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A heat pump is an electrical device that heats a building
Chapter 4, Problem 14P(choose chapter or problem)
PROBLEM 14P
A heat pump is an electrical device that heats a building by pumping heat in from the cold outside. In other words, it’s the same as a refrigerator, but its purpose is to warm the hot reservoir rather than to cool the cold reservoir (even though it does both). Let us define the following standard symbols, all taken to be positive by convention:
Th = temperature inside building
Tc = temperature outside
Qh = heat pumped into building in 1 day
Qc = heat taken from outdoors in 1 day
W = electrical energy used by heat pump in 1 day
(a) Explain why the “coefficient of performance” (COP) for a heat pump should be defined as Qh/W.
(b) What relation among Qh, Qc and W is implied by energy conservation alone? Will energy conservation permit the COP to be greater than 1?
(c) Use the second law of thermodynamics to derive an upper limit on the COP, in terms of the temperatures Th and Tc alone.
(d) Explain why a heat pump is better than an electric furnace, which simply converts electrical work directly into heat. (Include some numerical estimates.)
Questions & Answers
QUESTION:
PROBLEM 14P
A heat pump is an electrical device that heats a building by pumping heat in from the cold outside. In other words, it’s the same as a refrigerator, but its purpose is to warm the hot reservoir rather than to cool the cold reservoir (even though it does both). Let us define the following standard symbols, all taken to be positive by convention:
Th = temperature inside building
Tc = temperature outside
Qh = heat pumped into building in 1 day
Qc = heat taken from outdoors in 1 day
W = electrical energy used by heat pump in 1 day
(a) Explain why the “coefficient of performance” (COP) for a heat pump should be defined as Qh/W.
(b) What relation among Qh, Qc and W is implied by energy conservation alone? Will energy conservation permit the COP to be greater than 1?
(c) Use the second law of thermodynamics to derive an upper limit on the COP, in terms of the temperatures Th and Tc alone.
(d) Explain why a heat pump is better than an electric furnace, which simply converts electrical work directly into heat. (Include some numerical estimates.)
ANSWER:
Step 1 of 4
a) The coefficient of performance is the benefit-to-cost ratio. The benefit of a heat pump is the heat pushed into the building, while the expense is the electrical energy used by the heat pump.
The coefficient of performance of the heat pump is
