A refrigerator works by absorbing heat from one region (the interior) and expell

Question

A refrigerator works by absorbing heat from one region (the interior) and expelling it into another (typically behind it, where those dusty coils are). The trick is expanding a gas in contact with the interior so that it absorbs heat and compressing it in contact with the exterior so that it gives off heat. Let's say you have an ideal refrigerator (whose engine works without friction) but a non-ideal roommate (who never works without coercion) who leaves the door ajar. Hence the distinction between "interior" and "exterior" is lost as air circulates freely between them. Can your refrigerator be good enough that it expels exactly the same amount of heat as it absorbs, thus not raising the temperature of the room? Make your argument using the first law of thermodynamics.

Explanation / Answer

Because it's given that the Refrigerator is ideal there is no heat produced from the engine's friction.All the refrigerator does is suck the heat from the interior of the refrigerator which is now open to the room and it at the back of the refrigerator which is also open to the room.So simply the ideal engine is now taking heat from the room and giving it to the room.That implies it is doing work and the energy for that work is produced from electricity.So no production of extra heat that might cause the room temperature to rise.SO there is no change of internal energy and the work done by the engine to absorb the heat is equal to the work done on the engine to expel it.Thus energy is conserved and this is the discussion using First law of thermodynamics.(Conservation of Energy)

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