Problem 16.81 Suppose city 1 leaves an entire block (100 m x 100 m) as a park wi

Question

Problem 16.81 Suppose city 1 leaves an entire block (100 m x 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 Part A At what rate does the park in city 1 deliver energy to the air at sunset? Express your answer to three significant figures and include appropriate units. Value Units My Answers Give Up Submit Part B At what rate does the asphalt in city 2 deliver energy to the air at sunset? Express your answer to three significant figures and include appropriate units Value L Units Submit My Answers Give Up

Explanation / Answer

Part A )

rate of energy delivered = e * A * (T^4 - T0^4) * sigma

rate of energy delivered = 0.96 * 5.6703 *10^-8 * 100 * 100 * (313^4 - 303^4)

rate of energy delivered = 636361 W

rate of energy delivered is 636361 W

part B)

for the city 2

rate of energy delivered = A * (T^4 - T0^4) * sigma

rate of energy delivered = 5.6703 *10^-8 * 100 * 100 * (313^4 - 303^4)

rate of energy delivered = 662876 W

rate of energy delivered is 662876 W

part C)

let the final temperture is Tf

636361 * 2.3 * 3600 = 100^3 * 1.16 * 1008 * (T - 30)

solving for T

T = 34.5 degree C

part D)

for the city 2

662876 * 2.3 * 3600 = 100^3 * 1.16 * 1008 * (T - 30)

solving for T

T = 34.7 degree C

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