Opening the fridge door to cool a room I'm well aware that the default answer to this textbook default question is "it doesn't work", but still, I believe it does.
To cool the insides of the fridge, the compressor must do work, and since the efficiency isn't 100% you are constantly warming the whole room to cool it's insides, the winning move here is simply turning the fridge off. However, let's suppose the fridge must stay on, wouldn't it be better to open the door? 
In other words: Isn't opened fridge turned on better than closed fridge turned on for the whole room temperature?
 A: No, you are making the fridge do extra work, so more energy is coming in (through the plug) as the pump continues to run since it's not reaching it's cold point.  A normal operating fridge does not manifest cold air; it just pumps all the heat out of the inside of the fridge.  
The action of pumping the heat out also has heat as a byproduct (which is waste heat from the power coming through the plug as it does work with the pump).  So you're really just generating more heat and moving heat around.
A: NO. What allows a fridge maintain cool inside is the fact that the walls of the CLOSE fridge prevents heat from outside (the room heat) flows to the inside of the fridge WHILE  the rate the fridge's compressor is drawing heat out (from the back or lower grills of the fridge). But if you open the door, the same amount of heat that flows INTO the fridge will be the same as the heat flowing out by the compressor.
If you open the door is like you taking the compressor of your air conditioning unit at home and moving it from its outside location to the center of the family room. All the heat taken from the AC unit bill be blown back into the inside of the house.
There are other details about entropy and maximum heat removal not explain here. But , for the sake of simplicity of your question statement, I offered to provide a simple none elaborated answer.
