Possibility of Using a Refrigerator to Cool the Earth
I understand that the Earth as a whole cannot be cooled directly by radiating energy away for theoretical reasons. Waste heat has low entropy; effectively raising its entropy to radiate it must cost more than it gains.
I thought about building an impossibly-high tower and pumping refrigerant, ultimately making a mechanical connection between the Earth and space where black-body radiation will be effective to do the cooling. What if we wanted to cool the Moon instead, where there is little or no air to interfere? Could we build a moderately-high platform, using mirrors underneath and insulation, and ultimately lower the average temperature of the Moon significantly? This seems similar in principle to what is actually done to cool spacecraft.
Let us suppose we have a large platform, adequately insulated from the Earth or Moon and with a movable shield for the Sun. Is there a theoretical reason we could not use a refrigerator, powered (mostly) from the platform, and use black-body radiation in space to get net cooling on the attached moon or planet?
** Possible Configurations**
Platform perhaps a kilometer above the Moon. The hot reservoir could be connected to a buried structure to increase amount of heat transferred.
Platform above a (most likely impossible) hundred-kilometer tower. Too much pumping needed near bottom of tower is an obvious problem.
Platform above Mt Everest, hot reservoir exchanges heat via a deep drilled hole. Refrigerant may or may not be pumped through the hole. Less efficient due to residual atmosphere.
If there is a possibility this could be done, even though at huge cost, I would like to consider theoretical limits on how much heat could be transferred as a function of the size of the platform and refrigeration system.