Which of the following relations 1 point
is true, for coefficient of
performance (C.O.P)?
O
(C.O.P)heat pump
(C.O.P)refrigerator = 1
O
(C.O.P)heat pump
(C.O.P)refrigerator > 1
(C.O.P)heat pump
(C.O.P)refrigerator < 1
(C.O.P)heat pump - (
C.O.P)refrigerator = 0
Answers
Answer:
(C.O.P)heat pump − (C.O.P)refrigerator =1
0
The efficiencyof a refrigerator is expressed in terms of the coefficient of performance (COP), denoted by COPR. The objective of a refrigerator is to remove heat (QL) from the refrigerated space. To accomplish this objective, it requires a work input of Wnet,in. Then the COP of a refrigerator can be expressed as
COPrefrigerator=(desiredoutput)/(requiredinput)=QLW(net,in)………(1)
This relation can also be expressed in rate form by replacing QL by QL andWnet,in by Wnet,in.
The conservation of energy principle for a cyclic device requires that
W(net,in)=Q
H
−Q
L
(KJ)………(2)
Then the COP relation becomes
COPrefrigerator=
(Q
H
−Q
L
)
Q
L
=
Q
H
/Q
L
−1
1
………(3)
Notice that the value of COPR can be greater than unity.
Another device that transfers heat from a low-temperature medium to a high temperature one is the heat pump. Refrigerators and heat pumps operate on the same cycle but differ in their objectives. The objective of a heat pump, however, is to maintain a heated space at a high temperature. This is accomplished by absorbing heat from a low temperature source, such as well water or cold outside air in winter, and supplying this heat to the high-temperature medium such as a house.
The measure of performance of a heat pump is also expressed in terms of the coefficient of performance COP
H
eatPump, defined as
COPHeatPump=(Desiredoutput)/(Requiredinput)=QHW(net,in)……..(4)
This can also be expressed as,
COPHeatPump=
(Q
H
−Q
L
)
Q
H
=
(1−Q
L
/Q
H
)
1
………(5)
Comparing equation 3 and 5 reveals that,
COPHeatPump=COPrefrigerator+1
COPHeatPump−COPrefrigerator=1
for fixed values of QLand QH. This relation implies that the coefficient of performance of a heat pump is always greater than unity since COPR is a positive quantity.