heat bath at a constant temperature T (see Figure 10.1(a) ). The walls of the cavity emit and absorb electromagnetic waves. The cavity is h lled with radiation that is in equilibrium with the heat bath surrounding it, so that it can be assigned a temperature T . The energy is spread over a range of frequencies, and we de h ne u s ( , T ) d as the energy density (energy per unit volume) of the radiation with frequency between and + d when the temperature is T .
No longer available |Learn more- (Author)
- 2014(Publication Date)
- Learning Press(Publisher)
By the time an object is white, it is emitting substantial ultraviolet radiation. The term black body was introduced by Gustav Kirchhoff in 1860. When used as a compound adjective, the term is typically written as one word in blackbody radiation , but sometimes also hyphenated, as in black-body radiation . Blackbody emission gives insight into the thermal equilibrium state of a continuous field. In classical physics, each different Fourier mode in thermal equilibrium should have the same energy. This approach led to the paradox known as the ultraviolet catastrophe, that there would be an infinite amount of energy in any continuous field. Black bodies could test the properties of thermal equilibrium because they emit radiation which is distributed thermally. Studying the laws of the black body historically led to quantum mechanics. Explanation Blackbody radiation is electromagnetic radiation in thermal equilibrium with a black body at a given temperature. Experimentally, it is established as the steady state equili- ________________________ WORLD TECHNOLOGIES ________________________ brium radiation in a rigid-walled cavity. There are no ideal (perfect) black bodies in nature, but graphite is a good approximation, and a closed box with graphite walls at a constant temperature gives a good approximation to an ideal black body. An object at temperature T emits radiation, which is a visible glow if T is high enough. The Draper point is the name given to the point at which all solids glow a dim red (about 798 K). A black body is an object that absorbs all light that falls on it, and emits light in a wave-length spectrum determined solely by its temperature. A black body can be approximated by, for example, an oven: a cavity surround by walls at temperature T and with a small opening through which light can enter and leave. At 1000 K, the opening in the oven looks red; at 6000 K, it looks white.
eBook - PDFAstrophysics Processes
The Physics of Astronomical Phenomena
- Hale Bradt(Author)
- 2008(Publication Date)
- Cambridge University Press(Publisher)
6 Blackbody radiation What we learn in this chapter A photon gas in perfect thermal equilibrium with its surroundings at some temperature T will exhibit an energy spectrum of a specific amplitude and shape known as the blackbody spectrum , which was first proposed by Max Planck in 1901. In its form as a specific intensity I ( n ) (W m − 2 Hz − 1 sr − 1 ), the blackbody spectrum peaks at a frequency proportional to its temperature. At low frequencies (the Rayleigh–Jeans approximation) , it increases linearly with temperature and quadratically with frequency. At high frequencies (the Wien approximation ), it decreases quasi-exponentially. The energy density , ∝ T 4 , and photon number density , ∝ T 3 , follow directly from I ( n ). The former is closely related to the pressure of a photon gas, whereas the latter is closely related to the distribution function , the density in six-dimensional phase space. Calculation of the average photon energy yields 2.70 kT . The total energy flux (W) passing in one direction through a unit surface is proportional to T 4 . A normal gaseous (spherical) star emits a spectrum that approximates (roughly) that of a blackbody, which allows the l uminosity to be expressed in terms of the stellar radius and an effective temperature . Momentum transfer by the photons to a hypothetical surface yields a pressure that is one-third the energy density. The blackbody flux is the maximum intensity that can be obtained from a thermal body. The universe is permeated by photons with a blackbody spectrum of temperature 2.73 K, the cosmic microwave background (CMB) radiation. In the expanding universe, this radiation cools adiabatically while maintaining the spectral shape and intensity of a blackbody . Its temperature scales inversely as the scale factor of the expansion. 6.1 Introduction Blackbody radiation pervades much of astrophysics.
- Stefano Spezia(Author)
- 2019(Publication Date)
- Arcler Press(Publisher)
SECTION I: BLACKBODY RADIATION, THE PHOTONS AND THE ELECTRONS EXACT RESEARCH ON THE THEORY OF THE BLACKBODY THERMAL RADIATION 1 CHAPTER CITATION : Yang, X. and Wei, B., “Exact research on the theory of the blackbody thermal radiation”, Scientific Reports (2016), https://doi.org/10.1038/srep37214 COPYRIGHT: © 2016 The Authors. Published by Macmillan Publishers Limited, part of Springer Nature. This is an open access article under the CC BY license (http://creativecom-mons.org/licenses/by/4.0). https://www.nature.com/articles/srep37214. XinYang 1,2 & BingWei 1,2 1 College of Physics and Optoelectronic Engineering, Xidian University, Shannxi, 710071, China. 2 Collaborative Innovation Center of Information Sensing and Understanding at Xidian University, Xi’an, 710071, China. ABSTRACT After studying the normalized Planck equation in depth, a brand-new type of spectrum curves of blackbody thermal radiation is given. Two important parameters of the new type curves, namely relative width RW η and symmetric Basic Quantum Mechanics for Electrical Engineering 4 factor RSF η , are defined. The paper points out that the experimental verification of the parameters has three significant applications: (1) Giving a method to measure temperature by detecting the radiation wavelength. (2) Determining the blackbody grade. (3) The temperature obtained from the law of the blackbody thermal radiation can be used as a criterion. INTRODUCTION It is well known that, over the past hundred years, the theoretical basis of the blackbody thermal radiation is expressed in the form of Planck’s law, given by1 , 2 , 3 , 4 (1) where C 1 = 3.7415 × 10 −4 W·μm 2 , C 2 = 1.4388 × 10 −4 μm 2 ·K. e b (λ, T) is the monochromatic radiant emittance of the blackbody at the temperature T(K) and radiation wavelength λ(μm ). For a given temperature, the e b (λ, T) and wavelength λ are related by the traditional spectrum curve of the blackbody thermal radiation5, as shown in Fig.
