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As the temperature decreases, the peak of the black-body radiation curve moves to lower intensities and longer wavelengths. The black-body radiation graph is also compared with the classical model of Rayleigh and Jeans.
As the temperature decreases, the peak of the black-body radiation curve moves to lower intensities and longer wavelengths. The black-body radiation graph is also compared with the classical model of Rayleigh and Jeans.
The color (chromaticity) of black-body radiation depends on the temperature of the black body; the locus of such colors, shown here in CIE 1931 x,y space, is known as the Planckian locus.
The color (chromaticity) of black-body radiation depends on the temperature of the black body; the locus of such colors, shown here in CIE 1931 x,y space, is known as the Planckian locus. Chromaticity is an objective specification of the Quality of a Color regardless of its luminance that is as determined by its Colorfulness (or saturation In Mathematics, a locus ( Latin for "place" plural loci) is a collection of points which share a property In the study of the perception of Color, one of the first mathematically defined Color spaces was the CIE 1931 XYZ color space (also known as CIE 1931 color space In Color theory, the Planckian locus is generally the path or ''locus'' that the color of a Black body would take ina particular Color space

In physics, a black body is an object that absorbs all light that falls on it. Physics (Greek Physis - φύσις in everyday terms is the Science of Matter and its motion. In Physics, a physical body (sometimes called simply a body or even an object) is a collection of Masses taken to be one Electromagnetic radiation takes the form of self-propagating Waves in a Vacuum or in Matter. No electromagnetic radiation passes through it and none is reflected. Reflection is the change in direction of a Wave front at an interface between two different media so that the wave front returns into the medium from which Because no light is reflected or transmitted, the object appears black when it is cold.

If the black body is hot, these properties make it an ideal source of thermal radiation. Thermal radiation is Electromagnetic radiation emitted from the surface of an object which is due to the object's Temperature. If a perfect black body at a certain temperature is surrounded by other objects in thermal equilibrium at the same temperature, it will on average emit exactly as much as it absorbs, at every wavelength. In Thermodynamics, a thermodynamic system is said to be in thermodynamic equilibrium when it is in thermal equilibrium Mechanical equilibrium, and Since the absorption is easy to understand—every ray that hits the body is absorbed—the emission is just as easy to understand.

A black body at temperature T emits exactly the same wavelengths and intensities which would be present in an environment at equilibrium at temperature T, and which would be absorbed by the body. Since the radiation in such an environment has a spectrum that depends only on temperature, the temperature of the object is directly related to the wavelengths of the light that it emits. At room temperature, black bodies emit infrared light, but as the temperature increases past a few hundred degrees Celsius, black bodies start to emit at visible wavelengths, from red, through orange, yellow, and white before ending up at blue, beyond which the emission includes increasing amounts of ultraviolet. Infrared ( IR) radiation is Electromagnetic radiation whose Wavelength is longer than that of Visible light, but shorter than that of The Celsius Temperature scale was previously known as the centigrade scale. Ultraviolet ( UV) light is Electromagnetic radiation with a Wavelength shorter than that of Visible light, but longer than X-rays

The term "black body" was introduced by Gustav Kirchhoff in 1860. Gustav Robert Kirchhoff ( March 12, 1824 &ndash October 17, 1887) was a German Physicist who contributed to the fundamental Year 1860 ( MDCCLX) was a Leap year starting on Sunday (link will display the full calendar of the Gregorian Calendar (or a Leap year starting The light emitted by a black body is called black-body radiation. [1]

If a small window is opened into an oven, any light that enters the window has a very low probability of leaving without being absorbed. Conversely, the hole acts as a nearly ideal black-body radiator. This makes peepholes into furnaces good sources of blackbody radiation, and some people call it cavity radiation for this reason.

