Thermal radiation

thumb|right|Thermal radiation in visible light can be seen on this hot metalwork. Its emission in the [[infrared is invisible to the human eye. Infrared cameras are capable of capturing this infrared emission (see Thermography).]]

Thermal radiation is electromagnetic radiation emitted by the thermal motion of particles in matter. All matter with a temperature greater than absolute zero emits thermal radiation. The emission of energy arises from a combination of electronic, molecular, and lattice oscillations in a material.

Kinetic energy is converted to electromagnetism due to charge-acceleration or dipole oscillation. At room temperature, most of the emission is in the infrared (IR) spectrum, though above around enough of it becomes visible for the matter to visibly glow. This visible glow is called incandescence. Thermal radiation is one of the fundamental mechanisms of heat transfer, along with conduction and convection.

The primary method by which the Sun transfers heat to the Earth is thermal radiation. This energy is partially absorbed and scattered in the atmosphere, the latter process being the reason why the sky is visibly blue. Planck's law describes the spectrum of black-body radiation, and relates the radiative heat flux from a body to its temperature. Wien's displacement law determines the most likely frequency of the emitted radiation, and the Stefan–Boltzmann law gives the radiant intensity. Thermal radiation reflects the conversion of thermal energy into electromagnetic energy. Thermal energy is the kinetic energy of random movements of atoms and molecules in matter. It is present in all matter of nonzero temperature. These atoms and molecules are composed of charged particles, i.e., protons and electrons. The kinetic interactions among matter particles result in charge acceleration and dipole oscillation. This results in the electrodynamic generation of coupled electric and magnetic fields, resulting in the emission of photons, radiating energy away from the body. Electromagnetic radiation, including visible light, will propagate indefinitely in vacuum.

alt=Beer can thermal imaging|thumb|Beer can being imaged by a FLIR thermal camera to demonstrate temperature differences caused by emissivity

The characteristics of thermal radiation depend on various properties of the surface from which it is emanating, including its temperature and its spectral emissivity, as expressed by Kirchhoff's law. According to the Archimedes' heat ray anecdote, Archimedes is purported to have developed mirrors to concentrate heat rays in order to burn attacking Roman ships during the Siege of Syracuse (<abbr>c.</abbr> 213–212 BC), but no sources from the time have been confirmed. He found that darker color clothes got hotter when exposed to sunlight than lighter color clothes. One experiment he performed consisted of placing square pieces of cloth of various colors out in the snow on a sunny day. He waited some time and then measured that the black pieces sank furthest into the snow of all the colors, indicating that they got the hottest and melted the most snow.

Caloric theory

Antoine Lavoisier considered that radiation of heat was concerned with the condition of the surface of a physical body rather than the material of which it was composed. Lavoisier described a poor radiator to be a substance with a polished or smooth surface as it possessed its molecules lying in a plane closely bound together thus creating a surface layer of caloric fluid which insulated the release of the rest within.

In Marc-Auguste Pictet's famous experiment of 1790, it was reported that a thermometer detected a lower temperature when a set of mirrors were used to focus "frigorific rays" from a cold object.

In 1791, Pierre Prevost a colleague of Pictet, introduced the concept of radiative equilibrium, wherein all objects both radiate and absorb heat. When an object is cooler than its surroundings, it absorbs more heat than it emits, causing its temperature to increase until it reaches equilibrium. Even at equilibrium, it continues to radiate heat, balancing absorption and emission.

The discovery of infrared radiation is ascribed to astronomer William Herschel. Herschel published his results in 1800 before the Royal Society of London. Herschel used a prism to refract light from the sun and detected the calorific rays, beyond the red part of the spectrum, by an increase in the temperature recorded on a thermometer in that region.

Thomas Young who had adopted the wave theory of light writes in 1902:

In 1804, John Leslie experimented with different cubes filled with hot/cold water with different coated sides. The Leslie cube experiment showed black surfaces emitted more radiation than silvery surfaces.

Joseph Louis Gay-Lussac wrote in 1920 about the development of the theory of heat propagation in vacuum () would require a new theory of heat.

By 1884 the emissive power of a perfect blackbody was inferred by Josef Stefan using John Tyndall's experimental measurements, and derived by Ludwig Boltzmann from fundamental statistical principles. This relation is known as Stefan–Boltzmann law. In 1893, Wilhelm Wien empirically developed Wien's displacement law indicating at which wavelength the radiation is most intense at a certain temperature for black-body radiation.

