ken wrote:

Recently, I was given one of those 'cool box' mini fridges, a 10-litre job
that can run on either mains or 12v battery, but I'm wondering if it's a
false economy in terms of power consumption.

It's grossly inefficient hence a false economy. If you must use a small
fridge like that then an Electrolux caravan/boat fridge is more
efficient. And the Electrolux is inefficient compared to a modern fridge
with a compressor.

Also the larger a fridge is, the greater its relative efficiency. Sadly
modern fridge makers still don't use enough insulation, because of the
need to make fridges seem large inside compared to the outside. However
even given current poor insulation standards, the larger a fridge is the
better the ratio of surface area (through which heat is lost) to
internal volume.

All fridges necessarily have poor design features such as the front door
which spills all the cold air onto the floor when the door is opened.
That is where a big fridge wastes energy compared to a small one - more
cold air lost when you open the door.

If you want a small fridge then a "cube" counter-top unit would be
better than the coolbox. If you want the best balance between
efficiency, cost and size simply browse the units in a store. They all
have efficiency ratings and estimates of annual electricity consumption.