Black-body 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, leading to the nonsense prediction that there would be an infinite amount of energy in any continuous field. In Mathematics, a Fourier series decomposes a periodic function into a sum of simple oscillating functions In classical Statistical mechanics, the equipartition theorem is a general formula that relates the Temperature of a system with its average energies The ultraviolet catastrophe, also called the Rayleigh-Jeans catastrophe was a prediction of early 20th century Classical physics that an ideal Black body at 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. The history of Quantum mechanics as this interlaces with history of Quantum chemistry began essentially with the 1838 discovery of Cathode rays

Contents

Explanation

In the laboratory, black-body radiation is approximated by the radiation from a small hole entrance to a large cavity, a hohlraum. In Radiation Thermodynamics, a hohlraum (a German Loanword, originally a non-specific word for "hollow area" or "cavity" Any light entering the hole would have to reflect off the walls of the cavity multiple times before it escaped, in which process it is nearly certain to be absorbed. This occurs regardless of the wavelength of the radiation entering (as long as it is small compared to the hole). In Physics wavelength is the distance between repeating units of a propagating Wave of a given Frequency. The hole, then, is a close approximation of a theoretical black body and, if the cavity is heated, the spectrum of the hole's radiation (i. In Statistical signal processing and Physics, the spectral density, power spectral density ( PSD) or energy spectral density ( e. , the amount of light emitted from the hole at each wavelength) will be continuous, and will not depend on the material in the cavity (compare with emission spectrum). In Physics wavelength is the distance between repeating units of a propagating Wave of a given Frequency. An element's 'emission spectrum' is the relative intensity of Electromagnetic radiation of each Frequency it emits when it is Heated (or more generally when By a theorem proved by Kirchhoff, this curve depends only on the temperature of the cavity walls. See also Kirchhoff's laws for other laws named after Kirchhoff. Temperature is a physical property of a system that underlies the common notions of hot and cold something that is hotter generally has the greater temperature [2]

Calculating this curve was a major challenge in theoretical physics during the late nineteenth century. The problem was finally solved in 1901 by Max Planck as Planck's law of black-body radiation. For a general introduction see Black body. In Physics, Planck's law describes the spectral radiance of Electromagnetic radiation [3] By making changes to Wien's Radiation Law (not to be confused with Wien's displacement law) consistent with thermodynamics and electromagnetism, he found a mathematical formula fitting the experimental data in a satisfactory way. Wien's approximation (also sometimes called Wien's law or the Wien distribution law) is a law of Physics used to describe the Spectrum In Physics, thermodynamics (from the Greek θερμη therme meaning " Heat " and δυναμις dynamis meaning " Electromagnetism is the Physics of the Electromagnetic field: a field which exerts a Force on particles that possess the property of To find a physical interpretation for this formula, Planck had then to assume that the energy of the oscillators in the cavity was quantized (i. e. , integer multiples of some quantity). Einstein built on this idea and proposed the quantization of electromagnetic radiation itself in 1905 to explain the photoelectric effect. Albert Einstein ( German: ˈalbɐt ˈaɪ̯nʃtaɪ̯n; English: ˈælbɝt ˈaɪnstaɪn (14 March 1879 – 18 April 1955 was a German -born theoretical Introduction When a Metallic surface is exposed to Electromagnetic radiation above a certain threshold Frequency, the light is absorbed and Electrons These theoretical advances eventually resulted in the superseding of classical electromagnetism by quantum electrodynamics. Quantum electrodynamics ( QED) is a relativistic Quantum field theory of Electrodynamics. Today, these quanta are called photons and the black-body cavity may be thought of as containing a gas of photons. In Physics, the photon is the Elementary particle responsible for electromagnetic phenomena In physics a photon gas is a Gas -like collection of Photons which has many of the same properties of a conventional gas like Hydrogen or Neon In addition, it led to the development of quantum probability distributions, called Fermi-Dirac statistics and Bose-Einstein statistics, each applicable to a different class of particle, which are used in quantum mechanics instead of the classical distributions. In Statistical mechanics, Fermi-Dirac statistics is a particular case of Particle statistics developed by Enrico Fermi and Paul Dirac that In Statistical mechanics, Bose - Einstein statistics (or more colloquially B-E statistics determines the statistical distribution of See also fermion and boson. In Particle physics, fermions are particles which obey Fermi-Dirac statistics; they are named after Enrico Fermi. In Particle physics, bosons are particles which obey Bose-Einstein statistics; they are named after Satyendra Nath Bose and Albert Einstein

The temperature of a Pāhoehoe lava flow can be estimated by observing its color. The result agrees well with the measured temperatures of lava flows at about 1,000 to 1,200 °C.
The temperature of a Pāhoehoe lava flow can be estimated by observing its color. Lava is molten rock expelled by a Volcano during an eruption When first expelled from a volcanic vent it is a Liquid at Temperatures The result agrees well with the measured temperatures of lava flows at about 1,000 to 1,200 °C.

