Emissivity

Encyclopedia

The

by a particular material to energy radiated by a black body

at the same temperature. A true black body

would have an ε = 1 while any real object would have ε < 1. Emissivity is a dimensionless quantity

.

In general, the duller and blacker a material is, the closer its emissivity is to 1. The more reflective

a material is, the lower its emissivity. Highly polished silver

has an emissivity of about 0.02.

, emission angle

, and wavelength

. A typical physical

assumption is that a surface's spectral emissivity and absorptivity do not depend on wavelength, so that the emissivity is a constant. This is known as the "gray body assumption".

Although it is common to discuss the "emissivity of a material" (such as the emissivity of highly polished silver), the emissivity of a material does in general depend on its thickness. The emissivities quoted for materials are for samples of infinite thickness (which, in practice, means samples which are optically thick

) — thinner samples of material will have reduced emissivity.

When dealing with non-black surfaces, the deviations from ideal black body behavior are determined by both the geometrical

structure and the chemical composition

, and follow Kirchhoff's law of thermal radiation

: emissivity equals absorptivity (for an object in thermal equilibrium), so that an object that does not absorb all incident light will also emit less radiation than an ideal black body.

Most emissivities found in handbooks and on websites of many infrared imaging and temperature sensor companies are the type discussed here, total emissivity. However, the distinction needs to be made that the wavelength-dependent or spectral emissivity is the more significant parameter to be used when one is seeking an emissivity correction for a temperature measurement device.

Thus, it is important to understand the distinction between total and spectral emissivity and where they apply.

varies according to cloud cover and the concentration of gases that absorb and emit energy in the thermal infrared

(i.e., wavelengths around 8 to 14 micrometre

s). These gases are often called greenhouse gases, from their role in the greenhouse effect

. The main naturally-occurring greenhouse gases are water vapor, carbon dioxide, methane, and ozone. The major constituents of the atmosphere, N

for a blackbody at temperature T and emissivity .

For a uniform medium of optical depth

radiative transfer

means that the radiation will be reduced by a factor . The optical depth is often approximated by the ratio of the emitting frequency to the frequency where all raised to an exponent β. For cold dust clouds in the interstellar medium β is approximately two. Therefore Q becomes,

. (, is the frequency where )

and at a given wavelength, a certain fraction of the radiation of that wavelength just inside one wall will leave that wall and enter the other. By Kirchhoff's law of thermal radiation

for a given wavelength, whatever portion of the radiation incident on a surface, from either side, that does not pass through the surface as emission to the other side, is reflected. When this reflected radiation is neglected, the proportion of radiation emitted from the first wall is , and the proportion of that entering the second wall is therefore .

When reflection is taken into account, what does not enter the second wall is reflected back to the first wall, initially in an amount . A fraction of this is then reflected back to the second wall, thereby augmenting the original emission from the first wall. These reflections bounce back and forth in diminishing quantity. Solving for the steady state then gives as the total proportion of radiation entering the second wall

This formula is symmetric, and the proportion of radiation just inside the second wall that enters the first wall is the same. This is true regardless of what reflections and absorptions take place inside the two walls away from their facing surfaces, since the formula only concerns the radiation leaving one wall for the other.

The quantities in these formulas are intensities

rather than amplitude

s, the appropriate choice when the walls are many wavelengths apart as the reflected and transmitted beams will then combine incoherently

. When the walls are only a few wavelengths apart, as arises for example with the thin film

s used in the manufacture of optical coating

s, the reflections tend to combine coherently

, resulting in interference. In such a situation the above formula becomes invalid, and one must then add amplitudes instead of intensities, taking into account the phase

shift as the gap is traversed and the phase reversal that occurs with reflection, concerns that did not arise in the incoherent large-gap or thick-film case.

**emissivity**of a material (usually written*ε*or*e*) is the relative ability of its surface to emit energy by radiation. It is the ratio of energy radiatedRadiation

In physics, radiation is a process in which energetic particles or energetic waves travel through a medium or space. There are two distinct types of radiation; ionizing and non-ionizing...

by a particular material to energy radiated by a black body

Black body

A black body is an idealized physical body that absorbs all incident electromagnetic radiation. Because of this perfect absorptivity at all wavelengths, a black body is also the best possible emitter of thermal radiation, which it radiates incandescently in a characteristic, continuous spectrum...

at the same temperature. A true black body

Black body

A black body is an idealized physical body that absorbs all incident electromagnetic radiation. Because of this perfect absorptivity at all wavelengths, a black body is also the best possible emitter of thermal radiation, which it radiates incandescently in a characteristic, continuous spectrum...

would have an ε = 1 while any real object would have ε < 1. Emissivity is a dimensionless quantity

Dimensionless quantity

In dimensional analysis, a dimensionless quantity or quantity of dimension one is a quantity without an associated physical dimension. It is thus a "pure" number, and as such always has a dimension of 1. Dimensionless quantities are widely used in mathematics, physics, engineering, economics, and...

.

