$<img\; src="https://dsd5zvtm8ll6.cloudfront.net/questions/2024/04/661f863d508d9\_1713342012325.jpg"\; style="width:\; 300\%;\; display:\; block;\; vertical-align:\; top;\; margin:\; 5px\; auto;\; text-align:\; center;"\; width="300\%"\; height="488"\; alt="image\; text\; in\; transcribed">$ 

We want to estimate the average temperature of Earth using some basic principles. At the location of the Earth, the intensity of thermal radiation from the Sun is approximately 1370W/m. The average distance between the Earth and the Sun is 1.496 x 1011 m. Assume that the Earth reflects about thirty percent of the energy it receives from the Sun. This is called the albedo a of the Earth, where a = 0.30. A 25% Part (a) Use the intensity of solar radiation at the top of the Earth's atmosphere and the Earth-Sun distance to determine the total power in watts radiated from the Sun at any given time. A 25% Part (b) A portion of the power emitted by the Sun is intercepted by the Earth. Of the rays of light from the Sun that are parallel rays when they reach Earth, what is the area of the Earth in square kilometers that receives energy from the Sun? Assume the Earth is a perfect sphere with a radius of 6.38 x 100 m. A 25% Part (c) In terms of the intensity S of the sunlight received at the top of the atmosphere (which is called the solar constant) the radius of the Earth, RE: and the albedo of the Earth, a, write an expression for the rate at which the Earth absorbs energy from the Sun. A 25% Part (d) Assume that the Earth has an average emissivity of 0.83 and determine the Kelvin temperature of a body that radiates energy to space at the rate found in part (c).