A closed cubical box made of perfectly insulating material has walls of thickness \( 8 \mathrm{~...

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A closed cubical box made of perfectly insulating material has walls of thickness \( 8 \mathrm{~cm} \) and the only way for heat to enter or leave the box is through two solid, cylindrical, metallic plugs, each of cross-sectional area \( 12 \mathrm{~cm}^{2} \) and length \( 8 \mathrm{~cm} \) in opposite walls of the box. The outer surface of one plug is kept at \( 100^{\circ} \mathrm{C} \) while the outer surface of the other plug is maintained at \( 4^{\circ} \mathrm{C} \). The thermal conductivity of the plug is \( 50 \mathrm{cal} \mathrm{s}^{-1} \mathrm{~m}^{-1} \mathrm{~K}^{-1} \). A source of energy generating \( 36 \mathrm{cal} \mathrm{s}^{-1} \) is enclosed inside the box. Find the equilibrium temperature of the inner surface of the box, assuming that it is the same at all points on the inner surface.
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