The average temperature of Earth given the solar irradiance is 238.4K.
How to calculate the temperature?
The following can be deduced from the information:
Let Earth's albedo =α =0.33
Radius of the sun ( Rs) =6.955×10⁵
Value of Boltzmann constant= 5.67×10-⁸
L= 1350
T = average temperature
L= 4σ (Te)⁴ / (1-α)
1 - 0.33 = 4 × 5.67×10-⁸×(T)⁴ / 1350
0.67 × 1350 = 0.0000002268*(T)⁴
(T)⁴ = 3230357142.9
T = 238.4 k
In conclusion, the temperature is 238.4K.
Complete question:
Calculate the average temperature of Earth where the solar irradiance (L) is 1350W/m² and the albedo of Earth is 0.33. Consider Earth to be a perfect black body and the Stefan - Boltzmann constant to be 5.67 × 10^-8 W.
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