Visible spectrum region
10 8
Spectral emissive power,
E
l,b (W/m 2
mm)
10 6
10 4
10 2
10 0
10 –2
10 –4
10 –1
1000 K
300 K
800 K
Solar radiation
l max T=2898 mm K
5800 K
2000 K
10 0
10 1
10 2
Wavelength, l (mm)
�
�
Performing integration over the entire wavelength, one obtains Stefan–
Boltzmann law for blackbody radiation as
∞
∞
E b (T) = E λ,b (λ, T) dλ =
2
πI λ (λ, T) dλ = σT
4 W/m
(11.10)
0
0
with the Stefan–Boltzmann constant
σ = f (C 1 , C 2 ) = 5.67 × 10
−8 W/m
2 K
4
However, for a real surface the emissive power is lower than Planck’s blackbody radiation (because the emissivity for the real surface is less than unity).
Therefore, the emissive power for the real surface is
E = εσT
4
(11.11)
Figure 11.6 shows emissive power versus wavelength over a wide range of
temperatures [1–4]. In general, emissive power increases with absolute temperature; emissive power for the black surface (solid lines) is greater than that
for the real gray surface (lower than the solid lines, depending on emissivity)
for a given temperature.
226
Analytical Heat Transfer
FIGURE 11.6
Spectral blackbody emissive power.