At the end of the 19th century, it was shown that the transmission of light or of radiant heat was allowed by the propagation of electromagnetic waves. Television and radio broadcasting waves are types of electromagnetic waves with specific wavelengths. All electromagnetic waves travel at the same speed; therefore, shorter wavelengths are associated with high frequencies. All bodies generate and receive electromagnetic waves at the expense of heat exchange. The energy E of an electromagnetic wave in vacuum is found by the expression E = hf, where h is the Planck constant and f is its frequency.

Bodies at higher temperatures emit radiation at higher frequencies with an increasing energy per quantum. While the propagation of electromagnetic waves of all wavelengths is often referred as "radiation", thermal radiation is often constrained to the visible and infrared regions. For engineering purposes, it may be stated that thermal radiation is a form of electromagnetic radiation which varies on the nature of a surface and its temperature.

In the near field

In the 1953, Sergei Rytov pioneered the study of thermal radiation in the near-field using the fluctuation–dissipation theorem. At short distance, below the thermal wavelength, he showed that heat transfer could surpass the limits given by Planck's blackbody theory. In 1971, Dirk Polder and Michael Van Hove presented their work on near-field radiative heat transfer between closely spaced bodies based on Rytov's work and compared with experimental setups.

Characteristics

Frequency

Thermal radiation emitted by a body at any temperature consists of a wide range of frequencies. The frequency distribution is given by Planck's law of black-body radiation for an idealized emitter as shown in the diagram at top.

The dominant frequency (or color) range of the emitted radiation shifts to higher frequencies as the temperature of the emitter increases. For example, a red hot object radiates mainly in the long wavelengths (red and orange) of the visible band. If it is heated further, it also begins to emit discernible amounts of green and blue light, and the spread of frequencies in the entire visible range cause it to appear white to the human eye; it is white hot. Even at a white-hot temperature of 2000 K, 99% of the energy of the radiation is still in the infrared. This is determined by Wien's displacement law. In the diagram the peak value for each curve moves to the left as the temperature increases.

{| class="wikitable"

|+Subjective color to the eye of a black body thermal radiator

! °C (°F)

! Subjective color

| || faint red glow

| || dark red

| || bright red, slightly orange

| || bright orange

| || pale yellowish orange

| || yellowish white

| > || white (yellowish if seen from a distance through atmosphere)

Relationship to temperature

The total radiation intensity of a black body rises as the fourth power of the absolute temperature, as expressed by the Stefan–Boltzmann law. A kitchen oven, at a temperature about double room temperature on the absolute temperature scale (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 light bulb—roughly 3000 K, or 10 times room temperature—radiates 10,000 times as much energy per unit area.

As for photon statistics, thermal light obeys Super-Poissonian statistics.

Appearance

When the temperature of a body is high enough, its thermal radiation spectrum becomes strong enough in the visible range to visibly glow. The visible component of thermal radiation is sometimes called incandescence,

though this term can also refer to thermal radiation in general. The term derives from the Latin verb , 'to glow white'.

In practice, virtually all solid or liquid substances start to glow around , with a mildly dull red color, whether or not a chemical reaction takes place that produces light as a result of an exothermic process. This limit is called the Draper point. The incandescence does not vanish below that temperature, but it is too weak in the visible spectrum to be perceptible.

Reciprocity

The rate of electromagnetic radiation emitted by a body at a given frequency is proportional to the rate that the body absorbs radiation at that frequency, a property known as reciprocity. Thus, a surface that absorbs more red light thermally radiates more red light. This principle applies to all properties of the wave, including wavelength (color), direction, polarization, and even coherence. It is therefore possible to have thermal radiation which is polarized, coherent, and directional; though polarized and coherent sources are fairly rare in nature.

Fundamental principles

Thermal radiation is one of the three principal mechanisms of heat transfer. It entails the emission of a spectrum of electromagnetic radiation due to an object's temperature. Other mechanisms are convection and conduction.

Electromagnetic waves

thumb|Electromagnetic wave with perpendicular electric and magnetic components

Thermal radiation is characteristically different from conduction and convection in that it does not require a medium and, in fact it reaches maximum efficiency in a vacuum. Thermal radiation is a type of electromagnetic radiation which is often modeled by the propagation of waves. These waves have the standard wave properties of frequency, <math>\nu</math> and wavelength, <math>\lambda</math> which are related by the equation

<math display="block">\lambda=\frac{c}{\nu}</math>

where <math>c</math> is the speed of light in the medium.

Irradiation

Thermal irradiation is the rate at which radiation is incident upon a surface per unit area. (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.

