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 Problem Statement

Consider a black cube which is made
from a perfectly heatconducting material. A parallel beam of
light with intensity I (W/m2) falls onto this cube. The equilibrium
temperature T of the cube depends on its orientation;
find the minimal and maximal values of T (Tmin and Tmax,
respectively).
 Relevant Equations
 Stefan Boltzmann law
So i had this problem and I want a rigourous solution. The answer should be : Tmin=(I/sigma)^(1/4)
and Tmax=(sqrt(3I)/sigma)^1/4
and Tmax=(sqrt(3I)/sigma)^1/4