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A furnace can deliver heat, QH1 at TH1, and it is proposed to use this to drive a heat engine with a rejection at Tatm instead of direct room heating. The heat engine drives a heat pump that delivers QH2 at Troom using the atmosphere as the cold reservoir. Find the ratio QH2/QH1 as a function of the temperatures. Is this a better set-up than direct room heating from the furnace?
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