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A solid spherical black body has a radius R and steady surface temperature T. Heat sources ensure the heat evolution at a constant rate and distributed uniformly over its volume. The new steady surface temperature of the object if the radius is decreased by half is $\frac{T}{2^{x}}$ . The value of x is (Assume surrounding to be at absolute zero and heat evolution rate through unit volume remain same)

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Detailed Solution

Net heat getting generated in complete volume of sphere = rate of heat radiated by its surface.

$P (\frac{4}{3} π r^{3}) = σ e (4 π r^{2}) T_{s}^{4} T_{s}^{4} \propto r \frac{T^{'}}{T} = {(\frac{1}{2})}^{\frac{1}{4}} T^{'} = \sqrt[4]{\frac{1}{2}} T$

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