# Degree of absorption

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The degree of absorption , also: degree of swallowing , indicates which part of the power of an incident wave (e.g. sound or electromagnetic radiation such as light ) is absorbed by a surface , i.e. H. is recorded. ${\ displaystyle \ alpha}$

## Fundamental correlations of the disturbed spread

• The emissivity ε is a measure of the (directional or non-directional) intensity for which the body itself is the source
• The degree of remission , usually also ρ , is a measure of the total reflected intensity that results from reflection and emission.
• The degree of absorption α is a measure of the intensity absorbed by the body.
• The transmittance τ is a measure of the transmitted intensity.
• The degree of dissipation δ is a measure of the intensity that has been converted into thermal energy , ie that has been “lost” through dissipation .
• The degree of reflection ρ is a measure of the reflected intensity that comes from outside.

In acoustics , the degree of transmission  τ is used as part of the degree of absorption  α , because for room acoustics it does not matter whether the sound energy in a room is lost through conversion into thermal energy or into the open air or into a neighboring room:

${\ displaystyle \ alpha = \ delta + \ tau}$

This results in the following for the sound:

{\ displaystyle {\ begin {alignedat} {2} \ Rightarrow & \ rho + \ alpha && = 1 \\\ Leftrightarrow & \ rho + (\ delta + \ tau) && = 1 \ end {alignedat}}}

In the case of electromagnetic radiation , on the other hand, absorption and transmission are dealt with separately, since the overall emission of a body is usually of interest here, rather than the direction. In this case, the degree of absorption is a measure of the "lost" intensity:

${\ displaystyle \ rho + \ tau + \ alpha = 1}$

I.e. the radiated energy (intensity) is partly reflected, partly let through, and the rest is absorbed ( "swallowed" by the medium ).

## Sound waves

In the case of sound waves , the degree of absorption indicates how large the absorbed portion of the total incident sound is, expressed in each case in sound intensities : ${\ displaystyle I}$

${\ displaystyle \ alpha = {\ frac {I _ {\ mathrm {a}}} {I_ {0}}}}$
• at α = 1 the entire incident sound is absorbed, i.e. H. a reflection no longer takes place (example: open window or ideal anechoic room ).
• at α = 0.5 50% of the sound energy is absorbed and 50% reflected.
• at α = 0 there is no absorption, the entire incident sound is reflected.

Depending on the sound absorption system, the absorption coefficient is usually between 0.2 and 0.8, depending on the surface material and the frequency . Occasionally values ​​greater than 1 are given. This is determined under practical conditions and takes into account the fact that the effective area of ​​an absorber is slightly larger than its geometric area.

The ratio of absorbed and reflected sound energy plays a decisive role for the sound sensation in a room :${\ displaystyle {\ tfrac {\ alpha} {\ rho}} =?}$

### Absorbency

The absorption capacity  A (also equivalent absorption area or area of ​​open window ) of a wall indicates how small the wall could be with the same absorption effect if it would absorb ideally:

${\ displaystyle A = \ alpha \ cdot S}$

with the wall area  S in m².

The equivalent absorption area is given in the unit Sabin .

Since the absorption effect in a material increases with the speed of sound , the absorber should be effectively at the maximum speed at wall distance  d / 4 or have a corresponding density . The sound pressure minimum, which is exactly at the point of the rapid maximum, is easier to measure .

Part of the radiation hitting the surface of a body is usually reflected , part is transmitted through the body and the rest is absorbed. The absorbed energy increases the internal energy of the body. The degree of absorption (also absorption coefficient or spectral absorption coefficient SAK) indicates which fraction of the incident radiation is absorbed. It can assume values ​​between 0 and 1, the extreme values ​​0 and 1 are only approximately reached in practice. The degree of absorption can depend on the direction of incidence and the frequency of the incident radiation. Depending on whether these directional and frequency distributions should be explicitly taken into account or not, four different degrees of absorption can be specified.