In general, the duller and blacker a material is, the closer its emissivity is to 1. The more reflective

Reflectivity

In optics and photometry, reflectivity is the fraction of incident radiation reflected by a surface. In general it must be treated as a directional property that is a function of the reflected direction, the incident direction, and the incident wavelength...

a material is, the lower its emissivity. Highly polished silver

Silver

Silver is a metallic chemical element with the chemical symbol Ag and atomic number 47. A soft, white, lustrous transition metal, it has the highest electrical conductivity of any element and the highest thermal conductivity of any metal...

has an emissivity of about 0.02.

## Explanation

Emissivity depends on factors such as temperatureTemperature

Temperature is a physical property of matter that quantitatively expresses the common notions of hot and cold. Objects of low temperature are cold, while various degrees of higher temperatures are referred to as warm or hot...

, emission angle

Angle

In geometry, an angle is the figure formed by two rays sharing a common endpoint, called the vertex of the angle.Angles are usually presumed to be in a Euclidean plane with the circle taken for standard with regard to direction. In fact, an angle is frequently viewed as a measure of an circular arc...

, and wavelength

Wavelength

In physics, the wavelength of a sinusoidal wave is the spatial period of the wave—the distance over which the wave's shape repeats.It is usually determined by considering the distance between consecutive corresponding points of the same phase, such as crests, troughs, or zero crossings, and is a...

. A typical physical

Physical chemistry

Physical chemistry is the study of macroscopic, atomic, subatomic, and particulate phenomena in chemical systems in terms of physical laws and concepts...

assumption is that a surface's spectral emissivity and absorptivity do not depend on wavelength, so that the emissivity is a constant. This is known as the "gray body assumption".

Although it is common to discuss the "emissivity of a material" (such as the emissivity of highly polished silver), the emissivity of a material does in general depend on its thickness. The emissivities quoted for materials are for samples of infinite thickness (which, in practice, means samples which are optically thick

Optical depth

Optical depth, or optical thickness, is a measure of transparency. Optical depth is defined by the negative logarithm of the fraction of radiation that is not scattered or absorbed on a path...

) — thinner samples of material will have reduced emissivity.

When dealing with non-black surfaces, the deviations from ideal black body behavior are determined by both the geometrical

Geometry

Geometry arose as the field of knowledge dealing with spatial relationships. Geometry was one of the two fields of pre-modern mathematics, the other being the study of numbers ....

structure and the chemical composition

Chemical compound

A chemical compound is a pure chemical substance consisting of two or more different chemical elements that can be separated into simpler substances by chemical reactions. Chemical compounds have a unique and defined chemical structure; they consist of a fixed ratio of atoms that are held together...

, and follow Kirchhoff's law of thermal radiation

Kirchhoff's law of thermal radiation

In thermodynamics, Kirchhoff's law of thermal radiation, or Kirchhoff's law for short, is a general statement equating emission and absorption in heated objects, proposed by Gustav Kirchhoff in 1859, following from general considerations of thermodynamic equilibrium and detailed balance.An object...

: emissivity equals absorptivity (for an object in thermal equilibrium), so that an object that does not absorb all incident light will also emit less radiation than an ideal black body.

Most emissivities found in handbooks and on websites of many infrared imaging and temperature sensor companies are the type discussed here, total emissivity. However, the distinction needs to be made that the wavelength-dependent or spectral emissivity is the more significant parameter to be used when one is seeking an emissivity correction for a temperature measurement device.

Thus, it is important to understand the distinction between total and spectral emissivity and where they apply.

## Emissivity of Earth's atmosphere

The emissivity of Earth's atmosphereAtmosphere

An atmosphere is a layer of gases that may surround a material body of sufficient mass, and that is held in place by the gravity of the body. An atmosphere may be retained for a longer duration, if the gravity is high and the atmosphere's temperature is low...

varies according to cloud cover and the concentration of gases that absorb and emit energy in the thermal infrared

Infrared

Infrared light is electromagnetic radiation with a wavelength longer than that of visible light, measured from the nominal edge of visible red light at 0.74 micrometres , and extending conventionally to 300 µm...

(i.e., wavelengths around 8 to 14 micrometre

Micrometre

A micrometer , is by definition 1×10-6 of a meter .In plain English, it means one-millionth of a meter . Its unit symbol in the International System of Units is μm...

s). These gases are often called greenhouse gases, from their role in the greenhouse effect

Greenhouse effect

The greenhouse effect is a process by which thermal radiation from a planetary surface is absorbed by atmospheric greenhouse gases, and is re-radiated in all directions. Since part of this re-radiation is back towards the surface, energy is transferred to the surface and the lower atmosphere...

. The main naturally-occurring greenhouse gases are water vapor, carbon dioxide, methane, and ozone. The major constituents of the atmosphere, N

_{2}and O_{2}, do not absorb or emit in the thermal infrared.## Astrophysical graybody

The monochromatic flux density radiated by a greybody at frequency through solid angle is given by where is the Planck functionPlanck's law of black body radiation

In physics, Planck's law describes the amount of energy emitted by a black body in radiation of a certain wavelength . The law is named after Max Planck, who originally proposed it in 1900. The law was the first to accurately describe black body radiation, and resolved the ultraviolet catastrophe...

for a blackbody at temperature T and emissivity .

