Physics Question Problem 17.73 The sun\'s intensity at the distance of the earth
ID: 1441010 • Letter: P
Question
Physics Question
Problem 17.73 The sun's intensity at the distance of the earth is 1370 W/m2. 30% of this energy is reflected by water and clouds; 70% is absorbed Part A What would be the earth's average temperature (in oC) if the earth had no atmosphere? The emissivity of the surface is very close to 1. The actual average temperature of the earth, about 15 C, is higher than your calculation because of the greenhouse effect.) Express your answer to two significant figures and include the appropriate units Value UnitsExplanation / Answer
If we assume that the earth loses heat by radiation as a black body, then the temperature will rise until the heat lost by radiation is equal to the energy reaching the earth from the sun. The total radiated energy from the earth as a function of temperature is given by the Stefan-Boltzmann law.
Pr = **As*T
where Pr is the radiation from the earth, = emissivity, = Stefan-Boltzmann constant, T the absolute temperature and As the surface area of the earth. The area of a sphere gives As = 4**r² so
Pr = 4**r²***As*T
The totat irradiation of the earth is the amount of radiation intercepted by the earth, which is I0 (W/m²) time the projected area of the earth (the area of the earth's shadow), *r²
Pr = I0**r²
Equate these to get 4**r²***As*T = I0**r² or
T = I0*/(4**)
I0 = 0.70*1370
= 1.0
= 5.67*10^-8 W/(m²*K)
T = 255 K = -18.1 ºC