The wavelength at which the radiation is strongest is given by Wien's displacement law, and the overall power emitted per unit area is given by the Stefan-Boltzmann law. The Stefan–Boltzmann law, also known as Stefan's law, states that the total Energy radiated per unit surface Area of a Black body in unit So, as temperature increases, the glow color changes from red to yellow to white to blue. Even as the peak wavelength moves into the ultra-violet, enough radiation continues to be emitted in the blue wavelengths that the body will continue to appear blue. It will never become invisible — indeed, the radiation of visible light increases monotonically with temperature. [4]

The radiance or observed intensity is not a function of direction. Radiance and spectral radiance are radiometric measures that describe the amount of light that passes through or is emitted from a particular area and falls Therefore a black body is a perfect Lambertian radiator. See also Lambertian reflectance Lambert's cosine law in Optics says that the Radiant intensity observed from a " Lambertian "

Real objects never behave as full-ideal black bodies, and instead the emitted radiation at a given frequency is a fraction of what the ideal emission would be. The emissivity of a material specifies how well a real body radiates energy as compared with a black body. The emissivity of a material (usually written \epsilon is the ratio of energy radiated by a particular material to energy radiated by a Black body at This emissivity depends on factors such as temperature, emission angle, and wavelength. However, it is typical in engineering to assume that a surface's spectral emissivity and absorptivity do not depend on wavelength, so that the emissivity is a constant. This is known as the grey body assumption.

Although Planck's formula predicts that a black body will radiate energy at all frequencies, the formula is only applicable when many photons are being measured. For example, a black body at room temperature (300 K) with one square meter of surface area will emit a photon in the visible range once every thousand years or so, meaning that for most practical purposes, the black body does not emit in the visible range.

When dealing with non-black surfaces, the deviations from ideal black-body behavior are determined by both the geometrical structure and the chemical composition, and follow Kirchhoff's Law: emissivity equals absorptivity, so that an object that does not absorb all incident light will also emit less radiation than an ideal black body. See also Kirchhoff's laws for other laws named after Kirchhoff.

WMAP image of the cosmic microwave background radiation anisotropy. It has the most perfect thermal emission spectrum known and corresponds to a temperature of 2.725 kelvin (K) with an emission peak at 160.2 GHz.
WMAP image of the cosmic microwave background radiation anisotropy. Anisotropy (pronounced with stress on the third syllable ˌænaɪˈsɒtrəpi is the property of being directionally dependent as opposed to Isotropy, which means homogeneity It has the most perfect thermal emission spectrum known and corresponds to a temperature of 2. Thermal radiation is Electromagnetic radiation emitted from the surface of an object which is due to the object's Temperature. 725 kelvin (K) with an emission peak at 160. The kelvin (symbol K) is a unit increment of Temperature and is one of the seven SI base units The Kelvin scale is a thermodynamic 2 GHz. The hertz (symbol Hz) is a measure of Frequency, informally defined as the number of events occurring per Second.

In astronomy, objects such as stars are frequently regarded as black bodies, though this is often a poor approximation. Astronomy (from the Greek words astron (ἄστρον "star" and nomos (νόμος "law" is the scientific study A star is a massive luminous ball of plasma. The nearest star to Earth is the Sun, which is the source of most of the Energy on Earth An almost perfect black-body spectrum is exhibited by the cosmic microwave background radiation. Hawking radiation is black-body radiation emitted by black holes. Hawking radiation (also known as Bekenstein-Hawking radiation) is a Thermal radiation with a black body spectrum predicted to be emitted by Black holes A black hole is a theoretical region of space in which the Gravitational field is so powerful that nothing not even Electromagnetic radiation (e