### Directed spectral absorption

The spectral irradiance (unit: W · m −2 · Hz −1 · sr −1 ) to which a body is exposed indicates the radiation power at the frequency from the direction given by the polar angle and the azimuth angle per area, per frequency width and hits the body per solid angle . ${\ displaystyle K _ {\ Omega \ nu} (\ beta, \ varphi, \ nu)}$ ${\ displaystyle \ nu}$ ${\ displaystyle \ beta}$ ${\ displaystyle \ varphi}$

The directional spectral absorption coefficient of a body indicates which fraction of the spectral irradiance incident at the frequency from the angle and given direction is absorbed by a surface element of the body: ${\ displaystyle \ nu}$${\ displaystyle \ beta}$${\ displaystyle \ varphi}$${\ displaystyle K _ {\ Omega \ nu} (\ beta, \ varphi, \ nu)}$

${\ displaystyle a _ {\ nu} ^ {\ prime} (\ beta, \ varphi, \ nu, T) = {\ frac {K _ {\ Omega \ nu} ^ {\ mathrm {abs}} (\ beta, \ varphi, \ nu)} {K _ {\ Omega \ nu} (\ beta, \ varphi, \ nu)}} \,}$.

The directed spectral absorption coefficient is a material property and does not depend on the properties of the spectral irradiance (originating from external radiation sources). As a rule, it is directional and frequency-dependent and is also strongly influenced by the surface properties of the body (e.g. roughness).

### Hemispheric spectral absorbance

The spectral irradiance (unit: W m −2 Hz −1 ) to which a body is exposed indicates which radiation power hits the body at the frequency from the entire half-space per unit area and per unit frequency interval: ${\ displaystyle E _ {\ nu} (\ nu)}$${\ displaystyle \ nu}$

${\ displaystyle E _ {\ nu} (\ nu) = \ int _ {\ mathrm {half space}} \, K _ {\ Omega \ nu} (\ beta, \ varphi, \ nu) \, \ cos (\ beta) \, \ mathrm {d} \ Omega}$.

The cosine factor accounts for the fact that during irradiation from any through and only in this direction perpendicular projection given direction of the surface occurs as the effective receiving surface. is a solid angle element: ${\ displaystyle \ varphi}$${\ displaystyle \ beta}$${\ displaystyle \ cos (\ beta) \ mathrm {d} A}$${\ displaystyle \ mathrm {d} A}$${\ displaystyle \ mathrm {d} \ Omega}$

${\ displaystyle \ mathrm {d} \ Omega = \ sin (\ varphi) \, \ mathrm {d} \ beta \, \ mathrm {d} \ varphi}$.

The hemispherical spectral absorption coefficient of a body indicates which fraction of the spectral irradiance incident at the frequency from the half-space is absorbed by a surface element of the body: ${\ displaystyle \ nu}$${\ displaystyle E _ {\ nu} (\ nu)}$

${\ displaystyle a _ {\ nu} (\ nu, T) = {\ frac {E _ {\ nu} ^ {\ mathrm {abs}} (\ nu)} {E _ {\ nu} (\ nu)}} \ ,}$
${\ displaystyle = {\ frac {1} {E _ {\ nu} (\ nu)}} \, \ int _ {\ mathrm {half-space}} \, a _ {\ nu} ^ {\ prime} (\ beta, \ varphi, \ nu, T) K _ {\ Omega \ nu} (\ beta, \ varphi, \ nu) \, \ cos (\ beta) \, \ mathrm {d} \ Omega \,}$.

### Directed total absorption coefficient

The irradiance (unit: W m −2 sr −1 ) to which a body is exposed indicates which radiation power hits the body at all frequencies from the given direction through the angle and direction per unit area and per solid angle unit: ${\ displaystyle K _ {\ Omega} (\ beta, \ varphi)}$${\ displaystyle \ beta}$${\ displaystyle \ varphi}$

${\ displaystyle K _ {\ Omega} (\ beta, \ varphi) = \ int _ {\ nu = 0} ^ {\ infty} \, K _ {\ Omega \ nu} (\ beta, \ varphi, \ nu) \ , \ mathrm {d} \ nu}$.