eBook - PDF- Frank Grum(Author)
- 2012(Publication Date)
- Academic Press(Publisher)
4 Blackbody Radiation 4.1 INTRODUCTION In this chapter we consider the angular and spectral characteristics of the radiant energy emitted by a blackbody. A blackbody is an ideal body which allows all incident radiant energy to pass into it so that all incident energy is absorbed and none is reflected. The definition of a blackbody requires that this be true at all wavelengths and at all angles of incidence. A blackbody is therefore a perfect absorber. As might be expected, the emission properties of a blackbody are related to its absorption properties. The important emission properties are (1) the blackbody is a perfect emitter at each angle and at each wavelength, and (2) the total radiant energy emitted by a blackbody (over all angles and wavelengths) is a function only of its temperature. The blackbody is a perfect emitter in the sense that it emits the maximum possible radiant energy for a body at that temperature. That these emission properties of a blackbody are a direct consequence of its absorption properties can be seen by considering Fig. 4.1 which shows a Fig. 4.1 Arrangement of blackbody inside black isothermal cavity to demonstrate emission properties of blackbody. 98 4.2 Angular Characteristics of Blackbody Radiation 99 small blackbody of arbitrary shape inside a black isothermal enclosure. At thermal equilibrium the blackbody must be at the same temperature as the enclosure. To maintain this temperature the small blackbody must emit as much radiant energy as it absorbs, and this must remain true when the angular orientation of the blackbody is changed or when the black enclosure is arranged to radiate and absorb only within a narrow wavelength interval. Furthermore when the enclosure temperature changes, the energy absorbed and emitted by the blackbody must change in a corresponding way to maintain thermal equilibrium.
eBook - ePubEnergy and Entropy
A Dynamic Duo
- Harvey S. Leff(Author)
- 2020(Publication Date)
- CRC Press(Publisher)
Herschel’s findings showed a relation between light waves and thermal phenomena, and called the light rays “calorific rays.” We now know that what he measured came from absorption of energy from electromagnetic radiation. The reason that Herschel found the highest temperature in the infrared region is that at Earth’s surface, more than half the energy of sunlight is in the infrared, with 40–45 percent in the visible region and about 5 percent in the ultraviolet. Herschel’s accidental discovery has led to the development of infrared technology including non-invasive measurements of body organs and temperature measurements of ocean temperatures and dust galaxies.In the mid 1850s, Balfour Stewart compared the intensity of radiation of lamp-black surfaces with radiation from other sources at the same temperature. He found that a material that is a good absorber is also a good emitter, and established that radiation takes place throughout a radiating body and not simply at its surface.3 Lamp-black surfaces had the greatest absorption of radiation, and also emitted the largest radiation intensity.A modern example of the connection between emission and absorption is a lightweight thermal blanket with a highly reflective metallic coating that absorbs little, i.e., it mainly reflects radiation. Such a blanket also emits relatively little radiation and is definitely not a blackbody. In 1859, Gustav Kirchhoff defined a blackbody as an object that is a perfect emitter and absorber of radiation. By the 1890s, experimentalists were attempting to measure the spectral energy distribution of radiating objects. Modern radiation detectors fall into three main categories: disappearing filament optical pyrometers, thermal detectors, and photon or quantum detectors.The mental construction of a model that leads to an example of blackbody radiation is straightforward. Imagine a solid with a cavity that opens through a small hole in the surface. It has temperature T, and the cavity emits blackbody radiation through the opening with an energy distribution matching that temperature. A suitable radiation-measuring device pointed at the opening can detect radiation with the blackbody radiation spectrum.5.3The Photon Gas5.3.1What is a photon gas? In order to generate radiation in a cavity, I introduce what is perhaps the simplest, yet scientifically richest gas: the photon gas. Its richness comes from at least four things:
eBook - PDF- Peter Coates, David Lowe(Authors)
- 2016(Publication Date)
- CRC Press(Publisher)
It was soon apparent that if accurate and reliable thermometry was to be achieved, a better theoretical understanding of the laws of thermal radiation was required. It eventually turned out that two topics were fundamental to the un-derstanding and practice of radiation thermometry – the concept of a black-body radiator, and the Planck radiation law. The first provides a reference against which the characteristics of real surfaces may be established, and which moreover may be used in the theoretical calculation of the underlying laws of emission and absorption of radiation. Planck’s law, which gives the spectral distribution of the intensity of the radiation from a black-body, is fundamental to the calculation of the perfor-mance of any radiation thermometer, whatever the wavelength region and range involved in its operation. Because of their importance, we shall spend some time in this chapter discussing the properties of black-bodies and the development and derivation of Planck’s law. The properties of real surfaces, on the other hand, will form the subject of the next chapter. 2.2 THE CONCEPT OF A BLACK-BODY RADIATOR It is possible to derive many of the essential relationships required in radiation thermometry from simple arguments based upon the laws of thermodynamics and the assumption of geometrical optics, that is, that thermal radiation is composed of rays, which in a uniform isotropic medium travel in straight lines. In this case, the wave properties of electromagnetic radiation are neglected or treated as a small correction to be applied to the relationships derived from geometrical optics. Also, it will usually be assumed that the radiation is unpolarised; this is not necessarily the case, and the possible effects of partially polarised radiation upon the performance and accuracy of different radiation thermometers will be discussed where relevant.
