You have to specify the interior temperature to be maintained.
If it is cooler than ambient then the white one wins, but if it mostly warmer than ambient then the black one wins (except it is hardly ever sunny in the UK winter and the sun is so feeble). The right colour is almost certainly some shade of grey - you could try 50 different ones...
In the days before active airconditioning observatory domes were painted the most brilliant white possible to keep the daytime solar heat load down. But at night the dome would supercool and generate local turbulence. These days they are painted a white mixed with aluminium which looks slightly grey and is close to neutral after dark.
Not having a clue and assuming the UK therefore no air con, I will go for black as it would absorb heat from the sun more so than white, and thats the extent of my knowledge on the subject.
Well, maybe not quite black, but dark. Cover it with solar cells, insulate it with six feet of polystyrene, get the FIT on the generated electricity. And don't forget the sign "harry's tomb".
(Of course, the energy required to make the polystyrene and solar cells was used elsewhere - so doesn't count.)
Not at all a simple question. It's receiving energy from the sun (and scattered from the sky) with one spectrum, but at night radiating at much longer wavelengths because it is somewhere around ambient temperature. It turns out that "ordinary" white paint (which of course has a high reflectivity in visible light) normally has quite low reflectivity (i.e. it absorbs well, but also radiates well) in the thermal infra-red. Thanks to earlier posts by Martin, I now know that astronomers do quite clever things with observatory dome paints.
Modern spacecraft mostly seem to be wrapped with foil (but I don't know whether this is to keep them warm or cool).
Having had to do the sums recently for a box running at about 50 degrees C inside a container at ambient temperature, very little of the heat loss is by conduction. About half was by radiation, the rest by natural convection.
The standard way to make a passioe house in a HOT climate is a massively insulated roof, a high mass buiolding and massive overhanging eves. The internal mass stabilises temps to daily mean and the overhanging eaves counteract direct solar radiation, except in winter when the sun is low.
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