QuestionSeptember 18, 2025

12. How much longwave radiation is emitted by the Atmosphere back to Earth's surface?

12. How much longwave radiation is emitted by the Atmosphere back to Earth's surface?
12. How much longwave radiation is emitted by the Atmosphere back to Earth's surface?

Solution
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Answer

390 \ \text{W/m}^2 Explanation 1. Identify the relevant law Use the Stefan-Boltzmann Law: E = \epsilon \sigma T^4, where E is emitted energy, \epsilon is emissivity (≈1 for atmosphere), \sigma = 5.67 \times 10^{-8} \ \text{W m}^{-2} \text{K}^{-4}, and T is temperature in Kelvin. 2. Estimate atmospheric temperature Typical effective radiating temperature of the lower atmosphere ≈ 255 K to 288 K. Use 288 K for surface-level emission. 3. Calculate longwave radiation E = 1 \times 5.67 \times 10^{-8} \times (288)^4 = 390 \ \text{W/m}^2

Explanation

1. Identify the relevant law<br /> Use the Stefan-Boltzmann Law: $E = \epsilon \sigma T^4$, where $E$ is emitted energy, $\epsilon$ is emissivity (≈1 for atmosphere), $\sigma = 5.67 \times 10^{-8} \ \text{W m}^{-2} \text{K}^{-4}$, and $T$ is temperature in Kelvin.<br />2. Estimate atmospheric temperature<br /> Typical effective radiating temperature of the lower atmosphere ≈ 255 K to 288 K. Use 288 K for surface-level emission.<br />3. Calculate longwave radiation<br /> $E = 1 \times 5.67 \times 10^{-8} \times (288)^4 = 390 \ \text{W/m}^2$
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