### 8.1.1. Blackbody Emission

The energy spectrum for radiation emitted by a blackbody is represented by:

| (8–4)

where:

- = refractive index

- = Planck’s constant

- = speed of light in vacuum

- = Boltzmann’s constant

Writing , you have:

| (8–5)

where = Stefan-Boltzmann constant:

| (8–6)

The total blackbody emission is simply the integral of over all frequencies:

| (8–7)

Note that the blackbody emission is proportional to the fourth power of the temperature and because of this strong dependence, radiation is usually unimportant or totally dominant for heat transfer.

The sun, for example, is approximately a blackbody at a temperature of 5700 K. The spectrum peaks in the yellow part of the visible spectrum.

Combustion temperatures are typically 1000 - 2000 K, with spectrum peaks in the near infra-red range. Note that the peak of the spectrum as a function of wavelength is at:

| (8–8)

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