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The robot HooRU is lost in space, floating around aimlessly, and radiates heat into the depths of the cosmos at the rate of . HooRU's surface area is and the emissivity of its surface is . Ignore the radiation HooRU absorbs from the cold universe. What is HooRU's temperature?

1 Answer

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Answer: 150.427 K

Step-by-step explanation:

The complete question is as follows:

The robot HooRU is lost in space, floating around aimlessly, and radiates heat into the depths of the cosmos at the rate of
14.5 W . HooRU's surface area is
1.79 m^(2) and the emissivity of its surface is
0.279. Ignore the radiation HooRU absorbs from the cold universe. What is HooRU's temperature?

This problem can be solved by the Stefan-Boltzmann law for real radiator bodies:


P=\sigma A \epsilon T^(4) (1)

Where:


P=14.5 W is the energy radiated by HooRU


\sigma=5.6703(10)^(-8)(W)/(m^(2) K^(4)) is the Stefan-Boltzmann's constant.


A=1.79 m^(2) is the Surface of the robot


\epsilon=0.279 is the robot's emissivity


T is the effective temperature of the robot (its surface absolute temperature) in Kelvin

So, we have to find
T from (1):


T=((P)/(\sigma A \epsilon))^{(1)/(4)} (2)


T=((14.5 W)/((5.6703(10)^(-8)(W)/(m^(2) K^(4))) (1.79 m^(2)) (0.279)))^{(1)/(4)}

Finally:


T=150.427 K

User Rwold
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