A baking oven radiant heating panel operates at a surface temperature of $T = 200^\circ\text{C}$ ($473.15\text{ K}$) with a surface emissivity of $\epsilon = 0.85$. Taking the Stefan-Boltzmann constant $\sigma = 5.67 \times 10^{-8}\text{ W/(m}^2\,\text{K}^4\text{)}$, the total emissive power of the panel is ________ $\text{W/m}^2$ (round off to one decimal place).
Answer Key:
2415.4
Step-by-Step Solution & Explanation
From the Stefan-Boltzmann law for a gray surface:
$E = \epsilon \sigma T^4$
Given $\epsilon = 0.85$, $\sigma = 5.67 \times 10^{-8}\text{ W/(m}^2\text{ K}^4\text{)}$, and $T = 473.15\text{ K}$:
$E = 0.85 \times (5.67 \times 10^{-8}) \times (473.15)^4 = 2415.4\text{ W/m}^2$