Only truly gray systems (relative equivalent emissivity/absorptivity and no directional transmissivity dependence in all control volume bodies considered) can achieve reasonable steady-state heat flux estimates through the Stefan-Boltzmann law. Encountering this "ideally calculable" situation is almost impossible (although common engineering procedures surrender the dependency of these unknown variables and "assume" this to be the case). Optimistically, these "gray" approximations will get close to real solutions, as most divergence from Stefan-Boltzmann solutions is very small (especially in most standard temperature and pressure lab controlled environments).

Reflectivity

Reflectivity deviates from the other properties in that it is bidirectional in nature. In other words, this property depends on the direction of the incident of radiation as well as the direction of the reflection. Therefore, the reflected rays of a radiation spectrum incident on a real surface in a specified direction forms an irregular shape that is not easily predictable. In practice, surfaces are often assumed to reflect either in a perfectly specular or a diffuse manner. In a specular reflection, the angles of reflection and incidence are equal. In diffuse reflection, radiation is reflected equally in all directions. Reflection from smooth and polished surfaces can be assumed to be specular reflection, whereas reflection from rough surfaces approximates diffuse reflection.

Blackbodies are idealized surfaces that act as the perfect absorber and emitter. It is given by Planck's law per unit wavelength as:

<math display="block">I_{\lambda,b}(\lambda,T)=\frac{2 h c^2}{\lambda^5}\cdot\frac1{e^{hc/k_{\rm B}T\lambda}-1}</math>

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. Planck's law shows that radiative energy increases with temperature, and explains why the peak of an emission spectrum shifts to shorter wavelengths at higher temperatures. It can also be found that energy emitted at shorter wavelengths increases more rapidly with temperature relative to longer wavelengths.

The equation is derived as an infinite sum over all possible frequencies in a semi-sphere region. The energy, <math>E=h \nu</math>, of each photon is multiplied by the number of states available at that frequency, and the probability that each of those states will be occupied.

Stefan-Boltzmann law

thumb|upright=1.4|Power emitted by a black body plotted against the temperature according to the Stefan–Boltzmann law.The Planck distribution can be used to find the spectral emissive power of a blackbody, <math>E_{\lambda,b}</math> as follows,

If the filament could be made hotter, efficiency would increase; however, there are currently no materials able to withstand such temperatures which would be appropriate for use in lamps.

More efficient light sources, such as fluorescent lamps and LEDs, do not function by incandescence.

Thermal comfort

thumb|upright|Radiant heat panel for testing precisely quantified energy exposures at [[National Research Council (Canada)|National Research Council, near Ottawa, Ontario, Canada]]Thermal radiation plays a crucial role in human comfort, influencing perceived temperature sensation. Various technologies have been developed to enhance thermal comfort, including personal heating and cooling devices.

The mean radiant temperature is a metric used to quantify the exchange of radiant heat between a human and their surrounding environment.

Personal heating

Radiant personal heaters are devices that convert energy into infrared radiation that are designed to increase a user's perceived temperature. They typically are either gas-powered or electric. In domestic and commercial applications, gas-powered radiant heaters can produce a higher heat flux than electric heaters which are limited by the amount of current that can be drawn through a circuit breaker.

Personal cooling

Personalized cooling technology is an example of an application where optical spectral selectivity can be beneficial. Conventional personal cooling is typically achieved through heat conduction and convection. However, the human body is a very efficient emitter of infrared radiation, which provides an additional cooling mechanism. Most conventional fabrics are opaque to infrared radiation and block thermal emission from the body to the environment. Fabrics for personalized cooling applications have been proposed that enable infrared transmission to directly pass through clothing, while being opaque at visible wavelengths, allowing the wearer to remain cooler.

Windows

Low-emissivity windows in houses are a more complicated technology, since they must have low emissivity at thermal wavelengths while remaining transparent to visible light. To reduce the heat transfer from a surface, such as a glass window, a clear reflective film with a low emissivity coating can be placed on the interior of the surface. "Low-emittance (low-E) coatings are microscopically thin, virtually invisible, metal or metallic oxide layers deposited on a window or skylight glazing surface primarily to reduce the U-factor by suppressing radiative heat flow". By adding this coating we are limiting the amount of radiation that leaves the window thus increasing the amount of heat that is retained inside the window.

Spacecraft

Shiny metal surfaces, have low emissivities both in the visible wavelengths and in the far infrared. Such surfaces can be used to reduce heat transfer in both directions; an example of this is the multi-layer insulation used to insulate spacecraft.

