At our distance from the Sun, the intensity of solar radiation is 1370 W/m2. The

Question

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?

Explanation / Answer

when sun is radiating as seen by sun earth would be like a disc and its area would be pi*r^2 but when earth is radiating it would radiate from every part that is like a sphere whose surface area is 4*pi*r^2

1370*pi*r^2= 4*pi*r^2*5.67*10^-8*T^4

(stefan boltzmann law)

from here T=278.78 K

hence chilly

When there is an increase in these gases they would be trapped inside the earth atmosphere and they would be increase in the temperature of earth (also called global warming)

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