The directed total absorption coefficient of a body indicates what fraction of the radiation density incident at all frequencies from the angle and given direction is absorbed by a surface element of the body: ${\ displaystyle \ beta}$${\ displaystyle \ varphi}$${\ displaystyle K _ {\ Omega} (\ beta, \ varphi)}$

${\ displaystyle a ^ {\ prime} (\ beta, \ varphi, T) = {\ frac {K _ {\ Omega} ^ {\ mathrm {abs}} (\ beta, \ varphi)} {K _ {\ Omega} (\ beta, \ varphi)}}}$
${\ displaystyle = {\ frac {1} {K _ {\ Omega} (\ beta, \ varphi)}} \, \ int _ {\ nu = 0} ^ {\ infty} \, a _ {\ nu} ^ { \ prime} (\ beta, \ varphi, \ nu, T) K _ {\ Omega \ nu} (\ beta, \ varphi, \ nu) \, \ mathrm {d} \ nu}$.

### Total hemispherical absorption coefficient

The radiation intensity (unit: W m −2 ) to which a body is exposed indicates which radiation power hits the body at all frequencies from the entire half-space per unit area: ${\ displaystyle E}$

${\ displaystyle E = \ int _ {\ nu = 0} ^ {\ infty} \ int _ {\ mathrm {half-space}} \, K _ {\ Omega \ nu} (\ beta, \ varphi, \ nu) \, \ cos (\ beta) \, \ mathrm {d} \ Omega \, \ mathrm {d} \ nu}$.

The hemispherical total absorption coefficient of a body indicates which fraction of the irradiance incident on all frequencies from the half-space is absorbed by a surface element of the body: ${\ displaystyle E}$

${\ displaystyle a (T) \, = {\ frac {E ^ {\ mathrm {abs}}} {E}} = {\ frac {1} {E}} \, \ int _ {0} ^ {\ infty} \, \ int _ {\ mathrm {half space}} \, a _ {\ nu} ^ {\ prime} (\ beta, \ varphi, \ nu, T) K _ {\ Omega \ nu} (\ beta, \ varphi, \ nu) \, \ cos (\ beta) \, \ mathrm {d} \ Omega \, \ mathrm {d} \ nu}$.

All beam sizes and degrees of absorption can of course also be formulated as a function of the wavelength instead of the frequency.

### properties

(average) degree of absorption for solar radiation
material α
Aluminum polished 0.20
asphalt 0.93
Leaves , green 0.71 ... 0.79
Roofing felt , black 0.82
Iron, rough 0.75
Iron, galvanized 0.38
Gold , polished 0.29
Copper, oxidized 0.70
Copper polished 0.18
Marble , white 0.46
soot 0.96 (approx.)
slate 0.88
Snow , clean 0.20 ... 0.35
Silver , polished 0.13
Brick , red 0.75
Zinc white 0.22

The directional spectral absorption coefficient describes the direction and frequency dependence of the radiation absorption . The hemispherical spectral absorption coefficient describes only the frequency dependence, the directed total absorption coefficient only the directional dependence and the hemispherical total absorption coefficient only the total absorbed radiant power.

Only the directed spectral absorption coefficient is a material property of the body under consideration. The other degrees of absorption also depend on the direction and frequency distribution of the incident radiation (determined by external radiation sources). For example, white paint has a low spectral absorption coefficient in the visible frequency range, i.e. it only absorbs a small proportion of incident solar radiation : the total absorption coefficient is low for radiation in this frequency range. In the long-wave infrared, on the other hand, it has a high degree of spectral absorption, i.e. it absorbs a high proportion of incident thermal radiation (emitted at room temperature) : the total degree of absorption is high for radiation in this frequency range.

According to Kirchhoff's law of radiation , the directional spectral absorption coefficient for every body is the same as the directional spectral emissivity . For the other degrees of absorption and emissivity, the same applies only under additional conditions.

An ideally absorbing body that completely absorbs all electromagnetic radiation that hits it is called a black body . According to Kirchhoff's law of radiation, it is also an ideal emitter that emits the greatest physically possible thermal radiation output. The emitted radiation also has a universal frequency distribution, which is described by Planck's law of radiation .

A body whose directional spectral absorption factor does not depend on the direction is a diffuse absorber. A body whose directional spectral absorption factor does not depend on the frequency is a gray body . In both cases, there are often considerable simplifications for radiation calculations, so that real bodies are often - as far as possible - approximately viewed as diffuse absorbers and gray bodies.

## literature

• HD Baehr, K. Stephan: Heat and mass transfer . 4th edition. Springer, Berlin 2004, ISBN 3-540-40130-X , chap. 5: thermal radiation.