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  3. 32 for any planet the equilibrium surface temperature is determined...

Question: 32 for any planet the equilibrium surface temperature is determined...

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3.2 For any planet, the equilibrium surface temperature is determined by the balance between the radiation received and the radiation lost to space. The input is determined by input = [F(1-A)x(R*)]/4, where F is the solar constant: for Earth F 1379 W/m2 A is the albedo of the surface R = radius of the planet The loss of radiation is determined by the emission of infraradiation: Loss--(a)T4me where σ is the Stefan-Boltzmann constant (5.673 × 10-8 W/m2/K-4) T is the temperature in degrees Kelvin R radius of the planet Thus, if the input of radiation increases, the temperature will rise. But with a rise in temperature there is a dramatic increase in loss (ie., temperature to the 4th power), so eventually the input and loss will again be equal. At that time, the planet will be in thermal equilibrium but at a higher surface temperature. This is essentially the origin of the greenhouse effect on Earth, which is driven not by changes in the Suns luminosity but by the tendency for radiatively active gases (such as CO2 and H20) to reduce the loss of infrared radiation from Earths surface. (a) If the albedo of Earth was 0 (i.e., if the Earth were a perfect black-body absorber), what would be its equilibrium temperature? (b) Actually, the albedo of Earth is about 0.30. What should be its equilibrium temperature? Compared to the mean temperature on Earth, what is the greenhouse effect?

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