What is Spectral Emissivity?

Spectral emissivity and spectral emittance are optical properties of materials. The difference between the two terms, emissivity and emittance, used to be a source of arguments between scientists and engineers, but in practice, they have come to mean essentially the same thing.

Mathematically, spectral emissivity can be defined as the spectral distribution of the monochromatic emissivity of material and that, in turn, is described as the ratio of the actual (emitted) radiance of an object and that of a perfect blackbody radiator at the same temperature.

Sounds simple, and in fact, if you break it down into each of the component parts, “perfect blackbody” and “radiance” and understand what they mean, it is!

What is a Perfect Black Body?

A perfect blackbody is a mathematical construct; none exist in reality (as far as we know except possibly for Black Holes, but that’s a difficult area of science – no one has actually been to one, as far as we know), but blackbody simulators can, and have been, designed and built.

A perfect simulator would have a reflectivity of zero and a transparency of zero (it’s opaque), but real ones can come reasonably close, for instance, within a fraction of one percent of perfect, over some portions of the electromagnetic (EM) spectrum.

Fortunately, visible, infrared and UV portions of the EM spectrum are reasonably “easy” for creation of Blackbody simulators. However, the cost of a Blackbody simulator goes up considerably as a device gets closer to perfection. One with an emissivity error of 1.0% (emissivity of 0.99) is usually good enough to calibrate most commercial visible & short wavelength infrared* temperature radiation thermometers, and are not terribly expensive.

That’s all relative, of course.  A 0.1% device (emissivity of 0.999) costs usually orders of magnitude more and ones with 0.01% closeness(emissivity of 0.9999) are nearly impossible (I am not certain I have ever actually heard or seen anything with that level of emissivity).

As a result of the physical fact that all objects above a temperatures of absolute zero (0 K or -273.15  °C) emit electromagnetic radiation due to its temperature, or thermal electromagnetic radiation, according to Planck’s Law of Thermal Radiation.

This means that an object with zero reflectance and zero transmittance must, by definition be emitting with an emissivity of 1.0. This is due to conservation of energy, expressed in the form of Kirchoff’s Law, saying that the the coefficients of emittance, reflectance and transmittance (or emissivity, reflectivity and transmissivity) must add up to one.

Also, it means that the spectral emissivity and spectral absorptivity of any object must be equal. That in turn means that the total emittance and absorbtance of an obect must be equal.

Radiance is the amount of radiated electromagnetic power emitted per unit surface area per unit wavelength of a object that is due to the motion of molecules within the object.

That motion is related to the object’s temperature and the radiation is called “thermal electromagnetic radiation” or just “Thermal Radiation” for short. Its units, consistent with the physical concept of power (the rate of doing work), is usually expressed in watts or microwatts.

There always seems to be a confusion among newcomers to the concept of radiant energy and radiant power.

The mechanism by which radiation transmits energy from one place to another is often described as “Electromagnetic Energy”. But the quantitative (measurable) amount of actual energy transferred is expressed in the physical units of energy such as joules, calories, British Thermal Units (BTUs), watt-seconds, Kilowatt-Hours and the like. These are the things we pay for when we purchase energy like electrical energy, gasoline (petrol or benzene), methane or propane.

The rate at which measurable energy is transferred (both emitted, generated, used and absorbed) is in units of Power, that is, Energy per unit Time, or Watts, or Kilowatts, or calories/second.

The power rating of a light bulb for example, is expressed in Watts. But the cost of using it depends upon the electrical power it uses and the length of time that we use it in watts x hours, or in units of watt-hours.

One Watt-hour (often abbreviated as WH) is equal to a Kilowatt-Hour/1000 or KWH/1000. The charge an Electric Utility Company makes to us is in units of KWH or Kilojoules.

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* Short wavelength infrared is a relative term, too. It can be explained easiest (I think) in terms of Planck’s Law. Anyone familiar with the asymmetrical shape of the radiance versus temperature distribution of emitted thermal radiation realizes that “short wavelength” refers to measurements made (and device that function) to the short wavelength side of the peak of the curve.

Since the curve varies with temperature, the “definition” of short and long wavelength depends upon the temperature being measured. Fortunately there’s a relatively simple mathematical formula that enables one to determine where that peak lies, and thence, where the short and long wavelength regions begin.

It is called Wein’s Displacement Law and is ably described on a Wikipedia web page as follows:

Wien’s displacement law is a law of physics that states that there is an inverse relationship between the wavelength of the peak of the emission of a black body and its temperature.

$lambda_{mathrm{max}} = frac{b}{T}$

where


λ.max is the peak wavelength in meters,
T is the temperature of the blackbody in kelvins (K), and
b is a constant of proportionality, called Wien’s displacement constant and is equal to 2.8977685±51×10-3 m·K (2002 CODATA recommended value)

The two digits between the parentheses denotes the uncertainty (the standard deviation at 68.27% confidence level) in the two least significant digits of the mantissa.

There is a much shorter and possibly easier-to-read article on this subject on webpage: Thermal Emission Spectrometer/ Arizona State University that you can see by clicking here (http://tes.asu.edu/MARS_SURVEYOR/MGSTES/TES_emissivity.html)