Xmax = wavelength of peak intensity (tm)
T = Temperature of the object (K)
C3 = a radiation constant (2898 [tm K)
This formula is obtained by taking the derivative of Plank's law (Equation 3-1)
with respect to wavelength, X, and setting the result equal to zero. Another useful
formula when considering EM emissions is the Stefan-Boltzmann Law. This law states
that the total amount of radiation per unit area, M, emitted by an object can be described
by:
M = go-T4 (3-3)
M = total radiant power emitted by object (W/m2)
S= emissivity of objects' surface
T = Temperature of the object (K)
c = Stefan-Boltzmann constant (5.67 x 10-8 W/m2-K4)
The Stefan-Boltzmann law is simply the integration of Planck's law over all
wavelengths. This relationship also contains a factor to account for the surface
characteristic of the object: emissivity. Emissivity can be summarized by the following
relationship:
(A, T) IAT) (3-4)
Ib (A, T)
S= emissivity of the objects' surface
Io = Intensity of the radiation emitted by the surface
Ib = Intensity of radiation emitted by a black body (perfect emitter)
Another useful relationship describes what happens to the total radiation flux
incident on an object. The total incident flux is the sum of the reflected, transmitted, and
absorbed radiation. The behavior is illustrated in Figure 3-1 and is defined as:
0, =0, +O +0+D (3-5)
i = Total incident flux
Or = Total flux reflected by the surface