Chapter 16, Problem 81GP

Pave It Over Suppose city 1 leaves an entire block (100 m × 100 m) as a park with trees and grass (emissivity 0.96) while city 2 paves the same area over with asphalt (emissivity 1.0). Sunlight heats each surface to 40.0 °C by sunset, and then the surface radiates its heat into a cube of air 100 m on a side and at 30.0 °C. (a) At what rate does the park in city 1 deliver energy to the air at sunset? (b) At what rate does the asphalt in city 2 deliver energy to the air at sunset? (c) If each city block maintains the same radiated power for 2.0 h and there are no other energy losses, what are the final temperatures of the cubes of air above each city block? The density of air at 30.0 °C is 1.16kg/m³. Although this example is oversimplified, a more sophisticated analysis recently showed that a city park can cool the air that passes through it by more than 4 °C.