Solution:
Power radiated $P = \sigma A T^4 = \sigma (4\pi r^2) T^4 \Rightarrow P \propto r^2 T^4$. Given $r' = r/2$ and $T' = 2T$. Thus, $P' = P(1/2)^2 (2)^4 = P(1/4)(16) = 4P = 4 \times 450 = 1800\text{ W}$.
A spherical black body with a radius of $12\text{ cm}$ radiates $450\text{ watt}$ power at $500\text{ K}$. If the radius were halved and the temperature doubled, the power radiated in watt would be: (2017-Delhi)
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