Physics

Problem

A small artificial satellite is modelled as a hollow cubic box of side

0.50\,\text{m}

. All six outer faces have the same surface nature with emissivity

e = 0.70

. An on-board electronic system continuously generates a steady power of

500\,\text{W}

, which is entirely converted into thermal energy that must be radiated away into the surrounding deep space (assumed at

0\,\text{K}

). Answer the following: a. (i) Derive an expression that relates the steady-state operating temperature

T

of the satellite to the given parameters

P,\,e,\,\sigma

and the side length

\ell

. b. (ii) Using the derived expression, calculate the operating temperature of the satellite under the stated conditions. Take

\sigma = 5.67\times10^{-8}\,\text{W\,m}^{-2}\,\text{K}^{-4}

. c. (iii) Discuss qualitatively how the operating temperature would change if the emissivity of the outer surface were reduced to

0.40

while all other parameters remain the same.