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Though pure silicone caulk is not recommended for food preparation surfaces, using it inside a refrigerator is okay. Latex and polyurethane caulks would also be acceptable, though silicone has the widest useful temperature range. I would not use an exterior caulk inside a refrigerator. Since both silicone and polyurethane caulks have quite strong odors, you must leave the door open and refrigerator off till they thoroughly cure... typically 24-48 hours under ideal conditions. You can use clear, white, or colored caulk... it doesn't matter.
You should let the refrigerator warm to room temperature before attempting this repair. Refrigerator temperatures slow the curing process so the caulk will not adhere as well as it could. Also your initial cleanup will not be as effective since detergents don't work as well when used on cold surfaces. And that's not all... the condensation that forms on the cold surfaces will decrease the caulk's adhesion.
Clean the area to be caulked with detergent and then wipe it with alcohol. Smooth some caulk over the cracks and allow it to cure for at least 24-48 hours before restarting the refrigerator.
Best of luck in your new home!
According to our friends at RepairClinic.com, dehumidifiers have refrigeration systems identical to refrigerators and freezers. To quote... "The compressor of a dehumidifier is like a tiny car engine with a piston (or screw in a rotary compressor) and valves. To keep all of the parts lubricated there is oil in the compressor that sits at the bottom when the compressor is turned off. If the compressor is laid on it's side the oil will drain into the refrigerant tubes. If the compressor is then switched on, it will try to compress the oil... an impossibility. The compressor will then either stall or blow out an internal valve.
While conventional wisdom says you should let a system sit upright to let the oil drain back into the bottom of the compressor, this is no guarantee that it will. Many compressors are ruined when the oil doesn't all drain back down."
So the rule is... NEVER lay an appliance down that has a refrigeration system. This includes refrigerators, freezers, dehumidifiers, window air conditioners, free standing room air conditioners, stand-alone ice makers and wine and beverage coolers.