At high noon,the Sun delivers 990 W to each square meter of a blacktop road.What is the equilibrium temperature of the hot asphalt,assuming its emissivity e = 1? (σ = 5.67 × 10−⁸ W/m²⋅K⁴). A)364°C B)637°C C)90.5°C D)181°C E)136°C

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Quizplus · Accepted Answer

The equilibrium temperature of the asphalt can be found using the Stefan-Boltzmann law, which relates the power radiated per unit area of a black body to its temperature. The formula is $P = \sigma e T^4$, where $P$ is the power per unit area, $\sigma$ is the Stefan-Boltzmann constant ($5.67 \times 10^{-8} \, \text{W/m}^2\cdot\text{K}^4$), $e$ is the emissivity, and $T$ is the temperature in Kelvin.Given that the Sun delivers 990 W/m^2 and assuming the emissivity $e = 1$, we can set $P = 990 \, \text{W/m}^2$ and solve for $T$:$$990 = 5.67 \times 10^{-8} \times 1 \times T^4$$Solving for $T$ gives:$$T = \left(\frac{990}{5.67 \times 10^{-8}}\right)^{1/4}$$$$T \approx 364.5 \, \text{K}$$To convert to Celsius, subtract 273.15:$$364.5 \, \text{K} - 273.15 = 91.35 \, ^\circ\text{C}$$Rounding to the nearest option gives 90.5°C.

At High Noon,the Sun Delivers 990 W to Each Square