At our distance from the Sun, the intensity of solar radiation is 1370 W/m2. The temperature of the Earth is affected by the greenhouse effect of the atmosphere. This phenomenon describes the effect of absorption of infrared light emitted by the surface so as to make the surface tem- perature of the Earth higher than if it were airless. For comparison, consider a spherical object of radius r with no atmosphere at the same distance from the Sun as the Earth. Assume its emissivity is the same for all kinds of electromagnetic radiation and its temperature is uniform over its surface.
(a) Explain why the projected area over which it absorbs sunlight is ?r2 and the surface area over which it radiates is 4?r2.
(b) Compute its steady-state temperature. Is it chilly?
(c) Why would an increase in greenhouse gasses such as water vapor, carbon dioxide, and me- thane be cause for alarm?