Question

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?

Answer 1

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`