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how does a heat pump prove the law of conservation of energy?

MIT 8.01 Physics I Classical Mechanics, Fall 1999
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the heat pump basically draws some heat from the surrounding and puts it into the room.
The heat pump conveys the heat from an area to another against the temperature gradient that means from a cooler region to hotter. The above picture is of Carnot engine and Th=W+Tc where Qh & Qc are the heat energies. the W is the work done by the body and that is equal to Th-Tc. from this we can say that the heat is conserved.

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