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I remember it being quite hot in the last green house I went inside, and I'm imagining how hot you can make it has something to do with the difference between the temperature inside and outside, because that would determine the conduction of heat through the wall no? So if you construct a smaller green house inside of an existing larger green house, then it should get hotter in the smaller one, and if you keep nesting the green houses I'm imagining at some point you'd just melt your inner building materials and have a hot blob of plastic, which might burst into flames and bring the whole thing down... how many layers would that take?

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A greenhouse works by letting in visible light, which are absorbed by plants (and any other absorbing surfaces) inside, while blocking the IR radiation re-emitted by those plants. Suppose you had another smaller greenhouse inside the bigger one. Then what radiation passed through the bigger greenhouse shall also pass through the smaller one (whatever fraction is incident on it; to be sure there will be some reflection too). Radiation re-emitted by plants in the bigger greenhouse will not get through into the smaller greenhouse for the same reason that they cannot escape out of the bigger one. So for all intents and purposes the smaller greenhouse may be considered to be directly exposed to sunlight (albeit with enhanced reflection since the sunlight has to pass through two glass walls). Therefore if there are absorbing surfaces inside the smaller greenhouse too, then the temperature there can be no greater than that inside the bigger greenhouse. The argument may be extended to nested greenhouses, and the temperature inside any of the greenhouses would not be greater than that inside the biggest greenhouse.

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  • $\begingroup$ I hadn't thought about the outer greenhouses filtering out some of the higher frequency light. You're right, that's going to reduce the amount of light getting in. But I think your analysis neglects the increased temperature in the outer greenhouse. Some energy gets into the inner one, and that inner one is effectively better insulated, so it's less inclined to loose what little you give it. In other words you can think of that entire outer area as a thicker wall for the inner greenhouse, so it should stay warmer. $\endgroup$ – user273872 Jul 27 '17 at 9:46
  • $\begingroup$ @user273872 Increase in temperature of greenhouse is not neglected. Energy does get into inner one but that is from directly incident sunlight on the inner greenhouse. If internal energy of the outer greenhouse could make it into the inner one (through the glass wall of the inner one) then this transfer has to be from higher to lower temperature. If inner greenhouse were to have greater temperature what stops it from transferring heat to the outer greenhouse using the same mechanism? $\endgroup$ – Deep Jul 28 '17 at 4:57
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Deep's answer is correct.

I would just like to add a scheme to point out that, since there will always be some reflection at the glass/air interface, putting another greenhouse inside the first one could actually decrease the quantity of energy entering the system, thus making the whole thing colder.

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