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Thermal Properties Of Matter

Question
CBSEENPH11020829
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A spherical black body with a radius of 12 cm radiates 450-watt power at 500 K. If the radius were halved and the temperature doubled, the power
radiated in watt would be

  • 225

  • 450

  • 1800

  • 1000

Solution

C.

1800

Rate of power loss
straight r space proportional to space straight R squared straight T to the power of 4 straight r subscript 1 over straight r subscript 2 space equals space fraction numerator straight R subscript 1 superscript 2 straight T subscript 1 superscript 4 over denominator straight R subscript 2 superscript 2 space straight T subscript 2 superscript 4 end fraction space equals space 4 space straight x space 1 over 16 space 450 over straight r subscript 2 space equals space 1 fourth straight r subscript 2 space equals space 1800 space watt

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