If the sun's surface radiates heat at 6.3 tim | vedclass

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(A) According to Stefan-Boltzmann law,the power radiated per unit area (emissive power) $E$ of a black body is given by $E = \sigma T^4$,where $\sigma

Vedclass · Accepted Answer

$5.8 	imes 10^3 \ K$

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(A) According to Stefan-Boltzmann law,the power radiated per unit area (emissive power) $E$ of a black body is given by $E = \sigma T^4$,where $\sigma$ is the Stefan-Boltzmann constant and $T$ is the absolute temperature.Given: $E = 6.3 	imes 10^7 \ W m^{-2}$ and $\sigma = 5.7 	imes 10^{-8} \ W m^{-2} K^{-4}$.Rearranging the formula to solve for $T$: $T^4 = \frac{E}{\sigma}$.Substituting the values: $T^4 = \frac{6.3 	imes 10^7}{5.7 	imes 10^{-8}} = \frac{6.3}{5.7} 	imes 10^{15} \approx 1.105 	imes 10^{15} = 1105 	imes 10^{12}$.Taking the fourth root: $T = (1105 	imes 10^{12})^{1/4} \approx 5.77 	imes 10^3 \ K$.Rounding to the nearest given option,$T \approx 5.8 	imes 10^3 \ K$.

If the sun's surface radiates heat at $6.3 \times 10^7 \ W m^{-2}$,calculate the temperature of the sun assuming it to be a black body $(\sigma = 5.7 \times 10^{-8} \ W m^{-2} K^{-4})$.

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