Answer: 150.427 K
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 [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]
