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A spherical black body with a radius of 12 cm radiates 450 watt power at 500 K. If the radius were halved and the temperature doubled, the power radiated in watt would be
Explanation
$P \propto R^2T^4$: factor $(1/4)\times16 = 4$.
Detailed Solution
Rate of power loss $r \propto R^2T^4$
$\frac{r_1}{r_2} = \frac{R_1^2T_1^4}{R_2^2T_2^4} = 4\times\frac{1}{16} = \frac{1}{4}$
$\frac{450}{r_2} = \frac{1}{4}$
$r_2 = 1800$ watt