This question considers solar energy incident on a spherical celestial object of…
PHYSICS · Multi-part · IB Diploma Programme · Physics · The greenhouse effect · The greenhouse effect
Problem
This question considers solar energy incident on a spherical celestial object of radius r orbiting the Sun at a mean distance d. Suppose that the Sun radiates energy at a rate P.
(1) (a) At a distance d from the Sun, how much solar energy arrives per second per unit area? Call this quantity S.
(2) (b) How much solar energy is incident on the celestial object per second?
(3) (c) Hence give an expression, in terms of S, for the mean power incident on the total surface of the celestial object per unit area.
(4) (d) Suppose that the albedo of the celestial object is α. Give an expression for the mean power per unit area absorbed by the celestial object.
(5) (e) Now apply this to the Earth, for which S≈1400W/m2.
(6) (i) If the average albedo of the Earth is 0.3, show that the Earth would have to radiate 245W/m2 to be in thermal equilibrium.
(7) (ii) At what temperature would a black body have to be to radiate at 245W/m2?
(8) (iii) In fact, the globally averaged surface temperature of the Earth is 288K. For the Earth to maintain thermal equilibrium with its surroundings, how much more power per unit area must the Earth's surface absorb? Consider the Earth to radiate as a black body.
(9) (iv) Since the Earth is in thermal equilibrium with its surroundings, where does this extra power come from?
(10) (v) By what name is this phenomenon usually known?