Thermal radiation is electromagnetic radiation emitted from a material which is due to the heat of the material, the characteristics of which depend on its 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 charges in the material (electrons and protons in common forms of matter) is converted to electromagnetic radiation. Sunshine, or solar radiation, is thermal radiation from the extremely hot gasses of the Sun, and this radiation heats the Earth. The Earth also emits thermal radiation, but at a much lower intensity because it is cooler. The balance between heating by incoming solar thermal radiation and cooling by the Earth's outgoing thermal radiation is the primary process that determines the Earth's overall temperature.
If the object is a black body in thermodynamic equilibrium, the radiation is termed blackbody 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]}
Contents 
There are four main properties that characterize thermal radiation:
These properties apply if the distances considered are much larger than the wavelengths contributing to the spectrum (most significant from 825 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 (nearfield thermal radiation).
°C  Subjective colour [2] 

480  faint red glow 
580  dark red 
730  bright red, slightly orange 
930  bright orange 
1100  pale yellowish orange 
1300  yellowish white 
> 1400  white (yellowish if seen from a distance through atmosphere) 
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 roomtemperature 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 steadystate heat flux estimates through the StefanBoltzmann law. 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 StefanBoltzmann solutions is very small (especially in most STP lab controlled environments).
If objects appear white (reflective in the visual spectrum), they are not necessarily equally reflective (and thus nonemissive) 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^{[4]} (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.
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 frequencyindependent emissivity lower than that of a perfect black body, is often known as a gray body. For frequencydependent 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.
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} 
Definitions of variables, with example values:
Temperature  Average surface temperature on Earth = 288 K  
Surface area  A_{cuboid} = 2ab + 2bc + 2ac; A_{cylinder} = 2π·r(h + r); A_{sphere} = 4π·r^{2} 
Related reading:

