Intensity of the black body radiation as a function of the wavelength at different temperatures (logarithmic scales). The colored bar marks the area of ​​visible light. The curve for solar radiation at the sun's surface is beige, for the ambient temperature at the earth's surface it is red. Note the strong increase in intensity with temperature and the shift of the maximum to shorter wavelengths.

Because the maximum intensity of the thermal radiation is in the infrared range for surfaces that are "hot" by everyday standards , colloquial thermal radiation is usually only understood to mean this infrared (i.e. invisible) radiation. However shifts with increasing temperature, the maximum radiation of the heat radiation towards shorter and shorter wavelengths in sunlight reaching z. B. the visible area with runners up to the ultraviolet . The heat radiation of the earth, on the other hand, is, according to its surface temperature, mainly in the mid-infrared (strongest intensity at a wavelength of approx. 10 µm) - that is, at considerably larger wavelengths.

Thermal radiation is emitted by all solids , liquids , gases and plasmas that are in an excited state with a well-defined temperature above absolute zero . Just as each body takes the same time by other bodies emitted thermal radiation by absorption on (see exchange of radiation ), the sum of the heat radiation emission and absorption radiation balance called.

The highest thermal radiation emission (and absorption) shows the ideal black body at all wavelengths and temperatures . The radiation it emits is called blackbody radiation . The Planck's law describes the intensity of the blackbody radiation as a function of wavelength and temperature . This theoretical maximum is not completely reached by real bodies.

In addition to convection and thermal conduction, the emission and absorption of thermal radiation is a way of transferring heat ; in a vacuum it is the only way of transferring it.

## history

The concept of warming rays was already known in antiquity, see the (legend of the) burning mirror of Archimedes (3rd century BC or 2nd century AD). "Holy fires" were lit with focused sunlight. In the 16th century, Giambattista della Porta showed the “reflection of cold” and Francis Bacon that warm, non-glowing or burning bodies also emit heat rays, and in the 17th century Edme Mariotte blocked this invisible radiation with a pane of glass. Thermoscopes , air-filled glass round flasks with liquid caps, were used to measure the temperature .

These experiments have been repeated and refined many times, so that opinions differ as to who first demonstrated an effect convincingly. For the reflection of the supposed cold rays , on the one hand, there are students and followers of Galileo Galilei in the Accademia del Cimento around 1660 , where the cold object was a large pile of snow, which could have had an effect on the thermoscope other than radiation, as the experimenters self-critically noted. However, they saw a significant increase in temperature when they covered the concave mirror directed towards the snow, in the focus of which the thermoscope was located. On the other hand, there are Marc-Auguste Pictet and Horace-Bénédict de Saussure , who in 1790 brought a small, cold object into the focus of a second concave mirror; the aligned mirrors could be several meters apart.

For an interpretation, warned Carl Wilhelm Scheele in 1777, further observations had to be taken into account: Against the strong draft of the chimney effect , the heat radiation comes out through the oven door and is not deflected by air flowing across it. Conversely, smoke rises completely unaffected by the beam and sun rays cross the beam without streaking . Metal mirrors do not get warm when they reflect what they call “radiant heat”, but they do get warm from a stream of warm air.

In the 18th and early 19th centuries there were various ideas about the mechanism of radiant heat, the supporters of which can be roughly divided into emissionists and undulateurs . For the former, warm and sometimes cold bodies gave off something material, for the latter there was a medium that transmitted vibrations. Pictet tended towards the directed emission of a fire substance from the hot to the cold body, which comes to a standstill between equally warm bodies in the sense of a static equilibrium of the so-called thermometric tension . However, he admitted that the vibration hypothesis could explain his experiment just as well. Pierre Prévost was also an emissionsist, but spoke of heat particles that all bodies constantly emit, and that "the stronger heat rays from hotter bodies overcome the weaker [heat rays] from colder [bodies]". Thereafter there would be no cold radiation, only stronger or weaker heat radiation.

Benjamin Thompson alias Count Rumford was an undulateur throughout his life. He considered it impossible that a body could both receive, absorb and drive away heat at the same time. He also cited a supposedly convincing experimental finding. He had discovered that a thin linen cloth around a bare metal cylinder (or a thin coat of varnish, a layer of soot, etc.) allowed it to cool down faster by increasing the heat radiation. The same applied to a warming cold cylinder and the supposed cold radiation. He had a particularly sensitive differential thermoscope (after John Leslie ) made of two glass spheres connected by a capillary, one as a reference, the other in the middle between a hot and a cold cylinder (room temperature 22 ° C). The cylinders were both bright or both sooty. In both cases, the thermoscope showed no rash, which easily matched the hypothesis of compensating heat and cold rays. He did not realize that shiny metal not only emits less thermal radiation, but also absorbs less radiation in the same ratio, reflecting the rest. This correspondence is the content of Kirchhoff's radiation law , which was first formulated in 1859 . With this effect in mind, Rumford's experiments are consistent with Prévost's (correct) hypothesis.

In the first decades of the 19th century the suspicion of the light nature of thermal radiation was reinforced. In 1800 Wilhelm Herschel examined a solar spectrum generated by means of a prism with a gas thermometer and found the strongest temperature increase in the dark area beyond red . Other researchers found the maximum in different places. Thomas Johann Seebeck discovered in 1820 that this was due to the material of the prism. Two possible interpretations: Sunlight contains both visible and thermal radiation (and at the other end of the spectrum chemical radiation, see Johann Wilhelm Ritter ), all of which are split up by the prism. Or sunlight has all three properties to a different extent, depending on its position in the spectrum. Jacques Étienne Bérard studied (first together with Étienne Louis Malus ) the birefringence of light and found that regardless of the detection of the radiation (chemical, visual, thermal), polarization occurred in the same polarization direction, and the birefringence angle (at a given position in the spectrum ) agreed, which spoke in favor of the (applicable) second hypothesis.

Kirchhoff's law does not yet make a statement about how the thermal radiation depends on the temperature. The search for a formula that closes this gap in knowledge turned out to be fruitful for the advancement of physics. From experiments and theoretical considerations, with the Stefan-Boltzmann law and Wien's law of displacement, individual properties of the formula were found. Around 1900, first an approximation formula for high temperature was found with Wien's radiation law and a few years later with the Rayleigh-Jeans law an approximation formula for low temperature was found. Max Planck finally succeeded in combining the statements of these laws into Planck's law of radiation for black bodies. In deriving this formula, Max Planck took the first steps on the way to the development of quantum mechanics , without actually intending to do so .

## Emergence

Thermal radiation is a macroscopic phenomenon; a large number of particles and elementary excitations are necessarily involved in its formation. A single microscopic particle of the radiating body cannot be assigned a temperature , it cannot radiate thermally . The exact mechanism of these processes is not important. For every mechanism, the resulting spectrum is thermal, if only the energy characteristic of thermal excitation approaches or exceeds the energy levels typical for the mechanism ( is the Boltzmann constant and the temperature of the radiating body). Otherwise this mechanism would either not be involved or its excitation would not be thermal. ${\ displaystyle k _ {\ mathrm {B}} T}$${\ displaystyle k _ {\ mathrm {B}}}$${\ displaystyle T}$

Thermal equilibrium between radiation and matter presupposes that by far the largest part of the photons produced does not escape from the body (“decoupled”), but is absorbed again within the body. If this applies to photons of every wavelength, the wavelength dependence of the emission and absorption (i.e. the strength of the coupling of the particles to the radiation field) does not affect the spectrum of the radiation. The multiple sequence of elementary radiation processes - emission, scattering and absorption by the body's particles - creates the continuous thermal spectrum that corresponds to the body's temperature. For example, a single cubic meter from the photosphere of the sun would still be too small for this and therefore show a pronounced line spectrum (and only glow briefly and weakly). At wavelengths between the spectral lines, the material has an optical depth that is much greater than 1 m. However, at all wavelengths it remains less than the thickness of the photosphere of about 100 km. Therefore the spectrum of the sun is largely thermal.

Even if the radiation field in the source is thermal, its spectrum outside can deviate significantly from it if the outcoupling is dependent on the wavelength. This occurs z. B. by the jump in the wavelength-dependent refractive index on the surface. In metals, it creates the shine. The jump not only reflects external radiation, but also the thermal radiation from within. This would only not affect the spectrum if the external radiation were also thermally at the same temperature. However, this is never the case with measurements, because in order to be able to measure the spectrum of thermal radiation, the receiver must be colder than the source (with BOOMERanG it was 0.27 K).