Equations governing black bodies

Planck's law of black-body radiation

Main article: Planck's law
I(\nu)d\nu = \frac{2 h\nu^{3}}{c^2}\frac{1}{e^{\frac{h\nu}{kT}}-1}\, d\nu

where

  • I(\nu)d\nu \, is the amount of energy per unit surface area per unit time per unit solid angle emitted in the frequency range between ν and ν+dν;
  • T \, is the temperature of the black body;
  • h \, is Planck's constant;
  • c \, is the speed of light; and
  • k \, is Boltzmann's constant. For a general introduction see Black body. In Physics, Planck's law describes the spectral radiance of Electromagnetic radiation In Physics and other Sciences energy (from the Greek grc ἐνέργεια - Energeia, "activity operation" from grc ἐνεργός Surface area is the measure of how much exposed Area an object has For other uses see Time (disambiguation Time is a component of a measuring system used to sequence events to compare the durations of The solid angle, Ω, is the angle in three-dimensional space that an object Subtends at a point Temperature is a physical property of a system that underlies the common notions of hot and cold something that is hotter generally has the greater temperature The Planck constant (denoted h\ is a Physical constant used to describe the sizes of quanta. Bridge from macroscopic to microscopic physics Boltzmann's constant k is a bridge between Macroscopic and microscopic physics

Wien's displacement law

Main article: Wien's displacement law

The relationship between the temperature T of a black body, and wavelength λmax at which the intensity of the radiation it produces is at a maximum is

  • T \lambda_\mathrm{max} = 2.898... \times 10^6 \ \mathrm{nm \ K}. \,

The nanometer is a convenient unit of measure for optical wavelengths. A nanometre ( American spelling: nanometer, symbol nm) ( Greek: νάνος nanos dwarf; μετρώ metrό count) is a Note that 1 nanometer is equivalent to 10−9 meters. The metre or meter is a unit of Length. It is the basic unit of Length in the Metric system and in the International

Stefan–Boltzmann law

Main article: Stefan–Boltzmann law

The total energy radiated per unit area per unit time j^{\star} (in watts per square meter) by a black body is related to its temperature T (in kelvins) and the Stefan–Boltzmann constant σ as follows:

j^{\star} = \sigma T^4.\,

Radiation emitted by a human body

Much of a person's energy is radiated away in the form of infrared energy. The Stefan–Boltzmann law, also known as Stefan's law, states that the total Energy radiated per unit surface Area of a Black body in unit The watt (symbol W) is the SI derived unit of power, equal to one Joule of energy per Second. M^2 redirects here For other uses see M². CM2 redirects here The kelvin (symbol K) is a unit increment of Temperature and is one of the seven SI base units The Kelvin scale is a thermodynamic The Stefan–Boltzmann constant (also Stefan's constant) a Physical constant denoted by the Greek letter σ, is the Constant of proportionality Infrared ( IR) radiation is Electromagnetic radiation whose Wavelength is longer than that of Visible light, but shorter than that of Some materials are transparent to infrared light, while opaque to visible light (note the plastic bag). Other materials are transparent to visible light, while opaque or reflective to the infrared (note the man's glasses).

Black-body laws can be applied to human beings. For example, some of a person's energy is radiated away in the form of electromagnetic radiation, most of which is infrared. Infrared ( IR) radiation is Electromagnetic radiation whose Wavelength is longer than that of Visible light, but shorter than that of

The net power radiated is the difference between the power emitted and the power absorbed:

Pnet = Pemit − Pabsorb.

Applying the Stefan–Boltzmann law,

P_{net}=A\sigma \epsilon \left( T^4 - T_{0}^4 \right) \,.

The total surface area of an adult is about 2 m², and the mid- and far-infrared emissivity of skin and most clothing is near unity, as it is for most nonmetallic surfaces. The emissivity of a material (usually written \epsilon is the ratio of energy radiated by a particular material to energy radiated by a Black body at [5][6] Skin temperature is about 33°C,[7] but clothing reduces the surface temperature to about 28°C when the ambient temperature is 20°C. [8] Hence, the net radiative heat loss is about

P_{net} = 100 \ \mathrm{W} \,.

