Calculate the surface temperature of the plan | vedclass

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(C) The energy radiated per unit area per unit time is given by the Stefan-Boltzmann law: $I = \sigma T^4$,where $I$ is the intensity,$\sigma$ is the

Vedclass · Accepted Answer

$727 \, ^\circ C$

Vedclass · Answer

(C) The energy radiated per unit area per unit time is given by the Stefan-Boltzmann law: $I = \sigma T^4$,where $I$ is the intensity,$\sigma$ is the Stefan-Boltzmann constant $(5.67 	imes 10^{-8} \, W/m^2 K^4)$,and $T$ is the absolute temperature.Given $I = 5.67 	imes 10^4 \, W/m^2$.Substituting the values: $5.67 	imes 10^4 = 5.67 	imes 10^{-8} 	imes T^4$.Dividing both sides by $5.67 	imes 10^{-8}$,we get $T^4 = 10^{12}$.Taking the fourth root,$T = (10^{12})^{1/4} = 10^3 \, K = 1000 \, K$.To convert to Celsius: $T(^{\circ}C) = T(K) - 273 = 1000 - 273 = 727 \, ^{\circ}C$.

Calculate the surface temperature of the planet,if the energy radiated by unit area in unit time is $5.67 \times 10^4 \, W$. (Assume the planet is a black body).

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