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(B) According to Stefan-Boltzmann law,the power radiated by a black body is proportional to the fourth power of its absolute temperature $(P \propto T

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$4P$

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(B) According to Stefan-Boltzmann law,the power radiated by a black body is proportional to the fourth power of its absolute temperature $(P \propto T^4)$.Also,the intensity of radiation received at a distance $d$ follows the inverse square law,meaning the power received by the foil is inversely proportional to the square of the distance $(P \propto 1/d^2)$.Combining these,the power received by the foil is given by $P \propto T^4 / d^2$.Let the initial power be $P_1 = P$ at temperature $T_1 = T$ and distance $d_1 = d$.Let the final power be $P_2$ at temperature $T_2 = 2T$ and distance $d_2 = 2d$.Using the ratio: $P_2 / P_1 = (T_2 / T_1)^4 	imes (d_1 / d_2)^2$$P_2 / P = (2T / T)^4 	imes (d / 2d)^2$$P_2 / P = (2)^4 	imes (1/2)^2$$P_2 / P = 16 	imes (1/4) = 4$$P_2 = 4P$.

$A$ black metal foil is warmed by radiation from a small sphere at temperature $T$ and at a distance $d$. It is found that the power received by the foil is $P$. If both the temperature and the distance are doubled,the power received by the foil will be

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