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?

The robot HooRU is lost in space, floating around aimlessly, and radiates heat into the depths of the cosmos at the rate of [tex]14.5 W[/tex] . HooRU's surface area is [tex]1.79 m^{2}[/tex] and the emissivity of its surface is [tex]0.279[/tex]. 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:

[tex]P=\sigma A \epsilon T^{4}[/tex] (1)

Where:

[tex]P=14.5 W[/tex] is the energy radiated by HooRU

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

[tex]A=1.79 m^{2}[/tex] is the Surface of the robot

[tex]\epsilon=0.279[/tex] is the robot's emissivity

[tex]T[/tex] is the effective temperature of the robot (its surface absolute temperature) in Kelvin

So, we have to find [tex]T[/tex] from (1):

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

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

Finally:

[tex]T=150.427 K[/tex]