• In the microwave oven , the energy is only radiated at one frequency (2.45 GHz), which corresponds to a single line in the spectrum (at approx. 122 mm). Although this radiation is absorbed by water and it is thus heated, this line spectrum is not thermal radiation.
• The same also applies to a carbon dioxide laser : although you can melt metals and stones with a powerful CO 2 laser, it does not generate thermal radiation, but monochromatic radiation with a wavelength of 10.6 µm. Even if this line lies in the infrared range (also known colloquially as thermal radiation ), it does not mean here either that it is thermal radiation. A comparison with a laser pointer reveals that there is (in contrast to thermal radiation) no simple relationship between wavelength and temperature: The wavelength of the laser pointer is smaller by a factor of 20, so each photon transports twenty times the energy; however, it cannot be used to melt metals, since the total output power is lower by orders of magnitude .
• The spectrum of an X-ray tube consists of the bremsstrahlung and additional conspicuous spectral lines at certain wavelengths . The intensity of bremsstrahlung also shows a "hump" like thermal radiation; its shape deviates considerably from Planck's law of radiation and, in contrast to thermal radiation, has an upper limit frequency. Therefore this bremsstrahlung is not thermal radiation.
PAR curve of sunlight with a clear sky
• The spectrum of fluorescent lamps of any type or gas discharge lamps such as sodium vapor lamps has no resemblance to the thermal spectrum of a Planckian radiator. Rather, the material of these light generators is chosen so that as much power as possible is emitted in the visible range and as little as possible outside of it (e.g. in the UV range). This is the only way to achieve the desired high level of efficiency. Strong deviations from a white, thermal spectrum can affect the color rendering of illuminated objects.

## Practical distinction

By comparing the intensity at different wavelengths, you can decide whether a light source is “thermal” or “non-thermal” and thus draw conclusions about the type of source. The result is also known as the signature of a light source.

• Example carbon dioxide laser : If you filter different wavelengths such as 9 µm, 10.6 µm and 13 µm, you only measure a noticeable light output at 10.6 µm. No thermal radiator can generate such a narrow spectrum.
• If you repeat the measurement on an incandescent lamp, you will get three results that hardly differ because the "hump" of Planck's radiation curve is relatively flat in this area. This is a strong indicator for a thermal radiator, because you can hardly build gas discharge lamps with such a large line width . In case of doubt, measurements must be carried out at other wavelengths.

Such comparison measurements are carried out by the infrared seeker heads of guided missiles in order to distinguish between hot aircraft engines and decoys , the light of which tends to have a non-thermal signature. Transferred to the visible area, this corresponds to a comparison of glowing sparks with colored fireworks , which have a distinctive line spectrum due to the flame coloring .

In radio astronomy and at SETI there is a constant search for non-thermal signatures: The 21 cm line of hydrogen and the 1.35 cm line of the water molecule are the basis for most research.

## calculation

The heat flow radiated by a body can be calculated using the Stefan-Boltzmann law as follows: ${\ displaystyle {\ dot {Q}}}$

${\ displaystyle {\ dot {Q}} = {\ frac {\ partial Q} {\ partial t}} = \ varepsilon \, \ sigma \, A \, T ^ {4},}$

in which

${\ displaystyle {\ dot {Q}}}$: Heat flow or radiation power
${\ displaystyle \ varepsilon}$: Emissivity . The values ​​are between 0 (perfect mirror) and 1 (ideal black body ).
${\ displaystyle \ sigma = 5 {,} 67 \ cdot 10 ^ {- 8} ~ \ mathrm {\ frac {W} {m ^ {2} \, K ^ {4}}}}$: Stefan-Boltzmann constant
${\ displaystyle A}$: Surface of the radiating body
${\ displaystyle T}$: Temperature of the radiating body

At the same time, the body absorbs radiation from its surroundings. If a body with the surface is in exchange with a body on the surface and both surfaces each have a homogeneous temperature and a uniform emissivity or , then this is the heat output given off by the surface${\ displaystyle A_ {1}}$${\ displaystyle A_ {2}}$${\ displaystyle T_ {1}}$${\ displaystyle T_ {2}}$${\ displaystyle \ varepsilon _ {1}}$${\ displaystyle \ varepsilon _ {2}}$${\ displaystyle A_ {1}}$

${\ displaystyle {\ dot {Q}} = {\ dfrac {\ sigma (T_ {1} ^ {4} -T_ {2} ^ {4})} {{\ dfrac {1- \ varepsilon _ {1} } {A_ {1} \ varepsilon _ {1}}} + {\ dfrac {1} {A_ {1} F_ {1 \ rightarrow 2}}} + {\ dfrac {1- \ varepsilon _ {2}} { A_ {2} \ varepsilon _ {2}}}}}}$

with the visual factor . ${\ displaystyle F_ {1 \ rightarrow 2}}$

If the area of ​​an object that is surrounded by a much larger emissive area (e.g. a teacup in an office), the above formula is simplified to ${\ displaystyle A_ {1}}$${\ displaystyle A_ {2}}$

