# Q & A: radiator thermal emissivity

Q:
In an old house, the heating system uses radiators, which are hollow metal devices through which hot water or steam circulates. In one room the radiator has a dark color (emissitivity = 0.891). It has a temperature of 62.5 oC. The new owner of the house paints the radiator a lighter color (emissitivity = 0.407). Assuming that it emits the same radiant power as it did before being painted, what is the temperature (in degrees Celsius) of the newly painted radiator?
- kurt (age 40)
Australia
A:

Although this has the general sound of a homework problem, which we would not answer, it does raise some issues worth discussing. The calculation called for is simple enough, since you just use that the thermal emission is proportional to T4, where T is the absolute temperature. More importantly, the answer you get by setting the problem up that way has very little to do with the real world. The main complication is that radiators lose a great deal of heat by convection, rather than by thermal radiation. Another complication is that emissivity of paints can be a strong function of frequency. It makes little sense to characterize the emissivity for broad-spectrum thermal radiation by a single number, especially one based on visible frequencies, which one hopes the radiator is not emitting.

Mike W. (posted without checking until Lee gets back)

(published on 05/22/2013)