The Stefan-Boltzmann law for the net rate of heat exchange by radiation between a blackbody and a surrounding medium should be modified for real surfaces. For non-blackbody surfaces, the spectral radiation intensity does not obey the Planck distribution and the emitted radiation has preferred direction for emission.
The modified Stefan-Boltzmann law for a non-blackbody is given by:
Qradiation = ε σ A ( Ts4 - Ta4 )
where e is the emissivity of the radiating surface defined as the ratio of the emissive power of the surface to the emissive power of a blackbody at the same temperature. Materials are assigned an emissivity value between 0 and 1.0. A blackbody, therefore, has an emissivity of 1.0 and a perfect reflector has an emissivity of 0.
The emissivity is a material property that is dependent on the surface temperature and the surface finish. The following table lists the emissivity values for some materials:
| Metal |
|
Temperature (ºC)
|
Emissivity
|
|---|
Aluminum
|
Polished
Rough surface
Oxidized
|
50 - 500
20 - 50
200
|
0.04 - 0.06
0.06 - 0.07
0.11
|
Brass
|
Polished
Rolled Sheet
Unoxidized
Oxidized
|
200
20
25
200
|
0.03
0.06
0.035
0.61
|
Bronze
|
Polished
|
50
|
0.1
|
Carbon
|
Filament
Graphite
Unoxidized
|
1000 - 1400
0 - 3600
100
|
0.53
0.7 - 0.8
0.81
|
Copper
|
Calorized
Commercial
Polished
Unoxidized
Oxidized
|
100
20
50 - 100
100
50
|
0.26
0.07
0.02
0.02
0.6 - 0.7
|
Glass
|
|
20 - 100
|
0.94 - 0.91
|
Cast Iron
|
Rusted
Oxidized
Unoxidized
|
25
200
100
|
0.65
0.64
0.21
|
Lead
|
Oxidized
Unoxidized
|
200
200
|
0.96
0.63
|
Nickel
|
Polished
Oxidized
Unoxidized
|
200 = 400
200
25
|
0.05 - 0.1
0.37
0.045
|
Platinum
|
Polished
Unoxidized
|
200 - 600
25
|
0.05 - 0.1
0.037
|
Porcelain
|
|
20
|
0.92
|
Quartz
|
|
----
|
0.92
|
Rubber
|
Hard
Soft
|
20
20
|
0.95
0.86
|
Silicon
|
|
----
|
0.92
|
Silver
|
Polished
Unoxidized
|
20 - 600
100
|
0.02 - 0.03
0.02
|
Steel
|
Rough Surface
Polished
Oxidized
Unoxidized
Alloyed
|
50
750 - 1050
200 - 600
100
500
|
0.95 - 0.98
052 - 0.56
0.8
0.08
0.35
|
Zinc
|
Oxidized
Unoxidized
|
200 - 300
300
|
0.04 - 0.05
0.05
|