${\ displaystyle {\ dot {Q}} = \ varepsilon _ {1} \ sigma A_ {1} (T_ {1} ^ {4} -T_ {2} ^ {4}).}$

## intensity

The spectrum of the microwave background measured by the satellite COBE corresponds to that of a black body with a temperature of 2.725 K. The measurement uncertainty and the deviations from the theoretical curve are smaller than the line width.

With increasing temperature of a body, the intensity of its heat radiation also increases drastically (see Stefan-Boltzmann law ), and the emission maximum shifts to shorter wavelengths (see Wien's law of displacement ). To illustrate some examples of bodies; the temperatures decrease from example to example by a factor of 10:

• A white dwarf : a star with a particularly high surface temperature, here it is 57,000 K. It emits 10,000 times as much power per unit area of ​​its surface as our sun, the maximum intensity is 50 nm, which is ultraviolet radiation . The Stefan-Boltzmann law provides a radiated output per square centimeter of 60 MW - corresponding to the output of a small power plant.
• Sunlight is emitted from the sun's 5700K surface . The maximum intensity is at 500 nm in the green area of ​​the electromagnetic spectrum . The radiated power per square centimeter is 6 kW - this roughly corresponds to the heating output for a single-family house in winter.
• Each square centimeter of the black surface of a 570 K (297 ° C) furnace emits only 1 / 10,000 of the power that an equally large piece of solar surface would emit (see Stefan-Boltzmann's law ). The maximum intensity is 5 µm, i.e. in the infrared.
• Every square centimeter of the black surface of a 57 K (−216 ° C) cold body radiates electromagnetic waves, the power of which corresponds to 1 / 10,000 that of the same size piece of furnace surface. The intensity maximum is 50 µm in the far infrared.
• In principle, nothing changes when the body is frozen to 5.7 K (−267 ° C). The emitted power drops again by a factor of 10,000 and the maximum intensity is 0.5 mm - almost in the radar range. With very sensitive radio astronomy receivers , very weak noise, the cosmic background radiation , can be detected.

Of these five examples of thermal radiation, only the hot oven is in the range of our everyday experience. The spectrum of such a furnace with its maximum in the infrared range is the cause of the colloquial narrowing of the meaning of the term thermal radiation to the infrared range mentioned in the introduction . For certain galactic nuclei, on the other hand, the maximum radiation is even in the X-ray range of the electromagnetic spectrum .

## Influence of different body surfaces

The transmitter tube 3-500 C has an anode made of graphite, since the gray color and the rough surface radiate heat well.

The surface quality of the body also has a strong influence on the emitted intensity . This is characterized by the emissivity , which is almost zero with mirrors and reaches its maximum with matt black surfaces. If the temperature is to be determined without contact using thermography , a huge error can arise from incorrectly estimating the emissivity, as shown here .

Since the emission maximum of the heat radiation of the earth's surface is at a wavelength of 8 to 10 µm and coincidentally coincides with the absorption minimum of the air, the earth's surface cools down on clear nights due to heat radiation into space. Above all, clouds and water vapor, and to a lesser extent so-called greenhouse gases such as carbon dioxide, are not transparent to this radiation; they reduce or prevent this cooling through reflection or remission (see also greenhouse , greenhouse effect ). The proportions of these gases influence the temperature balance of the earth.

Of particular importance in physics is the concept of the black body , an emitter and absorber of thermal radiation that has an emission or absorption level of one. If such an absorber is kept in thermal equilibrium with its surroundings with a thermostat , the radiation output of thermal and non-thermal radiation sources can be determined via its heat absorption.

Some materials such as colored polyethylene foils are transparent in the IR range, but opaque in the visible range.
With other materials like glass it is exactly the opposite of what the lens shows.

