A spherical black body with a radius of 24;cm | vedclass

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(D) The power radiated by a black body is given by the Stefan-Boltzmann law: $P = A\sigma T^4$,where $A = 4\pi r^2$ is the surface area.Therefore,$P \

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$1760$

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(D) The power radiated by a black body is given by the Stefan-Boltzmann law: $P = A\sigma T^4$,where $A = 4\pi r^2$ is the surface area.Therefore,$P \propto r^2 T^4$.Given the initial state: $P_1 = 440\;W$,$r_1 = 24\;cm$,$T_1 = 500\;K$.For the final state: $r_2 = r_1 / 2 = 12\;cm$ and $T_2 = 2T_1 = 1000\;K$.Using the proportionality ratio:$\frac{P_2}{P_1} = \left( \frac{r_2}{r_1} ight)^2 \left( \frac{T_2}{T_1} ight)^4$$\frac{P_2}{440} = \left( \frac{1}{2} ight)^2 \left( \frac{2}{1} ight)^4$$\frac{P_2}{440} = \frac{1}{4} 	imes 16 = 4$$P_2 = 440 	imes 4 = 1760\;W$.

$A$ spherical black body with a radius of $24\;cm$ radiates $440\;W$ power at $500\;K$. If the radius were halved and the temperature doubled,the power radiated in watt would be

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