Question

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 = 0.830). It has a temperature of 64.1 oC. The new owner of the house paints the radiator a lighter color (emissitivity = 0.426). 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?

Answer 1

T = 125.30C

Step-by-step explanation:

Using Stefan-Boltzmann law

P/A = e* Stefan-Boltzmann constant * T^4

Where p= radiant power in watts

e = emissivity

T = Temperature in kelvin

A= Surface area of the object measured in m^2

Considering that after painting the object have the radiant power then

0.83* A* Stefan-Boltzmann constant *(337.1^4) = 0.46 * A* Stefan-Boltzmann constant * Tnew^4

Cancelling the common terms yields

0.83*(337.1^4) = 0.426*Tnew^4

Fourthroot(0.83*(337.1^4)) = Tnew

Tnew = 398.3k = in degree Celsius 125.3