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(C) According to Stefan-Boltzmann Law,the rate of energy emission $E$ is proportional to the fourth power of the absolute temperature $T$,i.e.,$E \pro

Vedclass · Accepted Answer

$527$

Vedclass · Answer

(C) According to Stefan-Boltzmann Law,the rate of energy emission $E$ is proportional to the fourth power of the absolute temperature $T$,i.e.,$E \propto T^4$.Given:$E_1 = 1.0 	imes 10^6 \ J/	ext{s} \cdot 	ext{m}^2$$T_1 = 127^{\circ}C = 127 + 273 = 400 \ K$$E_2 = 16.0 	imes 10^6 \ J/	ext{s} \cdot 	ext{m}^2$Using the ratio formula:$\frac{E_2}{E_1} = \left( \frac{T_2}{T_1} ight)^4$Substituting the values:$\frac{16.0 	imes 10^6}{1.0 	imes 10^6} = \left( \frac{T_2}{400} ight)^4$$16 = \left( \frac{T_2}{400} ight)^4$$2^4 = \left( \frac{T_2}{400} ight)^4$$2 = \frac{T_2}{400}$$T_2 = 800 \ K$Converting back to Celsius:$T_2(^{\circ}C) = 800 - 273 = 527^{\circ}C$.

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