The expression for the work done by an ideal heat pump is:
Win = Qh - Qc
By now you should be familiar with heat engines--devices, theoretical or actual, designed to convert heat into work. You should understand the following:
Heat engines must be cyclical; that is, they must return to their original state some time after having absorbed some heat and done some work).
Heat engines cannot convert heat into work without generating some waste heat in the process.
The second characteristic is a rigorous result even for a perfect engine and follows from thermodynamics. A perfect heat engine is reversible, another result of the laws of thermodynamics.
If a heat engine is run backward (i.e., with every input and output reversed), it becomes a heat pump (as pictured schematically (Figure 1) ). Work Win must be put into a heat pump, and it then pumps heat from a colder temperature Tc to a hotter temperature Th, that is, against the usual direction of heat flow (which explains why it is called a "heat pump").
The heat coming out the hot side Qh of a heat pump or the heat going into the cold side Qc of a refrigerator is more than the work put in; in fact it can be many times larger. For this reason, the ratio of the heat to the work in heat pumps and refrigerators is called the coefficient of performance, K. In a refrigerator, this is the ratio of heat removed from the cold side Qc to work put in:
In a heat pump the coefficient of performance is the ratio of heat exiting the hot side Qh to the work put in:
Take Qh, and Qc to be the magnitudes of the heat emitted and absorbed respectively.
Find Qh, the heat pumped out by the ideal heat pump. Express Qh in terms of Qc and Win.
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