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

Question

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, 225, 450, 1000, 1800

MARKS App · Accepted Answer

By Stefan's law rate of heat radiation from a black body = σ A T 4 ⇒ Rate of power loss r ∝ R 2 T 4 r 1 r 2 = R 1 2 T 1 4 R 2 2 T 2 4 = 4 × 1 16 450 r 2 = 1 4 r 2 = 1800 w a t t

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