A heat pump used to warm a home must employ a cycle that produces a working fluid at temperatures greater than typical indoor temperature so that heat transfer to the inside can take place. Similarly, it must produce a working fluid at temperatures that are colder than the outdoor temperature so that heat transfer occurs from outside. Its hot and cold reservoir temperatures therefore cannot be too close, placing a limit on its
. (See
[link] .) What is the best coefficient of performance possible for such a heat pump, if it has a hot reservoir temperature of
and a cold reservoir temperature of
?
Strategy
A Carnot engine reversed will give the best possible performance as a heat pump. As noted above,
, so that we need to first calculate the Carnot efficiency to solve this problem.
Solution
Carnot efficiency in terms of absolute temperature is given by
:
The temperatures in kelvins are
and
, so that
Thus, from the discussion above,
or
so that
Discussion
This result means that the heat transfer by the heat pump is 5.30 times as much as the work put into it. It would cost 5.30 times as much for the same heat transfer by an electric room heater as it does for that produced by this heat pump. This is not a violation of conservation of energy. Cold ambient air provides 4.3 J per 1 J of work from the electrical outlet.
Heat transfer from the outside to the inside, along with work done to run the pump, takes place in the heat pump of the example above
. Note that the cold temperature produced by the heat pump is lower than the outside temperature, so that heat transfer into the working fluid occurs. The pump’s compressor produces a temperature greater than the indoor temperature in order for heat transfer into the house to occur.
Real heat pumps do not perform quite as well as the ideal one in the previous example; their values of
range from about 2 to 4. This range means that the heat transfer
from the heat pumps is 2 to 4 times as great as the work
put into them. Their economical feasibility is still limited, however, since
is usually supplied by electrical energy that costs more per joule than heat transfer by burning fuels like natural gas. Furthermore, the initial cost of a heat pump is greater than that of many furnaces, so that a heat pump must last longer for its cost to be recovered. Heat pumps are most likely to be economically superior where winter temperatures are mild, electricity is relatively cheap, and other fuels are relatively expensive. Also, since they can cool as well as heat a space, they have advantages where cooling in summer months is also desired. Thus some of the best locations for heat pumps are in warm summer climates with cool winters.
[link] shows a heat pump, called a “
reverse cycle” or “
split-system cooler” in some countries.
In hot weather, heat transfer occurs from air inside the room to air outside, cooling the room. In cool weather, heat transfer occurs from air outside to air inside, warming the room. This switching is achieved by reversing the direction of flow of the working fluid.
Questions & Answers
I'm interested in biological psychology and cognitive psychology
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miss
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Samuel
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