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?

Question

Physics

Anne Downs

15 August, 00:34

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?

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Answers (1)

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Daniela Spears · Answer 1

T = 125.30C

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