Suppose we had a heat pump of COP x and we reversed it to an air conditioner.
We know that Qh = Qc + W
and
COPheat = Qh/W = (Qc + W)/W
COPcold = Qc/W
then
(W)(COPheat) = Qc + W
(W)(COPheat) - W = Qc
W(COPheat - 1) = Qc
COPheat - 1 = Qc/W = COPcold
Is my working correct and is this true for all heat pumps that can be reversed? Is COPheat always greater than COPcold by 1?
We know that Qh = Qc + W
and
COPheat = Qh/W = (Qc + W)/W
COPcold = Qc/W
then
(W)(COPheat) = Qc + W
(W)(COPheat) - W = Qc
W(COPheat - 1) = Qc
COPheat - 1 = Qc/W = COPcold
Is my working correct and is this true for all heat pumps that can be reversed? Is COPheat always greater than COPcold by 1?
-
Yes.
COPheat= Qh/(Qh-Qc)
COPcold= Qc/(Qh -Qc)
which makes it easy to see that
COPheat -COPcold = 1
COPheat= Qh/(Qh-Qc)
COPcold= Qc/(Qh -Qc)
which makes it easy to see that
COPheat -COPcold = 1