eBook - ePub- Mario Bertolotti(Author)
- 2004(Publication Date)
- CRC Press(Publisher)
CHAPTER 3BLACKBODY RADIATION
At the end of the 19th century, as we have seen, the conclusion was reached that light is an electromagnetic wave. However, at the same time at which the wave theory was gathering support, new phenomena were being discovered which contrasted with it. The study of the way in which a body absorbs or emits heat was among these phenomena. It was expected that the problem should attract a simple and immediate solution. However, this was not forthcoming, and when eventually it was found, it dealt the first blow to the wave theory of light.Radiation and temperature
If we touch a body with our hand we may feel, if it has a high temperature, a warm sensation. This is the same sensation we experience if we are nearby without touching it, because the heat is transmitted through the air. However, even if we remove all the air which surrounds the body, heat transmission still takes place.Today we know that the body transmits its heat, that is its energy, partly in the form of electromagnetic waves. The waves which transport the greatest part of the energy and are responsible for the warm sensation have the name of ‘infrared radiation’. They have wavelengths which span almost the entire range between a millimetre and a thousandth of millimetre (micron) and are invisible to our eyes. However, the energy transported by visible light from the Sun over millions of kilometres may also transform into heat, as is well known by those who in summer like to become tanned by the sun’s rays.Friedrich Wilhelm Herschel (1738–1822), who was born in Hanover and later naturalized English, demonstrated early in the 19th century the heating effect of infrared radiation, showing that it may increase the temperature of a body. The experimental detection of infrared radiation improved notably in 1881 when Samuel Pierpont Langley (1834–1906) invented the so-called ‘bolometer’, an instrument able to measure the temperature of a platinum wire which was blackened with carbon, through the change of its electrical resistance.
eBook - PDF- K. Ya. Kondrat'Yev(Author)
- 2013(Publication Date)
- Pergamon(Publisher)
The relation (1.34) is called Wien's displacement law. An examina-tion of this relation shows that it gives the displacement in wavelength of the intensity maximum of the perfect black body as a function of the temperature of the latter. Equation (1.35) points out that the maximum intensity of the perfect black body is proportional to the fifth power of absolute temperature. It should be pointed out 15 that it was recently suggested that the spectral distribution of intensity (or of flux) could be specified in the (Ε λ λ, In λ) or (E n n, In n) coordinates, where n = l/λ is the wave num-ber. The advantage of this method is that Ε λ λ = E n n and consequently, in this case, the spectral functions of wavelength or wave number are identical. (This identity does not hold for the usual specification in (Ε λ , λ) of (E n ,n) coordinates.) It should also be noted that the spectral distribution of the quantities Ε λ λ or E n n is identical with the spectral distribution of the function -^ which charac-b terizes the fraction of energy contained within the wave internal άλ. If the coordinate system (Ε λ λ, In λ) or (E n n, In n) is used, then Wien's constant a assumes the value 3668 cm. deg. In this case the radiation maximum T — 5500° K corresponds to the wavelength X m = 0.668 μ instead of X m = 0.527 μ for the coordinates (Ε λ , λ) or X m = 0.927 μ for the coordinates (E n , n). THERMAL RADIATION 15 Neither the earth's surface nor the atmosphere is a perfect black body. It is therefore impossible to make direct use of the equations obtained above for the calculation of the radiation of the earth's surface or the atmosphere. However, no substantial difficulties are encountered in calculating the radiative flux of the earth's surface since with a high degree of accuracy it can be considered as a grey body, i.e. it can be assumed that its absorbing and radiating proper-ties are independent of wavelength.
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