A measure for rating the performance of refrig- eration and heat pump cycles -wh

Question

A measure for rating the performance of refrig-
eration and heat pump cycles -which are ba-
sically heat engines running in reverse -is the
coefficient of performance. Similar to thermal
efficiency, the COP is the ratio of the useful
effect to the energy input. They are defned as
COPref =QL/W, COPHP =QH/W

The difference between the refrigerator and
heat pump COP defnitions is because, for a re-
frigerator, the useful effect is the heat removed
from the cold space, whereas for the heat pump
the useful effect is the heat delivered to the hot
space. Say QH = 30 kW is needed to keep
a house at a temperature of 25 degrees C when the
outside temperature is -5 Degrees C. Determine the
minimum power required (via a reversible heat
pump) needed to heat the house.

Explanation / Answer

COP heating = Qhot/(Work) <= Th/(Th-Tc)
Th = 25+273 = 298K
Tc = -5+273 = 268K
For minimum work, COP = Th/Th-Tc = 298/30 = 9.933
work = 30*10^3 / 9.933 = 3020.134 W

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