Black cube, maximal and minimal value of equilibrium temperature T

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andrea1313
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Homework Statement
Consider a black cube which is made
from a perfectly heat-conducting 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
 
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The power radiated is going to be equal to the power incident. Then think of how the normal vectors will behave when a single face of the cube, two faces, and three faces are pointing in the direction of the light. Also, it looks that the answers presented are for a single face of the cube and not the whole cube itself.