At our distance from the Sun, the intensity of solar radiation is 1370 W/m 2 . T

Question

At our distance from the Sun, the intensity of solar radiation is 1370 W/m 2 . 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 temperature 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 r 2 and the sur- face area over which it radiates is 4 r 2 . (b) Compute its steady - state temperature. Is it chilly? (c) Why would an increase in greenhouse gases such as water vapor, carbon dioxide, and methane be cause for alarm?

Explanation / Answer

When suns rays reach earth the ways i.e spherical radiation waves have large radius, they can almost be treated vertical.

THe projected area is the surface area that is occupied by a shape when projected on to a plane.

So when a sphere is projected on to a surface which is parallel to the waves i.e vertical, the projected area is a circle with radius equal to that of the sphere

So projected area = pi * r^2 which is the area of circle.

(b)

We have heat absorbed from sun = 1370 * projected area

Heat emitted by earth as a black body = sigma * emissivity * 4 * pi * r^2 * T^4

When in steady state, heat lost = heat gained . and emissivity is 1

So 1370 = 5.67* 10^-8 * 4 * T^4

SO T = 278.78 Kelvin approximately 5 degrees centigrade

Yes plaanet is chilly.

(c) When earthly gases are present, The radiation emitted by earth is absorbed by the atmosphere and reflected back to earth surface. So the amount of radiation lost by earths radiation is far less as it is reflected back to earth from atmosphere.

If the amount of green house gases increases, the reflection back on to earths surface increases making the earth temperature hotter and hotter. This will damage environment as most flora and fauna reproduce at warmer temperatures than red hot hotter temperatures.

Related Questions

Navigate

• Browse (All)
• Browse A
• Subjects

Integrity-first tutoring: explanations and feedback only — we do not complete graded work. Learn more.