A spherical black body with a radius of 12 cm radiates 450 W power at 500 K . If the radius were halved and the temperature doubled, the power radiate - Physics MCQ NEET (UG) 2017 2026 | ExamTest.live

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A spherical black body with a radius of 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:

Solution & Step-by-step Explanation

Power radiated by a black body: P = σ A T^{4} = σ (4 π r^{2}) T^{4} .Thus, P \propto r^{2} T^{4} . \frac{P _{2}}{P _{1}} = (\frac{r _{2}}{r _{1}})^{2} (\frac{T _{2}}{T _{1}})^{4} Given r_{2} = r_{1} /2 and T_{2} = 2 T_{1} : \frac{P _{2}}{450} = (\frac{1}{2})^{2} (2)^{4} = \frac{1}{4} \times 16 = 4 P_{2} = 450 \times 4 = 1800 W

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A spherical black body with a radius of 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:

450

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1800

225

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