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(* = Graphable)

Hot metalwork from a blacksmith. The yellow-orange glow is the visible part of the thermal radiation emitted due to the high temperature. Everything else in the picture is glowing with thermal radiation, too, but less brightly and at longer wavelengths that our eyes cannot see. A far-infrared camera will show this radiation (See Thermography).
This diagram shows how the peak wavelength and total radiated amount vary with temperature. Although this plot shows relatively high temperatures, the same relationships hold true for any temperature down to absolute zero.

## Contents

There are three main properties that characterize thermal radiation:

• Thermal radiation, even at a single temperature, occurs at a wide range of frequencies. How much of each frequency is given by Planck’s law of radiation (for idealized materials). This is shown by the curves in the diagram at the right.
• The main frequency (or color) of the emitted radiation increases as the temperature increases. For example, a red hot object radiates most in the long wavelengths of the visible band, which is why it appears red. If it heats up further, the main frequency shifts to the middle of the visible band, and the spread of frequencies mentioned in the first point make it appear white. We then say the object is white hot. This is Wien's law. In the diagram the peak value for each curve moves to the left as the temperature increases.
• The total amount of radiation, of all frequencies, goes up very fast as the temperature rises (it grows as T4, where T is the absolute temperature of the body). An object at the temperature of a kitchen oven (about twice room temperature in absolute terms - 600 K vs. 300 K) radiates 16 times as much power per unit area. An object the temperature of the filament in an incandescent bulb (roughly 3000 K, or 10 times room temperature) radiates 10,000 times as much per unit area. Mathematically, the total power radiated rises as the fourth power of the absolute temperature, the Stefan-Boltzmann law. In the plot, the area under each curve rises rapidly as the temperature increases.

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. ... 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. ... 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...

## Interchange of energy

Radiant heat panel for testing precisely quantified energy exposures at National Research Council, near Ottawa, Ontario, Canada.

$alpha+rho+tau=1 ,$

Here, $alpha ,$ represents spectral absorption factor, $rho ,$ spectral reflection factor and $tau ,$ spectral transmission factor. All these elements depend also on the wavelength $lambda,$. The spectral absorption factor is equal to the emissivity $epsilon ,$; this relation is known as Kirchhoff's law of thermal radiation. An object is called a black body if, for all frequencies, the following fomula applies: 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. ... Kirchhoffs law in thermodynamics, also called e. ...

$alpha = epsilon =1,$

In a practical situation and room-temperature setting, objects lose considerable energy due to thermal radiation. However, the energy lost by emitting infrared heat is regained by absorbing the heat of surrounding objects. For example, a human being, roughly 2 square meter in area, and about 307 kelvins in temperature, continuously radiates about 1000 watts. However, if people are indoors, in a room of 296 K, they receive back about 900 watts from the wall, ceiling, and other surroundings, so the net loss is only about 100 watts. Clothes (having poorer thermal conductivity than human skin, therefore reducing the speed of heat loss from the human body to surrounding environment) reduce this loss still further. For other uses, see Infrared (disambiguation). ... For other uses, see Kelvin (disambiguation). ...

If objects appear white (reflective in the visual spectrum), they are not necessarily equally reflective (and thus non-emissive) in the thermal infrared; e. g. most household radiators are painted white despite the fact that they have to be good thermal radiators. Acrylic and urethane based white paints have 93% blackbody radiation efficiency at room temperature (meaning the term "black body" does not always correspond to the visually perceived color of an object). The optical spectrum (light or visible spectrum) is the portion of the electromagnetic spectrum that is visible to the human eye. ...

## Formula

Thermal radiation power of a black body per unit of area, unit of solid angle and unit of frequency ν is given by This article is about the physical quantity. ... A solid angle is the three dimensional analog of the ordinary angle. ... For other uses, see Frequency (disambiguation). ...

$u(nu,T)=frac{2 hnu^3}{c^2}cdotfrac1{e^frac{hnu}{k_BT}-1}$

This formula mathematically follows from calculation of spectral distribution of energy in quantized electromagnetic field which is in complete thermal equilibrium with the radiating object. Generally, quantization is the state of being constrained to a set of discrete values, rather than varying continuously. ... In thermodynamics, a thermodynamic system is in thermodynamic equilibrium if its energy distribution equals a Maxwell-Boltzmann-distribution. ...

Integrating the above equation over ν the power output given by the Stefan-Boltzmann law is obtained, as: 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...

$W = sigma cdot A cdot T^4$

Further, the wavelength $lambda ,$, for which the emission intensity is highest, is given by Wien's Law as: 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. ...

$lambda_{max} = frac{b}{T}$

For surfaces which are not black bodies, one has to consider the (generally frequency dependent) emissivity correction factor ε(υ). This correction factor has to be multiplied with the radiation spectrum formula before integration. The resulting formula for the power output can be written in a way that contains a temperature dependent correction factor which is (somewhat confusingly) often called ε as well:

$W = epsilon(T) cdot sigma cdot A cdot T^4$

### Constants

Definitions of constants used in the above equations:

 $h ,$ Planck's constant 6.626 0693(11)×10-34 J·s = 4.135 667 43(35)×10-15 eV·s $b ,$ Wien's displacement constant 2.897 7685(51)×10–3 m·K $k_B ,$ Boltzmann constant 1.380 6505(24)×10−23 J·K-1 = 8.617 343(15)×10−5 eV·K-1 $sigma ,$ Stefan-Boltzmann constant 5.670 400(40)×10−8 W·m-2·K-4 $c ,$ Speed of light 299,792,458 m·s-1 $T ,$ Temperature Average surface temperature on Earth = 288 K $A ,$ Surface area Acuboid = 2ab + 2bc + 2ac; Acylinder = 2π·r(h + r); Asphere = 4π·r2

A commemoration plaque for Max Planck on his discovery of Plancks constant, in front of Humboldt University, Berlin. ... 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. ... The Boltzmann constant (k or kB) is the physical constant relating temperature to energy. ... 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... 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.[1] It is the speed of all electromagnetic radiation, including visible light, in a vacuum. ... For other uses, see Temperature (disambiguation). ... This article is about the physical quantity. ...

Results from FactBites:

 Night Vision, Objective Lens, Image Intensifier, Fibro Optic, Night Vision Photography, How Night Vision Works (0 words) Thermal images are normally fl and white in nature, where fl objects are cold and white objects are hot. In this method, a device that is sensitive to invisible near infrared radiation is used in conjunction with an infrared illuminator. Infrared radiation spans the wavelengths between approximately 750 nm (0.75 microns) and 1 mm (1000 microns).
 CRR 285/2000 Thermal radiation criteria for vulnerable popu... (97 words) CRR 285/2000 Thermal radiation criteria for vulnerable popu... The many factors that affect human response are considered, and the differences between the response of children and the elderly to those of an 'average' population are identified. Concludes that existing dangerous dose criterion for thermal radiation for vulnerable populations is reasonable.
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