What will happen if you leave a refrigerator door open in a room?

The room will warm up.

The fridge with the door left open will run pretty much continuously to try to cool the inside. Our fridge doesn't know the door is open, so it keeps running. The thermostat inside never senses that the inside has cooled, so it tells the compressor to stay on. The room will be cooled by the fridge, but remember that the compressor dumps heat out into the room all the while that it's running. And because the fridge is not 100% efficient, there will be more heat generated than there will be cooling. The result? The room will eventually warm up.

I would disagree partially with the above answer. 1) Efficiency is a term not really used for refrigerators. The term coefficient of performance is used because it can be and usually is greater than one (or greater than 100% in other words) and equals the heat removed from the inside of the fridge divided by the work input. 2) Now, if a perfect fridge was running on a Carnot cycle (no friction in the parts and other criteria) that gives the most cooling for the least amount of work, the room would still heat up as governed by the first law of thermodynamics. W=Heat from the condenser - heat from the evaporator or W+QL=QH. In this case all the terms are considered to be positive numbers. Clearly QH>QL which means the room is getting warmer.

Probably the easiest was to understand this is that work is going into the insulated room which means the overall energy and therefore temperature is going up.