The internal walls work like insulation. The open space is easier to initially heat/cool. The compartmentalized space requires less energy to maintain temp
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PV= nRT —> you would prefer to work with small volumes (thermodynamics)
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I would think the most important factor is probably the area of the outside walls. One big apartment building should be roughly equivalent to a warehouse of the same size. But if the apartments are broken up into multiple towers, that would work against them.
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Apartments are definitely more efficient than individual houses, for instance. On the other hand, one big open space will support convection currents that transport heat more efficiently that conduction through walls, so that might increase heating losses through the roof.
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Why isolate to a “physics” cost? Energy cost differences, if any, would be negligible compared to construction costs.
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Easier to make rapid temp change at the former, but to maintain temperature at the latter, due to insulating qualities of smaller units.
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If the volume and the surface area for heat conduction are the same, there should be no difference. (Imagine cooling the mall, and then putting in walls—no temperature change.)
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Also: the Buckminster Fuller "domed city" approach can use the sun to heat, even in winter, ...unless you're in Alaska, and there's no sun (and no flowing water, for a turbine!) So, maybe geothermal really makes sense in AK, I don't know if there's magma near surface...
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more walls/layering = more insulation, I would presume. ~Same reason we're supposed to wear layers when it's cold! perhaps an interesting follow-on question: given x sq ft of wall, how should it be arranged to minimize energy spent to stabilize internal climate?
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[My gut is having a single interior with a ~double wall is close to optimal] [also not quite sure how to add volume to that equation but it seems important too]
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