For a uniform medium of optical depth

Optical depth

Optical depth, or optical thickness, is a measure of transparency. Optical depth is defined by the negative logarithm of the fraction of radiation that is not scattered or absorbed on a path...

radiative transfer

Radiative transfer

Radiative transfer is the physical phenomenon of energy transfer in the form of electromagnetic radiation. The propagation of radiation through a medium is affected by absorption, emission and scattering processes. The equation of radiative transfer describes these interactions mathematically...

means that the radiation will be reduced by a factor . The optical depth is often approximated by the ratio of the emitting frequency to the frequency where all raised to an exponent β. For cold dust clouds in the interstellar medium β is approximately two. Therefore Q becomes,

. (, is the frequency where )

## Emissivity between two walls

Given two parallel walls whose facing surfaces have respective emissivitiesand at a given wavelength, a certain fraction of the radiation of that wavelength just inside one wall will leave that wall and enter the other. By Kirchhoff's law of thermal radiation

Kirchhoff's law of thermal radiation

In thermodynamics, Kirchhoff's law of thermal radiation, or Kirchhoff's law for short, is a general statement equating emission and absorption in heated objects, proposed by Gustav Kirchhoff in 1859, following from general considerations of thermodynamic equilibrium and detailed balance.An object...

for a given wavelength, whatever portion of the radiation incident on a surface, from either side, that does not pass through the surface as emission to the other side, is reflected. When this reflected radiation is neglected, the proportion of radiation emitted from the first wall is , and the proportion of that entering the second wall is therefore .

When reflection is taken into account, what does not enter the second wall is reflected back to the first wall, initially in an amount . A fraction of this is then reflected back to the second wall, thereby augmenting the original emission from the first wall. These reflections bounce back and forth in diminishing quantity. Solving for the steady state then gives as the total proportion of radiation entering the second wall

This formula is symmetric, and the proportion of radiation just inside the second wall that enters the first wall is the same. This is true regardless of what reflections and absorptions take place inside the two walls away from their facing surfaces, since the formula only concerns the radiation leaving one wall for the other.

The quantities in these formulas are intensities

Intensity (physics)

In physics, intensity is a measure of the energy flux, averaged over the period of the wave. The word "intensity" here is not synonymous with "strength", "amplitude", or "level", as it sometimes is in colloquial speech...

rather than amplitude

Amplitude

Amplitude is the magnitude of change in the oscillating variable with each oscillation within an oscillating system. For example, sound waves in air are oscillations in atmospheric pressure and their amplitudes are proportional to the change in pressure during one oscillation...

s, the appropriate choice when the walls are many wavelengths apart as the reflected and transmitted beams will then combine incoherently

Coherence (physics)

In physics, coherence is a property of waves that enables stationary interference. More generally, coherence describes all properties of the correlation between physical quantities of a wave....

. When the walls are only a few wavelengths apart, as arises for example with the thin film

Thin film

A thin film is a layer of material ranging from fractions of a nanometer to several micrometers in thickness. Electronic semiconductor devices and optical coatings are the main applications benefiting from thin film construction....

s used in the manufacture of optical coating

Optical coating

An optical coating is one or more thin layers of material deposited on an optical component such as a lens or mirror, which alters the way in which the optic reflects and transmits light. One type of optical coating is an antireflection coating, which reduces unwanted reflections from surfaces, and...

s, the reflections tend to combine coherently

Coherence (physics)

In physics, coherence is a property of waves that enables stationary interference. More generally, coherence describes all properties of the correlation between physical quantities of a wave....

, resulting in interference. In such a situation the above formula becomes invalid, and one must then add amplitudes instead of intensities, taking into account the phase

Phase (waves)

Phase in waves is the fraction of a wave cycle which has elapsed relative to an arbitrary point.-Formula:The phase of an oscillation or wave refers to a sinusoidal function such as the following:...

shift as the gap is traversed and the phase reversal that occurs with reflection, concerns that did not arise in the incoherent large-gap or thick-film case.

## See also

- Radiant barrierRadiant barrierRadiant barriers or reflective barriers inhibit heat transfer by thermal radiation. Thermal energy may also be transferred via conduction or convection, however, and radiant barriers do not necessarily protect against heat transfer via conduction or convection....
- ReflectivityReflectivityIn optics and photometry, reflectivity is the fraction of incident radiation reflected by a surface. In general it must be treated as a directional property that is a function of the reflected direction, the incident direction, and the incident wavelength...
- Thermal radiationThermal radiationThermal radiation is electromagnetic radiation generated by the thermal motion of charged particles in matter. All matter with a temperature greater than absolute zero emits thermal radiation....
- Form factor (radiative transfer)
- Sakuma–Hattori equation

## External links

- Emissivity of some common materials
- An open community-focused website & directory with resources related to spectral emissivity and emittance. On this site, the focus is on available data, references and links to resources related to spectral emissivity as it is measured & used in thermal radiation thermometry and thermography (thermal imaging)