The total energy radiated in one day is about 9 MJ (Mega joules), or 2000 kcal (food calories). The joule (written in lower case ˈdʒuːl or /ˈdʒaʊl/ (symbol J) is the SI unit of Energy measuring heat, Electricity This article is about the unit of energy For its use in Nutrition and Food labelling regulations, see the article on Food energy. Basal metabolic rate for a 40-year-old male is about 35 kcal/(m²·h),[9] which is equivalent to 1700 kcal per day assuming the same 2 m² area. Basal metabolic rate ( BMR) is the amount of energy expended while at rest in a neutrally temperate environment in the post-absorptive state (meaning that the digestive system However, the mean metabolic rate of sedentary adults is about 50% to 70% greater than their basal rate. [10]

There are other important thermal loss mechanisms, including convection and evaporation. Convection in the most general terms refers to the movement of molecules within Fluids (i Evaporation is the process by which Molecules in a Liquid state (e Conduction is negligible since the Nusselt number is much greater than unity. In Heat transfer at a boundary (surface within a Fluid, the Nusselt number is the ratio of convective to conductive heat transfer Evaporation (perspiration) is only required if radiation and convection are insufficient to maintain a steady state temperature. Free convection rates are comparable, albeit somewhat lower, than radiative rates. [11] Thus, radiation accounts for about 2/3 of thermal energy loss in cool, still air. Given the approximate nature of many of the assumptions, this can only be taken as a crude estimate. Ambient air motion, causing forced convection, or evaporation reduces the relative importance of radiation as a thermal loss mechanism.

Also, applying Wien's Law to humans, one finds that the peak wavelength of light emitted by a person is

\lambda_{peak} = \frac{2.898\times 10^6 \ \mathrm{K} \cdot \mathrm{nm}}{305 \ \mathrm{K}} = 9500 \ \mathrm{nm} \,.

This is why thermal imaging devices designed for human subjects are most sensitive to 7–14 micrometers wavelength.

Temperature relation between a planet and its star

Here is an application of black-body laws. It is a rough derivation that gives an order of magnitude answer. The actual Earth is warmer due to the greenhouse effect. The Greenhouse effect refers to the change in the Thermal equilibrium temperature of a planet or moon by the presence of an Atmosphere containing gas that absorbs [12]

Factors

Earth's longwave thermal radiation intensity, from clouds, atmosphere and ground
Earth's longwave thermal radiation intensity, from clouds, atmosphere and ground

The surface temperature of a planet depends on a few factors:

For the inner planets, incident and emitted radiation have the most significant impact on surface temperature. This derivation is concerned mainly with that.

Assumptions

If we assume the following:

  1. The Sun and the Earth both radiate as spherical black bodies.
  2. The Earth is in thermal equilibrium. In Thermodynamics, a thermodynamic system is said to be in thermodynamic equilibrium when it is in thermal equilibrium Mechanical equilibrium, and
  3. The Earth absorbs all the solar energy that it intercepts from the Sun.

then we can derive a formula for the relationship between the Earth's surface temperature and the Sun's surface temperature.

Derivation

To begin, we use the Stefan–Boltzmann law to find the total power (energy/second) the Sun is emitting:

The Earth only has an absorbing area equal to a two dimensional circle, rather than the surface of a sphere.
The Earth only has an absorbing area equal to a two dimensional circle, rather than the surface of a sphere. The Stefan–Boltzmann law, also known as Stefan's law, states that the total Energy radiated per unit surface Area of a Black body in unit In Physics, power (symbol P) is the rate at which work is performed or energy is transmitted or the amount of energy required or expended for
P_{S emt} = \left( \sigma T_{S}^4 \right) \left( 4 \pi R_{S}^2 \right) \qquad \qquad (1)
where
\sigma \, is the Stefan–boltzmann constant,
T_S \, is the surface temperature of the Sun, and
R_S \, is the radius of the Sun. The Stefan–Boltzmann law, also known as Stefan's law, states that the total Energy radiated per unit surface Area of a Black body in unit

The Sun emits that power equally in all directions. Because of this, the Earth is hit with only a tiny fraction of it. This is the power from the Sun that the Earth absorbs:

P_{E abs} = P_{S emt} \left( \frac{\pi R_{E}^2}{4 \pi D^2} \right) \qquad \qquad (2)
where
R_{E} \, is the radius of the Earth and
D \, is the distance between the Sun and the Earth.

