At what net rate does heat radiate from a \( 275 \mathrm{~m}^{2} \) black roof on a night when the roof's temperature is \( 30.0^{\circ} \mathrm{C} \) , and the surrounding temperature is \( 15.0^{\circ} \mathrm{C} \) ? The emissivity of the roof is 0.90 [Stefan-Boltzamann Constant \( =5.67 \times \) \( 10^{8} \mathrm{Js}^{-1} \mathrm{~m}^{-2} \mathrm{~K}^{-4} \mathrm{]} \) .

A \( -5.11 \times 10^{3} \mathrm{~W} \)

B \( 4.18 \times 10^{4} \mathrm{~W} \)

C \( 6.54 \times 10^{5} \mathrm{~W} \)