No, the work done in this particular case is zero.
Work is the energy transferred to/from an object via the application of force along a displacement. In its simplest form, for constant force aligned with the direction of motion, it is the product of the force and the distance traveled. It is defined as the multiplication of magnitude of displacement d and the component of the force that is in the direction of displacement.
W = F × d
Where, W = Work
F = Force
d = displacement
Since, for the given case there is no displacement in the position of refrigerator there will be no work done.
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