Even though the earth only absorbs as a circular area πR2, it emits equally in all directions as a sphere:

P_{E emt} = \left( \sigma T_{E}^4 \right) \left( 4 \pi R_{E}^2 \right) \qquad \qquad (3)
where TE is the surface temperature of the earth.

Now, in the first assumption the earth is in thermal equilibrium, so the power absorbed must equal the power emitted:

P_{E abs} = P_{E emt}\,
So plug in equations 1, 2, and 3 into this and we get
\left( \sigma T_{S}^4 \right) \left( 4 \pi R_{S}^2 \right) \left( \frac{\pi R_{E}^2}{4 \pi D^2} \right) = \left( \sigma T_{E}^4 \right) \left( 4 \pi R_{E}^2 \right).\,

Many factors cancel from both sides and this equation can be greatly simplified.

The result

After canceling of factors, the final result is

T_{S}\sqrt{\frac{R_{S}}{2 D}} = T_{E}
where
T_S \, is the surface temperature of the Sun,
R_S \, is the radius of the Sun,
D \, is the distance between the Sun and the Earth, and
T_E \, is the average surface temperature of the Earth. See also Temperature record. The instrumental temperature record shows the fluctuations of the Temperature of the atmosphere and the oceans as

In other words, given the assumptions made, the temperature of the Earth depends only on the surface temperature of the Sun, the radius of the Sun, and the distance between the Earth and the Sun.

Temperature of the Sun

If we substitute in the measured values for Earth,

T_{E} \approx 14 \ \mathrm{{}^\circ C} = 287 \ \mathrm{K},
R_{S} = 6.96 \times 10^8 \ \mathrm{m},
D = 1.5 \times 10^{11} \ \mathrm{m},

we'll find the effective temperature of the Sun to be

T_{S} \approx 5960 \ \mathrm{K}.

This is within three percent of the standard measure of 5780 kelvins which makes the formula valid for most scientific and engineering applications. Star The effective temperature of a Star is the temperature of a Black body with the same luminosity per surface area (\mathcal{F}_{Bol}

Doppler effect for a moving blackbody

The Doppler effect is the well known phenomenon describing how observed frequencies of light are "shifted" when a light source is moving relative to the observer. The Doppler effect (or Doppler shift) named after Christian Doppler, is the change in Frequency and Wavelength of a Wave for If f is the emitted frequency of a monochromatic light source, it will appear to have frequency f' if it is moving relative to the observer :

f' = f \frac{1}{\sqrt{1-v^2/c^2}} (1 - \frac{v}{c} \cos \theta)

where v is the velocity of the source in the observer's rest frame, θ is the angle between the velocity vector and the observer-source direction, and c is the speed of light. [13] This is the fully relativistic formula, and can be simplified for the special cases of objects moving directly towards ( θ = π) or away ( θ = 0) from the observer, and for speeds much less than c.

To calculate the spectrum of a moving blackbody, then, it seems straightforward to simply apply this formula to each frequency of the blackbody spectrum. However, simply scaling each frequency like this is not enough. We also have to account for the finite size of the viewing aperture, because the solid angle receiving the light also undergoes a Lorentz transformation. In Physics, the Lorentz transformation converts between two different observers' measurements of space and time where one observer is in constant motion with respect to (We can subsequently allow the aperture to be arbitrarily small, and the source arbitrarily far, but this cannot be ignored at the outset. ) When this effect is included, it is found that a blackbody at temperature T that is receding with velocity v appears to have a spectrum identical to a stationary blackbody at temperature T' , given by: [14]

T' = T \frac{1}{\sqrt{1-v^2/c^2}} (1 - \frac{v}{c} \cos \theta)


For the case of a source moving directly towards or away from the observer, this reduces to


T' = T \sqrt{\frac{c-v}{c+v}}

Here v > 0 indicates a receding source, and v < 0 indicates an approaching source.

This is an important effect in astronomy, where the velocities of stars and galaxies can reach significant fractions of c. An example is found in the cosmic microwave background radiation, which exhibits a dipole anisotropy from the Earth's motion relative to this blackbody radiation field.

