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A spherical black body with a radius of 12 cm radiates 450 W power at 50 K. If the radius were halved and the temperature doubled, the power radiated in watts would be:

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225

450

900

1800

answer is D.

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Detailed Solution

Concept: The new radius and temperature first using the circumstances provided. Then, using the above information, utilize the formula for power emitted by a black body (in watts) to arrive at the necessary conclusion.

P = A σ T 4, A = 4 π R 2

and

P = 4 π R 2 σ T 4

p = 4 π R 2 σ T 4

Given that

= 4 π R 2 σ T 4

and that

r = R 2

and

t = 2 T

, respectively, the power radiated by
the newly created spherical black body is given by

P new = 4 r 2 t 4 ⋅ P new = 4 π R 2 2 σ (2 T) 4 using (1), P new = 4 π R 2 T 4 2422, P n e w = 45022, P n e w = 450 (4)

∴ P new = 1800

watts
Hence, the correct option is 4.

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