A spherical black body with a radius of 12cm radiates 450W power at 500K. If the radius were halved and the temperature doubled, the power radiated in watts would be

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225

1800

900

450

answer is D.

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Detailed Solution

For spherical black body of radius r and absolute temperature T

The power radiated = $(4 π r^{2}) (σ T^{4})$

$P \propto r^{2} T^{4}$

$\frac{P_{2}}{P_{1}} = {(\frac{r_{2}}{r_{1}})}^{2} {(\frac{T_{2}}{T_{1}})}^{4}$

$\frac{P_{2}}{P_{1}} = \frac{1}{4} \times 16 \Rightarrow P_{2} = 4 P_{1} = 1800 W$

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