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

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450

1000

1800

225

answer is C.

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Detailed Solution

According to Stefan-Boltzman law, rate of energy radiated by a black body is given asE=σAT4=σ4πR2T4 Given E1=450 W,T1=500 K,R1=12 cmR2=R12, T2=2T1,E2=?E2E1=σ4πR22T24σ4πR12T14=R2R12T2T14E2E1=14×16=4E2=E1×4=450×4=1800 W

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