Physical principles

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What physical processes determine emissivity?

All matter emits radiant energy, also referred to as thermal radiation, simply as a consequence of its temperature. The mechanism of emission is related to energy released by the constant motion of the constituent atoms or molecules of which the matter is composed. In similar fashion radiant energy emitted by the surroundings is partially absorbed by a material and converted into heat.

In thermal radiation there is an ideal entity called a blackbody (a term introduced by Kirchhoff) that absorbs all radiant energy incident on it and emits the maximum possible amount of radiant energy at any given temperature. This is an ideal concept since there is no real material that can completely absorb all radiation incidence on it. All real materials reflect part of the incident radiation on them and emit less radiant energy than a blackbody at the same temperature.

Emissivity can be calculated for a specularly reflecting (mirror-like) material surface by applying Maxwell's equations and it depends on the electrical and optical properties of the material.

The emissivity of a metal is determined largely by the behaviour of the free electrons within the material whilst for a dielectric it is largely due to the bound electrons.

Why is emissivity important?

At high temperatures or in evacuated environments thermal radiation is the main mode of heat transfer.

Total emissivity governs the amount of thermal radiation lost or gained by an object and can therefore either cool or heat it, respectively. The reliable prediction of energy gains and losses to and from such structures as buildings, greenhouses, radomes, space vehicles and industrial process plant has become an important part of energy conservation and control.

Finally, emissivity is required for radiation thermometry, i.e. to deduce the temperature of objects from a measurement of their thermal radiation and use of Planck's radiation law.

Physical laws

Planck radiation law: relates the spectral radiance Lλ of a blackbody to its absolute temperature T. It is the basis for all thermal radiation measurements. All of the other important relationships can be derived from this equation:



c1
and c2 are the radiation constants and λ is the wavelength.

  

Stefan-Boltzmann equation: determines the radiation emitted over all wavelengths Mλ at a particular temperature T:



where σ is the Stefan-Boltzmann constant. This equation can be derived by integrating the Planck equation over all wavelengths.

Wien's displacement equation: the blackbody spectral radiance is characterised by a maximum (see the illustration of blackbody radiation) and the wavelength of this maximum, λmax, depends on temperature. λmax may be obtained by differentiating the spectral radiance with respect to λ and setting the result equal to zero:

λmaxĚT = constant = 2897.77 ÁmĚK

Kirchhoff's law of radiation: for any body in thermal equilibrium the emitted power equals the absorbed power.

A number of consequences follow:

- the total emissivity equals the total absorptivity,
ε = α
 
the spectral emissivity equals the spectral absorptivity, ελ = αλ
- ελ = 1 - αλ for opaque bodies

Conservation of energy:

α + ρ + τ = 1

where
α = absorptivity,
ρ = reflectivity,
τ = transmissivity

 

Gustav Kirchhoff (1824-87) showed that the rate of emission of thermal energy from a body is equal to the rate at which it absorbs thermal energy.

 


 

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