Since any electromagnetic radiation, including thermal radiation, conveys momentum as well as energy, thermal radiation also induces very small forces on the radiating or absorbing objects. Normally these forces are negligible, but they must be taken into account when considering spacecraft navigation. The Pioneer anomaly, where the motion of the craft slightly deviated from that expected from gravity alone, was eventually tracked down to asymmetric thermal radiation from the spacecraft. Similarly, the orbits of asteroids are perturbed since the asteroid absorbs solar radiation on the side facing the Sun, but then re-emits the energy at a different angle as the rotation of the asteroid carries the warm surface out of the Sun's view (the YORP effect).

Nanostructures

Nanostructures with spectrally selective thermal emittance properties offer numerous technological applications for energy generation and efficiency, e.g., for daytime radiative cooling of photovoltaic cells and buildings. These applications require high emittance in the frequency range corresponding to the atmospheric transparency window in 8 to 13 micron wavelength range. A selective emitter radiating strongly in this range is thus exposed to the clear sky, enabling the use of the outer space as a very low temperature heat sink.

Health and safety

Metabolic temperature regulation

In a practical, room-temperature setting, humans lose considerable energy due to infrared thermal radiation in addition to that lost by conduction to air (aided by concurrent convection, or other air movement like drafts). The heat energy lost is partially regained by absorbing heat radiation from walls or other surroundings. Human skin has an emissivity of very close to 1.0. A human, having roughly 2m<sup>2</sup> in surface area, and a temperature of about 307 K, continuously radiates approximately 1000 W. If people are indoors, surrounded by surfaces at 296 K, they receive back about 900 W from the wall, ceiling, and other surroundings, resulting in a net loss of 100 W. These estimates are highly dependent on extrinsic variables, such as wearing clothes.

Lighter colors and also whites and metallic substances absorb less of the illuminating light, and as a result heat up less. However, color makes little difference in the heat transfer between an object at everyday temperatures and its surroundings. This is because the dominant emitted wavelengths are not in the visible spectrum, but rather infrared. Emissivities at those wavelengths are largely unrelated to visual emissivities (visible colors); in the far infra-red, most objects have high emissivities. Thus, except in sunlight, the color of clothing makes little difference as regards warmth; likewise, paint color of houses makes little difference to warmth except when the painted part is sunlit.

Burns

Thermal radiation is a phenomenon that can burn skin and ignite flammable materials. The time to a damage from exposure to thermal radiation is a function of the rate of delivery of the heat. Radiative heat flux and effects are given as follows:

{| class="wikitable"

! kW/m<sup>2</sup> !! Effect

| 170 || Maximum flux measured in a post-flashover compartment

| 80 || Thermal Protective Performance test for personal protective equipment

| 52 || Fiberboard ignites at five seconds

| 29 || Wood ignites, given time

| 20 || Typical beginning of flashover at floor level of a residential room

| 16 || Human skin: sudden pain and second-degree burn blisters after 5 seconds

| 12.5 || Wood produces ignitable volatiles by pyrolysis

| 10.4 || Human skin: Pain after 3 seconds, second-degree burn blisters after 9 seconds

| 6.4 || Human skin: second-degree burn blisters after 18 seconds

| 4.5 || Human skin: second-degree burn blisters after 30 seconds

| 2.5 || Human skin: burns after prolonged exposure, radiant flux exposure typically encountered during firefighting

| 1.4 || Sunlight, sunburns potentially within 30 minutes. Sunburn is NOT a thermal burn. It is caused by cellular damage due to ultraviolet radiation.

Near-field radiative heat transfer

At distances on the scale of the wavelength of a radiated electromangetic wave or smaller, Planck's law is not accurate. For objects this small and close together, the quantum tunneling of EM waves has a significant impact on the rate of radiation.

Planck's law of thermal radiation has been challenged in recent decades by predictions and successful demonstrations of the radiative heat transfer between objects separated by nanoscale gaps that deviate significantly from the law predictions. This deviation is especially strong (up to several orders in magnitude) when the emitter and absorber support surface polariton modes that can couple through the gap separating cold and hot objects. However, to take advantage of the surface-polariton-mediated near-field radiative heat transfer, the two objects need to be separated by ultra-narrow gaps on the order of microns or even nanometers. This limitation significantly complicates practical device designs.

Another way to modify the object thermal emission spectrum is by reducing the dimensionality of the emitter itself. To achieve the required level of photon confinement, the dimensions of the radiating objects should be on the order of or below the thermal wavelength predicted by Planck's law. Most importantly, the emission spectrum of thermal wells, wires and dots deviates from Planck's law predictions not only in the near field, but also in the far field, which significantly expands the range of their applications.

References

External links

Black Body Emission Calculator
Heat transfer
Atmospheric Radiation
Infrared Temperature Calibration 101