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Encyclopedia > Black body  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 term "black body" was introduced by Gustav Kirchhoff in 1860. The light emitted by a black body is called black-body radiation (or cavity radiation), and has a special place in the history of quantum mechanics. Gustav Robert Kirchhof (March 12, 1824 â€“ October 17, 1887) was a German physicist who contributed to the fundamental understanding of electrical circuits, spectroscopy, and the emission of black-body radiation by heated objects. ... 1860 is the leap year starting on Sunday. ... As the temperature decreases, the peak of the black body radiation curve moves to lower intensities and longer wavelengths. ... Niels Bohrâ€™s 1913 quantum model of the atom, which incorporated an explanation of Johannes Rydbergs 1888 formula, Max Planckâ€™s 1900 quantum hypothesis, i. ... The temperature of a Pahoehoe 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 radiance or observed intensity is not a function of direction. Therefore a black body is a perfect Lambertian radiator. 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 within a given solid angle in a specified direction. ... Lamberts cosine law says that the total radiant power observed from a Lambertian surface is directly proportional to the cosine of the angle Î¸ between the observers line of sight and the surface normal. ...

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. 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. The emissivity of a material (usually written ) is the ratio of energy radiated by the material to energy radiated by a black body at the same temperature. ...

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. Kirchhoffs law in thermodynamics, also called e. ...

## Equations governing black bodies

### Planck's law of black-body radiation $I(nu) = frac{2 hnu^{3}}{c^2}frac{1}{e^{frac{hnu}{kT}}-1}$

where In physics, the spectral intensity of electromagnetic radiation from a black body at temperature T is given by the Plancks law of black body radiation: where: I(&#957;) is the amount of energy per unit time per unit surface area per unit solid angle per unit frequency. ...

• $I(nu)dnu ,$ 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.

Area is the measure of how much exposed area any two dimensional object has. ... Look up time in Wiktionary, the free dictionary. ... A solid angle is the three dimensional analog of the ordinary angle. ... For other uses, see Temperature (disambiguation). ... A commemoration plaque for Max Planck on his discovery of Plancks constant, in front of Humboldt University, Berlin. ... The speed of light in a vacuum is an important physical constant denoted by the letter c for constant or the Latin word celeritas meaning swiftness. It is the speed of all electromagnetic radiation, including visible light, in a vacuum. ... The Boltzmann constant (k or kB) is the physical constant relating temperature to energy. ...

### 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 Wiens displacement law is a law of physics that states that there is an inverse relationship between the wavelength of the peak of the emission of a black body and its temperature. ... $T lambda_mathrm{max} = 2.898... times 10^6 mathrm{nm K}. ,$

The nanometer is a convenient unit of measure for optical wavelengths. Note that 1 nanometer is equivalent to 10−9 meters. A nanometre (American spelling: nanometer) is 1. ... For the book by Sir Isaac Newton, see Opticks. ... This article is about the unit of length. ...

### 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: The Stefan-Boltzmann law, also known as Stefans law, states that the total energy radiated per unit surface area of a black body in unit time (known variously as the black-body irradiance, energy flux density, radiant flux, or the emissive power), j*, is directly proportional to the fourth... For other uses, see Watt (disambiguation). ... A square metre (US spelling: square meter) is by definition the area enclosed by a square with sides each 1 metre long. ... For other uses, see Kelvin (disambiguation). ... The Stefan-Boltzmann constant (also Stefans constant), denoted with a Greek letter &#963;, is a derivable physical constant, the constant of proportionality between the total energy radiated per unit surface area of a black body in unit time and the fourth power of the thermodynamic temperature, as per the... $j^{star} = sigma T^4.,$

## Radiation emitted by a human body  Much of a person's energy is radiated away in the form of infrared energy. 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 to the infrared (note the man's eyeglasses).

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. Image File history File links Human-Visible. ... Image File history File links Human-Infrared. ... For other uses, see Infrared (disambiguation). ... For other uses, see Infrared (disambiguation). ...

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

Pnet = PemitPabsorb.

Applying the Stefan-Boltzmann law, $P_{net}=Asigma epsilon left( T^4 - T_{0}^4 right) ,$.

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. Skin temperature is about 33°C, but clothing reduces the surface temperature to about 28°C when the ambient temperature is 20°C. Hence, the net radiative heat loss is about The emissivity of a material (usually written ) is the ratio of energy radiated by the material to energy radiated by a black body at the same temperature. ... $P_{net} = 100 mathrm{W} ,$.

The total energy radiated in one day is about 9 MJ (million joules), or 2000 kcal (food calories). Basal metabolic rate for a 40-year-old male is about 35 kcal/(m²·h), which is equivalent to 1700 kcal per day assuming the same 2 m² area. However, the mean metabolic rate of sedentary adults is about 50% to 70% greater than their basal rate. The joule (IPA: or ) (symbol: J) is the SI unit of energy. ... Etymology: French calorie, from Latin calor (heat), from calere (to be warm). ... 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 is inactive, which requires about twelve hours of fasting in humans). ...

There are other important thermal loss mechanisms, including convection and evaporation. Conduction is negligible since the Nusselt number is much greater than unity. 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. 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. Convection in the most general terms refers to the movement of currents within fluids (i. ... â€œVaporizationâ€ redirects here. ... The Nusselt number is a dimensionless number which measures the enhancement of heat transfer from a surface which occurs in a real situation, compared to the heat transfer that would be measured if only conduction could occur. ... Perspiration (also called sweating or sometimes transpiration) is the production and evaporation of a fluid, consisting primarily of water as well as a smaller amount of sodium chloride (the main constituent of table salt), that is excreted by the sweat glands in the skin of mammals. ...

Also, applying Wien's Law to humans, one finds that the peak wavelength of light emitted by a person is Wiens displacement law is a law of physics that states that there is an inverse relationship between the wavelength of the peak of the emission of a black body and its temperature. ... $lambda_{peak} = frac{2.898times 10^6 mathrm{K} cdot mathrm{nm}}{305 mathrm{K}} = 9500 mathrm{nm} ,$.

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. See p. 380-382 of Planetary Science, for further discussion.

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

The surface temperature of a planet depends on a few factors: Image File history File links No higher resolution available. ... Image File history File links No higher resolution available. ... The Earth can be considered as a physical system with an energy budget that includes all gains of incoming energy and all losses of outgoing energy. ...

• Incident radiation (from the Sun, for example)
• Emitted radiation (for example Earth's infrared glow)
• The albedo effect (the fraction of light a planet reflects)
• The greenhouse effect (for planets with an atmosphere)
• Energy generated internally by a planet itself (This is more important for planets like Jupiter)

For the inner planets, incident and emitted radiation have the most significant impact on surface temperature. This derivation is concerned mainly with that. The Earth can be considered as a physical system with an energy budget that includes all gains of incoming energy and all losses of outgoing energy. ... For other uses, see Albedo (disambiguation). ... Wikinews has related news: Scientists warn thawing Siberia may trigger global meltdown A schematic representation of the exchanges of energy between outer space, the Earths atmosphere, and the Earth surface. ...

### Assumptions

If we assume the following:

1. The Sun and the Earth both radiate as spherical black bodies in thermal equilibrium with themselves.
2. 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. In thermodynamics, a thermodynamic system is in thermodynamic equilibrium if its energy distribution equals a Maxwell-Boltzmann-distribution. ...

### Derivation

To begin, we use the Stefan-Boltzmann law to find the total power (energy/second) the Sun is emitting: The Stefan-Boltzmann law, also known as Stefans law, states that the total energy radiated per unit surface area of a black body in unit time (known variously as the black-body irradiance, energy flux density, radiant flux, or the emissive power), j*, is directly proportional to the fourth... 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 a given unit of time. ... The Earth only has an absorbing area equal to a two dimensional circle, rather than the surface of a sphere. $P_{S emt} = left( sigma T_{S}^4 right) left( 4 pi R_{S}^2 right) qquad qquad (1)$
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 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: Image File history File links Sun-Earth-Radiation. ... The Stefan-Boltzmann law, also known as Stefans law, states that the total energy radiated per unit surface area of a black body in unit time (known variously as the black-body irradiance, energy flux density, radiant flux, or the emissive power), j*, is directly proportional to the fourth... $P_{E abs} = P_{S emt} left( frac{pi R_{E}^2}{4 pi D^2} right) qquad qquad (2)$
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.

In other words, 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. The average surface temperature of the earth is defined as the combined temperature of near-surface air temperature over land and sea surface temperature. ...

### 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 The effective temperature of a star is the temperature of a black body with the same luminosity (L) as the star and is defined according to the Stefan-Boltzman law L = sigma T_{eff}^{4}. The effective temperature of our Sun is around 5,800 kelvins (K) and correspond to... $T_{S} approx 5960 mathrm{K}.$

This is within three percent of the standard measure of 5778 kelvins which makes the formula valid for most scientific and engineering applications.

The effective temperature of a star is the temperature of a black body with the same luminosity (L) as the star and is defined according to the Stefan-Boltzman law L = sigma T_{eff}^{4}. The effective temperature of our Sun is around 5,800 kelvins (K) and correspond to... The CIE 1931 x,y chromaticity space, also showing the chromaticities of black-body light sources of various temperatures, and lines of constant correlated color temperature Color temperature is a characteristic of visible light that has important applications in photography, videography, publishing and other fields. ... Infrared thermometers offer a great method for accurately and quickly measuring temperature of objects at a distance and/or in motion. ... 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 thermal equilibrium will emit radiation with infinite power. ... Results from FactBites:

 Black body - Wikipedia, the free encyclopedia (1866 words) As the temperature decreases, the peak of the fl body radiation curve moves to lower intensities and longer wavelengths. In physics, a fl body is an object that absorbs all electromagnetic radiation that falls onto it. The hole then is a close approximation of a theoretical fl body and if the cavity is heated, the spectrum of the hole's radiation (i.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).
 Planck's law of black body radiation - Wikipedia, the free encyclopedia (1024 words) In physics, the spectral intensity of electromagnetic radiation from a fl body at temperature T is given by Planck's law of fl body radiation: At the time, Planck believed that the quantization applied only to the tiny oscillators that were thought to exist in the walls of the cavity (what we now know to be atoms), and made no assumption that light itself propagates in discrete bundles or packets of energy. Contrary to another myth, Planck did not derive his law in an attempt to resolve the "ultraviolet catastrophe", the name given to the paradoxical result that the total energy in the cavity tends to infinity when the equipartition theorem of classical statistical mechanics is applied to fl body radiation.
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