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Q.

The rectangular surface of area 8cm × 4cm of a black body at a temperature of 127⁰C emits energy at rate of E per second. If the length and breadth are reduced to half of its initial value and the temperature is raised to 327⁰C, the rate of emission of energy will be

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a

large left ( frac {3E}{8} right )

b

large left ( frac {9E}{16} right )

c

large left ( frac {81E}{16} right )

d

$large left ( frac {81E}{64} right )$

answer is D.

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Detailed Solution

l₁ = 8cm, b₁ = 4cm; l₂ = cm, b₂ = 2cm
T₁ = 127⁰C = 400k, T₂ = 327⁰C = 600k
$large frac {E_2}{E_1}=left ( frac {T_2}{T_1} right )^4left ( frac {l_2b_2}{l_1b_1} right )$
$large frac {E_2}{E}=left ( frac {600}{400} right )^4left ( frac {4times 2}{8times 4} right )$
$large E_2=frac {81}{64}E$

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