In one room the radiator has a dark color (emissitivity = 0.818). It has a temperature of 64.8 oC. The new owner of the house paints the radiator a lighter color (emissitivity = 0.417). 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?
The Stefan-Boltzmann equation must use temperature in K.
T1 = 64.8 C = 338.0 K
If the radiating area stays the same,
0.818 T1^4 = 0.417 T2^4, so
T2 = 1.1835*T1 = 400.0 K = 126.8 C