If you imagine a giant freezer filled with ice it will eventually melt. This takes energy, a larger freezer will take more, an empty one will take less than a full one.
Counteracting the heat transferred through the freezer walls from the outside in will require an amount of energy proportional to the mass in the freezer and the leakage from the outside.
It takes energy to maintain that imbalance, the bigger the imbalance the faster the heat will transfer.
If the stuff in the freezer is light (air) then it will take less energy to keep it cold than if the stuff in the freezer is heavy (ice), because there simply is less leakage from air (a thermal insulator) to the walls than there is from ice (a pretty good thermal conductor).
Thermal conductivity is not very tightly coupled to mass but it usually is a good indicator, in the case of ice vs air it works pretty good.
So, it takes more energy to keep a freezer full of ice at a low temperature than a freezer full of air...
For an encore, which is heavier: A cubic meter of dry air vs a cubic meter of humid air ?
I believe the inefficiency of an empty freezer/fridge actually comes from it being inefficient to cycle the compressor. The low heat capacity of air leads to the compressor cycling often.
If you imagine a giant freezer filled with ice it will eventually melt. This takes energy, a larger freezer will take more, an empty one will take less than a full one.
Counteracting the heat transferred through the freezer walls from the outside in will require an amount of energy proportional to the mass in the freezer and the leakage from the outside.
It takes energy to maintain that imbalance, the bigger the imbalance the faster the heat will transfer.
If the stuff in the freezer is light (air) then it will take less energy to keep it cold than if the stuff in the freezer is heavy (ice), because there simply is less leakage from air (a thermal insulator) to the walls than there is from ice (a pretty good thermal conductor).
Thermal conductivity is not very tightly coupled to mass but it usually is a good indicator, in the case of ice vs air it works pretty good.
So, it takes more energy to keep a freezer full of ice at a low temperature than a freezer full of air...
For an encore, which is heavier: A cubic meter of dry air vs a cubic meter of humid air ?