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Which one of the following is correct relation between (COP)HP and (COP)R
- a)(COP)HP – (COP)R = 1
- b)(COP)R – (COP)HP = 1
- c)(COP)HP + (COP)R = 1
- d)(COP)HP + (COP)R = 0
Correct answer is option 'A'. Can you explain this answer?
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Which one of the following is correct relation between (COP)HP and (CO...
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
COPR=(desiredoutput)/(requiredinput)=Q(L)/W(net,in) ---(1)
This relation can also be expressed in rate form by replacing QL by QL and Wnet, in by W(net,in).
The conservation of energy principle for a cyclic device requires that
W(net,in)=QH−QL(KJ) ----(2)
Then the COP relation becomes
COPR=QL/(QH−QL)=1/(QH/QL−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_HP, defined as
COP(HP) = (Desiredoutput)/(Requiredinput)=QH/W(net,in) --(4)
This can also be expressed as,
COP(HP) = QH/(QH−QL) = 1(1−(QL/QH)) --(5)
Comparing equation 3 and 5 reveals that,
COP(HP) = COP(R) + 1
(COP)HP – (COP)R = 1
for fixed values of QL and QH. This relation implies that the coefficient of performance of a heat pump is always greater than unity since COPR is a positive quantity. government policy or in trade arrangements, and by development of irrigation, roads, and other infrastructures.
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Which one of the following is correct relation between (COP)HP and (CO...
Explanation:
To understand the correct relation between (COP)HP and (COP)R, let's first define what COP stands for.
COP stands for Coefficient of Performance, which is a measure of the efficiency of a refrigeration or heat pump system. It is defined as the ratio of the desired output to the required input.
Now let's look at the given options and analyze each one:
a) (COP)HP (COP)R = 1
This option states that the COP of a heat pump (COP)HP multiplied by the COP of a refrigeration system (COP)R is equal to 1. This relation is incorrect because the COPs of a heat pump and a refrigeration system are not inversely proportional to each other. Therefore, option 'A' is incorrect.
b) (COP)R (COP)HP = 1
This option states that the COP of a refrigeration system (COP)R multiplied by the COP of a heat pump (COP)HP is equal to 1. This relation is also incorrect for the same reason mentioned above. Therefore, option 'B' is incorrect.
c) (COP)HP (COP)R = 1
This option states that the COP of a heat pump (COP)HP multiplied by the COP of a refrigeration system (COP)R is equal to 1. This relation is incorrect for the same reason mentioned above. Therefore, option 'C' is incorrect.
d) (COP)HP (COP)R = 0
This option states that the COP of a heat pump (COP)HP multiplied by the COP of a refrigeration system (COP)R is equal to 0. This relation is also incorrect because a COP value of 0 is not physically possible. Therefore, option 'D' is incorrect.
Therefore, the correct relation between (COP)HP and (COP)R is none of the given options.
To understand the correct relation between (COP)HP and (COP)R, let's first define what COP stands for.
COP stands for Coefficient of Performance, which is a measure of the efficiency of a refrigeration or heat pump system. It is defined as the ratio of the desired output to the required input.
Now let's look at the given options and analyze each one:
a) (COP)HP (COP)R = 1
This option states that the COP of a heat pump (COP)HP multiplied by the COP of a refrigeration system (COP)R is equal to 1. This relation is incorrect because the COPs of a heat pump and a refrigeration system are not inversely proportional to each other. Therefore, option 'A' is incorrect.
b) (COP)R (COP)HP = 1
This option states that the COP of a refrigeration system (COP)R multiplied by the COP of a heat pump (COP)HP is equal to 1. This relation is also incorrect for the same reason mentioned above. Therefore, option 'B' is incorrect.
c) (COP)HP (COP)R = 1
This option states that the COP of a heat pump (COP)HP multiplied by the COP of a refrigeration system (COP)R is equal to 1. This relation is incorrect for the same reason mentioned above. Therefore, option 'C' is incorrect.
d) (COP)HP (COP)R = 0
This option states that the COP of a heat pump (COP)HP multiplied by the COP of a refrigeration system (COP)R is equal to 0. This relation is also incorrect because a COP value of 0 is not physically possible. Therefore, option 'D' is incorrect.
Therefore, the correct relation between (COP)HP and (COP)R is none of the given options.
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