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Notes -
The greenhouse effect is so trivially shown experimentally that it's a fairly standard activity for 6th grade kids to do.
I'm wondering where you got this rather interesting sequence of thoughts from. There are a whole bunch of various obvious errors that jump out - for example you seem to be confused as to what is actually warming, as you seem to think the Earth itself is a single system (like when you say no substance can raise the temperature of its heat source).
Actually that does not demonstrate the greenhouse effect!
From the PDF at the link: "This activity mirrors how a greenhouse works, but it’s not exactly the same as the greenhouse effect that is taking place in the Earth’s atmosphere."
The effect of the actual greenhouses is due to the glass preventing the air dissipating its heat due to convection.
The poorly-named “greenhouse effect” doesn’t actually explain how greenhouses work, it has to do with the so-called “back-radiation”.
Do you have a link to an experiment that demonstrates the actual effect in action? It should be easy to find one if the effect is real.
Whoops, I linked the wrong one. The normal idea is to mix baking powder and vinegar in a jar to create CO2 and then compare it to various controls, like here.
That experiment seems to demonstrate that a jar with a higher concentration of CO2 in it will be hotter than a jar with regular air in it, after a period of being heated by an external source (eg a heat lamp) for 5 to 10 minutes.
The “greenhouse effect” however isn’t quite this. It is rather that the surface of the Earth is said to supposed to be -18C, but then the surface of the Earth heats the atmosphere which in turn heats the surface of the Earth to a higher temperature, raising it by +33C to reach +15C. i.e. the atmosphere is externally heated (by the Earth) and it then heats its heat source (the Earth) to a greater than original temperature.
As such the experiment you cited doesn’t demonstrate this. It would need to, for example, show that the gas in the jar ends up raising the heat source (e.g. the heat lamp)'s temperature.
Specifically what's warming is not "the Earth" but the oceans and troposphere. The other layers of the atmosphere are actually cooling because of the enhanced greenhouse effect within the troposphere. So it's not the "heat source" that is being heated (most of the infrared radiation being captured by GHGs comes from radioactive decay of elements within the Earth's crust).
Earth's internal power = 44 TW. Sunlight striking the Earth = 170 PW = 170,000 TW.
(from Atomic Rockets' Boom Table)
Even accounting for albedo reflecting like 30% of that number straight back into space, Earth's internal heating is a tiny contributor to its energy balance. It's not like the giant planets, where internal heat is much more significant to overall energy balance (because radioactive heat scales with mass i.e. radius^3 and leftover heat from their formation scales with radius^5 while solar heat scales with radius^2, and also because they're further from the Sun); Neptune actually does radiate over twice as much energy as it receives from the Sun, though I don't think this is true of the others.
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