The efficiency that goes with the larger volume is from the reduced exterior surface area per unit volume.
E.g., assuming a simple model with walls of zero thickness, 10 cube shaped freezers with 1 cu. ft. of total interior volume would have 60 sq. ft. of exterior surface area, a 6:1 ratio, but a cube shaped freezer with 10 cu. ft. of interior space would only have 28 sq. ft of exterior surface area, a 2.8:1 ratio.
In other words, the ten smaller freezers providing the same volume have more than twice the exposed surface area, and twice the thermal leakage.
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