A furnace delivers heat at a rate of QH1 at TH1. Instead of directly using this for

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A furnace delivers heat at a rate of Q⋅H1 at TH1. Instead of directly using this for room heating, it is used to drive a heat engine that rejects the waste heat to atmosphere at T0. The heat engine drives a heat pump that delivers Q⋅H2 at Troom using the atmosphere as the cold reservoir. Find the ratio Q⋅H2/Q⋅H1, the energetic efficiency of the system as a function of the given temperatures. Why is this a better set-up than direct room heating from the furnace?
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