A spherical black body with a radius of 12 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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$Radiated power by blackbody P = \frac{Q}{t} = A \sigma T^{4} \\ \Rightarrow \mathrm{P} \propto A T^{4} \propto r^{2} T^{4} \Rightarrow \frac{P_{1}}{P_{2}} = \left(\frac{r_{1}}{r_{2}}\right)^{2} \left(\frac{T_{1}}{T_{2}}\right)^{4} \\ \Rightarrow \frac{440}{P_{2}} = \left(\frac{12}{6}\right)^{2} \left(\frac{500}{1000}\right)^{4} \Rightarrow P_{2} = 1760 \mathrm{W} \approx 1800 \mathrm{W}$
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