The emissivity (power radiated per unit area) | vedclass

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(C) According to Stefan-Boltzmann law, the power radiated per unit area $E$ is proportional to the fourth power of the absolute temperature $T$ of the

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$2$

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(C) According to Stefan-Boltzmann law, the power radiated per unit area $E$ is proportional to the fourth power of the absolute temperature $T$ of the black body:$E = \sigma T^4$Given that the final emissivity $E_2$ is $16$ times the initial emissivity $E_1$:$E_2 = 16 E_1$Substituting the Stefan-Boltzmann law into the ratio:$\frac{E_2}{E_1} = \frac{\sigma T_2^4}{\sigma T_1^4} = \left( \frac{T_2}{T_1} \right)^4$$16 = \left( \frac{T_2}{T} \right)^4$Taking the fourth root on both sides:$\sqrt[4]{16} = \frac{T_2}{T}$$2 = \frac{T_2}{T}$$T_2 = 2 \,T$

The emissivity (power radiated per unit area) of a perfect black body is increased to $16$ times by increasing its temperature. If the initial temperature is $T$, then the final temperature of that black body is: (in $\,T$)

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