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

225

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450

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900

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1800

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Solution

The correct option is D
1800

Power radiated is given by

$P = (4 π r^{2}) σ T^{4} o r P \propto r^{2} T^{4} ∴ \frac{P_{2}}{P_{1}} = {(\frac{r_{2}}{r_{1}})}^{2} \times {(\frac{T_{2}}{T_{1}})}^{2} = {(\frac{1}{2})}^{2} \times {(\frac{2}{1})}^{2} = 4 O r P_{2} = 4 P_{1} = 4 \times 450 = 1800 W$

which is choice (d)

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

The correct option is D 1800 Power radiated is given by P=(4πr2)σT4 or P∝ r2 T4∴ P2P1=(r2r1)2×(T2T1)2=(12)2×(21)2=4Or P2=4P1=4×450=1800 W which is choice (d)