In the article "The Climatic Effects of Nuclear War" (Scientific American, August 1984), the authors calculate a global energy balance corresponding to the first few months following a 5,000-megaton nuclear exchange. The resulting smoke and dust in the atmosphere absorb 75 percent of the incoming sunlight (257 W/m2), while the albedo is reduced to 20 percent. Convective and evaporative heating of the atmosphere from the Earth's surface is negligible, as is the energy reflected from the Earth's surface. The Earth's surface radiates 240 W/m2 , all of which is absorbed by the atmosphere. Assuming that the Earth can be modeled as a blackbody emitter as shown below, find the following (equilibrium) quantities: a. The temperature of the surface of the Earth (this is "nuclear winter") b. X, the rate at which radiation is emitted from the atmosphere to space c. Y, the rate of absorption of short-wavelength solar radiation at the Earth's surface d. Z, the rate at which the atmosphere radiates energy to the Earth's surface