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I have two perfectly isolated rooms of equal volume and I want to cool down the temperature of room one. I don't care about how hot is it in room two though.

If the hot air going to room two is at 40° C, will the fact that the hot air is pumped to another isolated room reduce how much room 1 can be cooled? Opposed to if the hot air was just pumped outside.

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Since you have assumed perfectly isolated space, therefore the ambient heat cannot enter room 1, but the heat from higher temperature room 2 will leak into room 1 via the wall hole. As long as the rate at which heat is removed from room 1 is greater than the rate at which heat is entering room 1 (from room 2) , room 1 may continue to get cooler, but you cannot keep on dumping heat to room 2 forever. At some point the rate at which heat is entering room 1 will become equal to the rate at which heat is removed from room 1 and thus the temperature will not get any lower for room 1.

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Heat rejection is heat rejection it doesn't matter where you put it as long as it is away from where you are doing the cooling. You can even run it to hot water tanks to get free energy or to heat exchangers in an air handler. Most the time it is rejected outside to the atmosphere.

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