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

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

$\sigma=5.6703(10)^{-8}\frac{W}{m^{2} K^{4}}$ 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):

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

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

Finally:

$T=150.427 K$