Thermal radiation

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 as well, but less brightly and at longer wavelengths that the human eye 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. Visible light is between 380 to 750 nm.

Thermal radiation is electromagnetic radiation emitted from the surface of an object which is due to the object's temperature. An example of thermal radiation is the infrared radiation emitted by a common household radiator or electric heater. A person near a raging bonfire will feel the radiated heat of the fire, even if the surrounding air is very cold. Thermal radiation is generated when heat from the movement of charged particles within atoms is converted to electromagnetic radiation. Solar radiation heats the earth during the day, while at night the earth re-radiates some heat back into space.

If the object is a black body in thermodynamic equilibrium, the radiation is termed black-body radiation^[1]. The emitted wave frequency of the black body thermal radiation is described by a probability distribution depending only on temperature, and for a genuine black body in thermodynamic equilibrium is given by Planck’s law of radiation. Wien's law gives the most likely frequency of the emitted radiation, and the Stefan–Boltzmann law gives the radiant intensity.^[2]

Properties

There are four 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 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 displacement 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 at 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. The total radiative intensity in a cavity that contains a black body in thermodynamic equilibrium 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.
• Thermal radiation in a cavity in thermodynamic equilibrium is isotropic and unpolarized.

These properties apply if the distances considered are much larger than the wavelengths contributing to the spectrum (around 10 micrometres at 300 K). Indeed, thermal radiation here takes only travelling waves into account. A more sophisticated framework involving electromagnetics has to be used for lower distances (near-field thermal radiation).

Subjective colors

[1]

Interchange of energy

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

Thermal radiation is an important concept in thermodynamics as it is partially responsible for heat exchange between objects, as warmer bodies radiate more heat than colder ones. (Other factors are convection and conduction.) The interplay of energy exchange is characterized by the following equation:

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

In a practical situation and room-temperature setting, humans lose considerable energy due to thermal radiation. However, the energy lost by emitting infrared heat is partially regained by absorbing the heat of surrounding objects (the remainder resulting from generated heat through metabolism). Human skin has an emissivity of very close to 1.0 .^[3] Using the formulas below then shows 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, surrounded by surfaces at 296 K, they receive back about 900 watts from the wall, ceiling, and other surroundings, so the net loss is only about 100 watts. These heat transfer estimates are highly dependent on extrinsic variables, such as wearing clothes (decreasing total thermal "circuit" conductivity, therefore reducing total output heat flux.) Only truly "grey" systems (relative equivalent emissivity/absorptivity and no directional transmissivity dependence in all control volume bodies considered.) can achieve reasonable irradiative flux estimates through the Stefan-Boltzmann law. However, encountering this "ideally calculable" situation is virtually impossible (although common engineering procedures surrender the dependency of these unknown variables and "assume" this to be the case). Optimistically, these "grey" approximations will get you close to real solutions, as most divergence from Stefan-Boltzmann solutions is small (especially in most lab controlled environments).

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^{[citation needed]} (meaning the term "black body" does not always correspond to the visually perceived color of an object). These materials that do not follow the "black color = high emissivity/absorptivity" caveat will most likely have functional spectral emissivity/absorptivity dependence.

Calculation of radiative heat transfer between groups of object, including a 'cavity' or 'surroundings' requires solution of a set of simultaneous equations using the Radiosity method. In these calculations, the geometrical configuration of the problem is distilled to a set of numbers called view factors, which give the proportion of radiation leaving any given surface that hits another specific surface. These calculations are important in the fields of solar thermal energy, boiler and furnace design and raytraced computer graphics.

Formula

Thermal radiation power of a black body per unit of area, unit of solid angle and unit of frequency ν is given by Planck's law as:

or

where β is a constant.

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.

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

where the constant of proportionality σ is the Stefan–Boltzmann constant and A is the radiating surface area.

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

For surfaces which are not black bodies, one has to consider the (generally frequency dependent) emissivity factor ε(υ). This factor has to be multiplied with the radiation spectrum formula before integration. If it is taken as a constant, the resulting formula for the power output can be written in a way that contains ε as a factor:

This type of theoretical model, with frequency-independent emissivity lower than that of a perfect black body, is often known as a gray body. For frequency-dependent emissivity, the solution for the integrated power depends on the functional form of the dependence, though in general there is no simple expression for it. Practically speaking, if the emissivity of the body is roughly constant around the peak emission wavelength, the gray body model tends to work fairly well since the weight of the curve around the peak emission tends to dominate the integral.

Constants

Definitions of constants used in the above equations:

	Planck's constant	6.626 0693(11)×10−34 J·s = 4.135 667 43(35)×10−15 eV·s
	Wien's displacement constant	2.897 7685(51)×10−3 m·K
	Boltzmann constant	1.380 6505(24)×10−23 J·K−1 = 8.617 343(15)×10−5 eV·K−1
	Stefan–Boltzmann constant	5.670 400(40)×10−8 W·m−2·K−4
	Speed of light	299,792,458 m·s−1

Variables

Definitions of variables, with example values:

	Temperature	Average surface temperature on Earth = 288 K
	Surface area	Acuboid = 2ab + 2bc + 2ac; Acylinder = 2π·r(h + r); Asphere = 4π·r2

See also

• Thermography
• Infrared photography
• Planck radiation
• Thermal dose unit
• Color temperature

References

This article includes a list of references, related reading or external links, but its sources remain unclear because it lacks inline citations. Please improve this article by introducing more precise citations where appropriate. (October 2007)

Related reading:

• Siegel, John R. Howell, Robert; Howell. John R. (2001-11). Thermal radiation heat transfer. New York: Taylor & Francis, Inc.. pp. (xix - xxvi list of symbols for thermal radiation formulas). ISBN 9781560328391. http://books.google.com/books?id=O389yQ0-fecC&pg=PA1&dq=Thermal+radiation. Retrieved 2009-07-23. 

External links

• Free Black Body Emission Calculator
• Heat Transfer
• Thermal Radiation
• Atmospheric Radiation
• Infrared Temperature Calibration 101