I think the main thing you are missing to a heat pump, and its efficiency, is that you are only compressing/decompressing, but there is no phase change. It is the evaporation/condensing which allows taking or giving up heat from/to the environment.
I will now excuse myself to free the stage for more knowledgeable users...
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Ecorenovation - the bottomless piggy bank that tries to tame the energy hog.
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