Question

Imagine an earth-like planet in radiative equilibrium, i.e. it emits the same amount of radiation it receives from the Sun. The planet has a constant albedo of A=30 % and solar constant So=1370 W/m2. In the distant past, the civilization on that planet had some trouble getting their surface temperature under control. So, they build a temperature-controlled glass window around the entire planet that can be opened or closed. The window is intransparent to infrared radiation but completely transparent to solar radiation, the glass has a constant temperature of 220 K and the width of the opening can be adjusted.

• How sensitive is the average temperature at the surface to how wide open the window is?

• How wide open does the window have to be in order to reach 298 K surface temperature?

• How warm is it going to be at the surface if the window is closed completely?

• Are these considerations relevant for the earth or any other planet?

Answer 1

1) Average temperature will raise as the window opening will wider and temp temperature will constant for closed window.

2) 25% of total area of window need to open to reach temp of 298K

3) 50+273 : 323 Kelvin

4) Earth and Mars similarity for consideration.