Yes.
Think of the refrigerator as a heat engine that takes away heat from a cold reservoir and transfers it to a hot reservoir in order to keep the cold reservoir more cooler and at a much lower temperature. Now in order to move heat from the cold reservoir to the hot one, work must be done on the refrigerator which is usually the power supplied to it. The power supplied to the refrigeration unit (usually consists of a compressor) is used to move a cooling refrigerant from the cold area to the outside and thereby transferring heat from the interior to the outside keeping the interior cool.
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