Question

1.  a) Estimate the total solar heating absorbed by the Earth every second.  Assume 36% of the incoming solar radiation is rejected by clouds and lost.  You can assume that the Earth intercepts sunlight with an effective area of (pi)r^2 where r is Earth's radius.

b)

Estimate the total heat lost by the Earth as infrared radiation every second.  Assume Earth has an effective temperature of 252 K (-21 C).

c)

Compare your estimates for part a) and b).  Describe the implications of the two estimates having these values relative to each other.

d)

The average surface temperature of the Earth is about 15 C. Explain why there is a difference

between the effective temperature and the average surface temperature.

Answer 1

We have to find the total solar heating absorbed by the earth every second. And also estimate the total heat lost by the earth as infrared radiation every second.

1. a) Here we have to find the total Solar heating absorbed big the earth every second inter- Now, the total amount of energy cepted by Earth Eintercepted = Ks X. It pr Where Ks = = solas constant 1361 Datts per square meter. pa radius of Earth = 63.71 km = 6371000 meters Now as 36% of the incoming energy is reflected by clouds and lost. We have to determine how much energy Easith absorbs from sunlight Equation o beco Eabsorbed = Rs *(1-albedo) x-et ry Now, becomes where, albedo represents the light reflected away = 36V, 20.36

from 2) ni Eabsorbed = 1361 x (1-0.36) * 3.1416 * (6371000) 1. 110 x 1017 watts the The solar heating absorbed by earth is 1 110x id7 watts Joule per seconda we have the the total heat lost by the Earth as infrared radiation every second is Emitted o Thx400 or 1'110x107 b) Now, = 3 Where, 0... Stefan - Boltzmann constant = 5.670373* 109 watts / mik! T= temperature = 252 K 1 from ) 6(252)4x4 *3.1416 *(5371000) = 5.670373x10 femitted 17 Watts . 1.166 810 . The total heat lost by the Earth as infrared radiation is 1.16681017 Watts 1.166 x 10 x 107 Joule per second- or

we. can see i. e, the greenhouse effect. Without it, & © 1 if we compare the estimates value for part a) and (b) ee that the two values are approximately same or equal . Eabsorbed - Eemitted which conserved the law of conservation of energy tells us that the energy absorbed must be equal to the energy emitted. d) The average surface temperatur of the earth is about 15°C and Earth has an effective temperature -21°c. So there is a difference between the effective temperature and the average 2 surface temperatur because certain gases in the atmosphere trap so me extra heat, warming our planet like a a blanket. This extra warming is called planet would be a frozen ball of ice. We are thankful to the natural greenhouse effect because earth is comfortable place for life as we know it. our

In recent decades, a rise in the amount of green hose gases has begun to warm Earth a bit too much.