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The first law of thermodynamics encompasses the concept that the total energy is constant in a closed system. This means that in a hot room, although the refrigerator will cool down the air directly in front of the refrigerator door, the temperature at the back of the refrigerator will increase correspondingly since the heat (which is a form of energy transfer) must go somewhere else in the room.
This implies that the overall temperature in the room will remain the same, even though the distribution of heat in the room may change when the refrigerator door is left open.
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