See also

References

  1. ^ When used as a compound adjective, the term is typically hyphenated, as in "black-body radiation", or combined into one word, as in "blackbody radiation". Star The effective temperature of a Star is the temperature of a Black body with the same luminosity per surface area (\mathcal{F}_{Bol} Color temperature is a characteristic of Visible light that has important applications in lighting photography videography publishing and other fields Infrared thermometers measure Temperature using Blackbody radiation (generally Infrared) emitted from objects Photon polarization is the quantum mechanical description of the classical polarized sinusoidal plane electromagnetic wave The ultraviolet catastrophe, also called the Rayleigh-Jeans catastrophe was a prediction of early 20th century Classical physics that an ideal Black body at In Physics, the Rayleigh–Jeans Law, first proposed in the early 20th century attempts to describe the Spectral radiance of Electromagnetic radiation A compound modifier (also called a compound adjective or a phrasal adjective) is an adjectival or adverbial phrase of two or more words The hyphenated and one-word forms should not generally be used as nouns.
  2. ^ Huang, Kerson (1967). Statistical Mechanics. New York: John Wiley & Sons.  
  3. ^ Planck, Max (1901). "On the Law of Distribution of Energy in the Normal Spectrum" (HTML). Annalen der Physik 4: 553. Annalen der Physik is one of the best-known and oldest (since 1790 Physics journals worldwide  
  4. ^ Landau, L. D. ; E. M. Lifshitz (1996). Statistical Physics, 3rd Edition Part 1, Oxford: Butterworth-Heinemann.  
  5. ^ Infrared Services. Emissivity Values for Common Materials. Retrieved on 2007-06-24. Year 2007 ( MMVII) was a Common year starting on Monday of the Gregorian calendar in the 21st century. Events 972 - Battle of Cedynia, the first documented victory of Polish forces takes place
  6. ^ Omega Engineering. Emissivity of Common Materials. Retrieved on 2007-06-24. Year 2007 ( MMVII) was a Common year starting on Monday of the Gregorian calendar in the 21st century. Events 972 - Battle of Cedynia, the first documented victory of Polish forces takes place
  7. ^ Farzana, Abanty (2001). Temperature of a Healthy Human (Skin Temperature). The Physics Factbook. Retrieved on 2007-06-24. Year 2007 ( MMVII) was a Common year starting on Monday of the Gregorian calendar in the 21st century. Events 972 - Battle of Cedynia, the first documented victory of Polish forces takes place
  8. ^ Lee, B. . Theoretical Prediction and Measurement of the Fabric Surface Apparent Temperature in a Simulated Man/Fabric/Environment System. Retrieved on 2007-06-24. Year 2007 ( MMVII) was a Common year starting on Monday of the Gregorian calendar in the 21st century. Events 972 - Battle of Cedynia, the first documented victory of Polish forces takes place
  9. ^ Harris J, Benedict F (1918). "A Biometric Study of Human Basal Metabolism. ". Proc Natl Acad Sci U S A 4 (12): 370–3. doi:10.1073/pnas.4.12.370. A digital object identifier ( DOI) is a permanent identifier given to an Electronic document. PMID 16576330.  
  10. ^ Levine, J (2004). "Nonexercise activity thermogenesis (NEAT): environment and biology". Am J Physiol Endocrinol Metab 286: E675–E685. doi:10.1152/ajpendo.00562.2003. A digital object identifier ( DOI) is a permanent identifier given to an Electronic document.  
  11. ^ DrPhysics. com. Heat Transfer and the Human Body. Retrieved on 2007-06-24. Year 2007 ( MMVII) was a Common year starting on Monday of the Gregorian calendar in the 21st century. Events 972 - Battle of Cedynia, the first documented victory of Polish forces takes place
  12. ^ Cole, George H. A. ; Woolfson, Michael M. (2002). Planetary Science: The Science of Planets Around Stars (1st ed.). Institute of Physics Publishing, 36–37, 380–382. ISBN 0-7503-0815-X.  
  13. ^ The Doppler Effect, T. P. Gill, Logos Press, 1965
  14. ^ McKinley, John M. , "Relativistic transformations of light power", Am. J. Phys. 47 (7), Jul 1979

Other textbooks

External links

Dictionary

black body

-noun

  1. (physics) alternative spelling of blackbody
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