Thermal_radiation

"Radiant heat" redirects here. For the heating method, see Radiant heating.

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.

Thermal radiation is electromagnetic radiation emitted from the surface of an object which is due to the object\'s temperature. Infrared radiation from a common household radiator or electric heater is an example of thermal radiation, as is the light emitted by a glowing incandescent light bulb. Thermal radiation is generated when heat from the movement of charged particles within atoms is converted to electromagnetic radiation. The emitted wave frequency of the thermal radiation is a probability distribution depending only on temperature, and for a genuine black body 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 heat intensity.

Properties

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 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 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.

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:

$\backslash alpha+\backslash rho+\backslash tau=1\; \backslash ,$

Here, $\backslash alpha\; \backslash ,$ represents spectral absorption factor, $\backslash rho\; \backslash ,$ spectral reflection factor and $\backslash tau\; \backslash ,$ spectral transmission factor. All these elements depend also on the wavelength $\backslash lambda\backslash ,$. The spectral absorption factor is equal to the emissivity $\backslash epsilon\; \backslash ,$; 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:

$\backslash alpha\; =\; \backslash epsilon\; =1\backslash ,$

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.

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).

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 $\backslash nu$ is given by

$u(\backslash nu,T)=\backslash frac\{2\; h\backslash nu^3\}\{c^2\}\backslash cdot\backslash frac1\{e^\backslash frac\{h\backslash nu\}\{k\_BT\}-1\}$

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.

Integrating the above equation over $\backslash nu$ the power output given by the Stefan–Boltzmann law is obtained, as:

$W\; =\; \backslash sigma\; \backslash cdot\; A\; \backslash cdot\; T^4$

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

$\backslash lambda\_\{max\}\; =\; \backslash frac\{b\}\{T\}$

For surfaces which are not black bodies, one has to consider the (generally frequency dependent) emissivity correction factor $\backslash epsilon(\backslash upsilon)$. 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 $\backslash epsilon$ as well:

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

Constants

Definitions of constants used in the above equations:

See also

• Thermography
• Infrared photography

External links

• Free Black Body Emission Calculator
• Heat Transfer
• Thermal Radiation
• Atmospheric Radiation

This article is licensed under the GNU Free Documentation License. It uses material from Wikipedia