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(D) The power radiated by a black body is given by the Stefan-Boltzmann law: $P = A \sigma T^4 = 4 \pi r^2 \sigma T^4$.From this,we can see that $P \p

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$1800$

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(D) The power radiated by a black body is given by the Stefan-Boltzmann law: $P = A \sigma T^4 = 4 \pi r^2 \sigma T^4$.From this,we can see that $P \propto r^2 T^4$.Let the initial radius be $r_1 = 12 \, cm$ and initial temperature be $T_1 = 500 \, K$. The initial power is $P_1 = 450 \, W$.For the new state,the radius is halved,so $r_2 = r_1 / 2$,and the temperature is doubled,so $T_2 = 2 T_1$.Taking the ratio of the powers:$\frac{P_2}{P_1} = \left( \frac{r_2}{r_1} ight)^2 \left( \frac{T_2}{T_1} ight)^4$$\frac{P_2}{P_1} = \left( \frac{1}{2} ight)^2 \left( \frac{2}{1} ight)^4 = \frac{1}{4} 	imes 16 = 4$.Therefore,$P_2 = 4 P_1 = 4 	imes 450 = 1800 \, W$.

$A$ spherical black body of radius $12 \, cm$ radiates $450 \, W$ of power at $500 \, K$. If the radius is halved and the temperature is doubled,the power radiated will be ..... $W$.

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