Radiation (blackbody Emission Contd.)

Lecture 34, March 29, 2004

Radiation contd. Blackbody Emission contd.

Where h is Planck’s constant Co is the speed of light in a vacuum K is the Boltzmann constant If n (index of refraction) is independent of wavelength, we can recast this expression in terms of wavelength.

This is the Planck distribution for emission from a blackbody.

Wavelength is plotted on the x-axis, and emissive power is plotted on the y-axis. Note that the maximum energy occurs at increasing wavelengths as the temperature decreases. This can be described by Wiens law,

Band Emission If we integrate Planck’s distribution over a specific range of wavelengths, we can determine how much energy is emitted in that range of wavelengths. This is often very useful, and one application of doing this is to determine how much energy from a tungsten

filament goes into visible radiation (how much useful energy do we get out of the light bulb). If we integrate Planck’s distribution over all possible wavelengths, we arrive at the Stefan Boltzmann law.

Once we have integrated, we have summed the energy at every wavelength, and therefore have no more information about spectral variations. Instead, we could have integrated over a specific range of wavelengths to get information about that particular band.

Table 12.1 in your text has a very nice table of these fractions tabulated for convenient use. On to the details and definitions, Spectral intensity,

This is the most general description, where a surface can emit at any range of wavelengths and directions.

If we integrate over a hemisphere (0 < theta < pi/2) and (0 < phi < 2 pi) then we have,

We can then integrate over all wavelengths to determine the total energy emitted from the surface,

Which is what is given by the Stefan-Boltzman law. A surface which emits equally in all directions is called a diffuse surface.