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 = e s 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 |
200-600 100 |
0.02-0.03 0.02 |
|
Steel Rough Surface Polished Oxidized Unoxidized Alloyed |
50 750-1050 200-600 100 500 |
0.95-0.98 0.52-0.56 0.8 0.08 0.35 |
|
Zinc Oxidized Unoxidized |
200-300 300 |
0.04-0.05 0.05 |