Question

Please show the steps.

D) As the Sun ages, it will cool and the amount of power it produces will decrease. If at some point in the future, this power drops such that the solar power/m^2 at the earth drops by 10% to 1250 Watts/m^2, what will the surface temperature of the Earth be? (Assume that the fraction of sunlight absorbed by the Earth's surface remains the same and that the fraction of the IR radiation emitted by the Earth's surface that reaches space remains the same as it is for today)

E) If in the future, the amount of greenhouse gases in the atmosphere rise so that 10% less of the IR radiation emitted from the earth's surface is getting out through the atmosphere than at present, calculate how many degrees Kelvin hotter the surface of the earth would be? (Assume that the amount of clouds and other complicated stuff like that does not change.)

Answer 1

D] Since it is assumed that the fraction of light absorbed by the Earth is the same, the albedo of Earth can be taken as:

Use Stefan-Boltzman law,

where is the amount of light absorbed by the Earth's surface (which is assumed to be reflected entirely).

here, I = Solar constant

The factor of 1/4 comes from the fact that only the cross-section of the sphere (Earth) receives this solar radiance. This cross-sectional area (area of a circle) is 1/4th of the curved surface area of the sphere.

is the Stefan-Boltzman constant.

Substitute these values to get,

T = 248.69 K = - 24.31^oC

This will be the average surface temperature of Earth's surface when the solar power drops by 10%.