### Understanding the Greenhouse Effect and its Impact on Earth's Temperature#### OverviewWithout the greenhouse effect, Earth's average surface temperature would be approximately 250 K. However, due to the greenhouse effect, the temperature is elevated by about 40 K, reaching roughly 290 K. This significant temperature increase is attributed to the absorption of infrared radiation by greenhouse gases in the atmosphere.#### ObjectiveUsing the provided information and Stefan's law, this task aims to calculate the fraction of infrared radiation leaving Earth's surface that is absorbed by greenhouse gases in the atmosphere.#### Stefan's LawStefan's Law, also known as the Stefan-Boltzmann Law, states that the power radiated per unit area of a black body is proportional to the fourth power of its absolute temperature (T).The Stefan-Boltzmann equation is given by:\[ P = \sigma T^4 \]where:- \( P \) is the power radiated per unit area,- \( \sigma \) is the Stefan-Boltzmann constant (\( 5.67 \times 10^{-8} \, \text{Wm}^{-2}\text{K}^{-4} \)),- \( T \) is the absolute temperature in Kelvins.#### Calculation1. **Temperature without the Greenhouse Effect:** \[ T_{\text{no greenhouse}} = 250 \, \text{K} \] Using Stefan's law, the power radiated per unit area is: \[ P_{\text{no greenhouse}} = \sigma (250 \, \text{K})^4 \] \[ P_{\text{no greenhouse}} = \sigma \times 390625 \, \text{K}^4 \]2. **Temperature with the Greenhouse Effect:** \[ T_{\text{with greenhouse}} = 290 \, \text{K} \] Similarly, \[ P_{\text{with greenhouse}} = \sigma (290 \, \text{K})^4 \] \[ P_{\text{with greenhouse}} = \sigma \times 707281 \, \text{K}^4 \]3. **Fraction of Infrared Radiation Absorbed:** The fraction of radiation absorbed by greenhouse gases is given by: \[ \text{Fraction absorbed} = \frac{P_{\text{with greenhouse}}

Stefan-Boltzmann's law states that the total heat power emitted by a surface will be directly…

Answered: Without the greenhouse effect, Earth's…

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