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

Abby Nguyen

9 May, 02:43

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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Adrien Horn · 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