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  4. If the temperature of a black body increased rom 27° C to 327° C , the radiation emitted increases by a fraction of:

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Q. If the temperature of a black body increased rom $ 27{}^\circ C $ to $ 327{}^\circ C $ , the radiation emitted increases by a fraction of:

JIPMERJIPMER 1999

Solution:

Radiation emitted $ {{T}_{1}}=27+273=300 $ $ {{T}_{2}}=327+273=600 $ $ E\propto {{T}^{4}} $ $ \frac{{{E}_{1}}}{{{E}_{2}}}=\frac{T_{1}^{4}}{T_{2}^{4}}={{\left( \frac{300}{600} \right)}^{4}} $ $ \frac{{{E}_{1}}}{{{E}_{2}}}=\frac{1}{16} $ Hence, $ {{E}_{2}}=16{{E}_{1}} $