If the temperature of a hot body is increased | vedclass

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Question

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

Vedclass · Accepted Answer

$400$

Vedclass · Answer

(D) According to 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 heat radiation be $Q_1 \propto T^4$.The temperature is increased by $50\%$,so the new temperature $T_2 = T + 0.5T = 1.5T = \frac{3}{2}T$.The new heat radiation $Q_2 \propto T_2^4 = (1.5T)^4 = (\frac{3}{2})^4 T^4 = \frac{81}{16} T^4$.Thus,$Q_2 = \frac{81}{16} Q_1 = 5.0625 Q_1$.The percentage increase in the quantity of emitted heat radiation is given by:$	ext{Percentage increase} = \frac{Q_2 - Q_1}{Q_1} 	imes 100\%$$= \frac{5.0625 Q_1 - Q_1}{Q_1} 	imes 100\%$$= 4.0625 	imes 100\% = 406.25\%$.Note: Based on standard textbook approximations for this specific problem type where $T_2 = 1.5T$,the result is $406.25\%$. Given the options provided,$400\%$ is the closest intended answer.

If the temperature of a hot body is increased by $50\%$,then the increase in the quantity of emitted heat radiation will be ..... $\%$

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