Like any other matter with a comparable temperature, the human body radiates a large part of the energy absorbed through food through thermal radiation, in this case mainly infrared light. However, energy can also be absorbed through infrared light, as can be seen, for example, when approaching a campfire. The difference between emitted and absorbed thermal radiation:

${\ displaystyle P _ {\ text {net}} = P _ {\ text {emitted}} - P _ {\ text {absorbed}}}$

corresponds to a difference in temperature between the human body and the external radiation source due to the Stefan-Boltzmann law :

${\ displaystyle P _ {\ text {net}} = A \ sigma \ varepsilon \ left (T ^ {4} -T_ {0} ^ {4} \ right)}$

The total surface area of an adult is about 2 m², the emissivity of human skin in the IR range is approximately 1, regardless of the wavelength. ${\ displaystyle A}$${\ displaystyle \ varepsilon}$

The skin temperature is 33 ° C, but only about 28 ° C is measured on the surface of the clothing. At an average ambient temperature of 20 ° C, a radiation loss of ${\ displaystyle T}$

${\ displaystyle P _ {\ rm {net}} = 100 \ \ mathrm {W}.}$

In addition to thermal radiation, the body also loses energy through convection and evaporation of water in the lungs and sweat on the skin. A rough estimate showed that for a standing adult, the heat output from radiation exceeds that from natural convection by a factor of two.

If one calculates the mean wavelength of the emitted IR radiation with the help of Wien's law of displacement , one obtains

${\ displaystyle \ lambda _ {\ text {peak}} = {\ frac {2 {,} 898 \ cdot 10 ^ {6} \, \ mathrm {K} \ cdot \ mathrm {nm}} {305 \, \ mathrm {K}}} = 9 {,} 50 \, {\ text {µm}}.}$

Thermal imaging cameras for thermographic diagnostics in medicine should therefore be particularly sensitive in the 7-14 µm range.

## Applications

Underfloor heating under ceramic tiles. The photographer was sitting on the armchair in front of the laptop immediately before the picture was taken.

When thermal radiation hits a body,

1. the radiation is partially let through ( transmitted ),
2. the radiation is partially reflected ,
3. the radiation is partially absorbed , i.e. absorbed by the body and converted into heat .

These three effects are quantified with the transmission, reflection and absorption coefficients.

The absorption coefficient is equal to the emissivity, i.e. In other words, a light gray surface with an emissivity or absorption level of 0.3 absorbs 30% of the incident radiation, but at a given temperature also emits only 30% of the thermal radiation compared to a black body.

Anodized aluminum heat sinks (heat radiation and convection)

Heat radiation can be reduced by using bare metal surfaces (examples: metal layers on rescue blankets and insulating bags, reflections on Dewar flasks such as in thermos flasks and super insulation ).

In order to increase the heat radiation of a metallic body, it can be provided with a "dark", matt coating in the relevant wavelength range:

• Painting of radiators with almost any color ( synthetic resin has an emissivity close to one in the mid-infrared).
• Anodizing of aluminum heat sinks in order to improve the radiation in addition to the convection (the anodizing layer has an emissivity close to one, regardless of the color in the middle infrared).
• Enamelling of furnace pipes and metal ovens (enamel, glass and ceramics have an emissivity close to one in the mid-infrared regardless of color).
• Dark radiation surfaces in radioisotope generators (nuclear thermal current sources) of satellites.

The color of such layers is irrelevant for heat radiation at normal operating temperatures.

However, the metal absorbers of solar collectors are provided with a black coating (e.g. titanium oxynitride), which, however, reflects in the mid-infrared - they should absorb the thermal energy of the visible solar spectrum and, however, as little heat as possible even at an intrinsic temperature of over 100 ° C radiate.

With the help of thermal imaging cameras , unwanted heat losses in buildings can be detected; Hot or cold water pipes hidden in the brickwork can be located very precisely.

The body temperature of mammals is almost always higher than the ambient temperature (except in the sauna, for example), which is why the heat radiation of their body is clearly different from the ambient radiation. Since some snakes have at least two pit organs with a remarkably high temperature resolution of up to 0.003 K, they can locate their warm-blooded prey with sufficient accuracy even at night.

The WISE space telescope was used to measure thermal radiation from asteroids in order to estimate their size when they are too far away to be done using radar . Because the emissivity in the IR range is almost one, this is more precise than using the visual brightness, which also depends on the often very low albedo .

## Individual evidence

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11. Footnote 26 in Evans & Popp
12. ^ Benjamin Graf von Rumford: Mémoires sur la chaleur. French from Pictet, Geneva and Paris, 1804, limited preview in Google Book search.
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15. P. 305f in Lardner 1833
16. J. Steketee: Spectral emissivity of skin and pericardium. In: Physics in Medicine and Biology (Phys. Med. Biol.). Volume 18, Number 5, 1973.
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