donald said:
The 'greenhouse effect' is clearly a misnomer because trapping in IR radiation is not how a greenhouse works. A greenhouse works by trapping warmed air.
A greenhouse inside a greenhouse doesn't work by trapping IR. A greenhouse on Earth, yes, works mostly (but not completely) by trapping warmed air. But that is a greenhouse inside a greenhouse. Not a greenhouse by itself.
A greenhouse by itself, in space, is different.
The Earth is a greenhouse in space. Rather than multiple panes of glass, it has a deep atmosphere with gases that block IR.
However, a greenhouse in space with panes of glass separated by vacuum is easier to analyze. Just simple algebra. No tricky assumptions. No tricky math.
Assume that the panes of glass are completely opaque in IR. Assume that space is at 0K rather than 3K (want extra credit? use 3K for space)
How does heat flow in such a greenhouse in space?
If there are N panes of glass, the inside of the greenhouse (and the first pane) is at 300K, what temperature is each pane of glass at?
How much heat flows per square meter into space?
Start with one pane of glass. We assume above that it would be at 300K. How much heat does it radiate?
Next, analyze two panes of glass. The first pane is at 300K and is radiating exactly as much heat as the first case. The second pane will absorb that heat, and radiate half of the total to space, and half back to the first pane of glass. Remember, vacuum, so no conductive or convective heat flow. Again, how much heat flows per square meter into space?
Need a hint?
http://en.wikipedia.org/wiki/Stefan%E2%80%93Boltzmann_law" onclick="window.open(this.href);return false;