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Question

(A) According to the Stefan-Boltzmann Law,the power radiated by a black body is proportional to the fourth power of its absolute temperature: $Q \prop

Vedclass · Accepted Answer

$46$

Vedclass · Answer

(A) According to the Stefan-Boltzmann Law,the power radiated by a black body is proportional to the fourth power of its absolute temperature: $Q \propto T^4$.Let the initial temperature be $T_1 = T$ and the initial radiation be $Q_1 \propto T^4$.If the temperature is increased by $10\%$,the new temperature is $T_2 = T + 0.1T = 1.1T$.The new radiation emitted is $Q_2 \propto (1.1T)^4$.Taking the ratio: $\frac{Q_2}{Q_1} = \left( \frac{1.1T}{T} ight)^4 = (1.1)^4 = 1.4641$.Thus,$Q_2 = 1.4641 Q_1$.The percentage increase in radiation is given by: $\frac{Q_2 - Q_1}{Q_1} 	imes 100 = (1.4641 - 1) 	imes 100 = 46.41\%$.Rounding to the nearest integer provided in the options,the answer is $46\%$.

If the temperature of the body is increased by $10\%$,the percentage increase in the emitted radiation will be ....... $\%$

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