Question

One homeowner uses electricity to heat a home (with 100% efficiency) at an annual cost of $2600. A second homeowner uses a heat pump with a coefficient of performance of 7 to heat an identical home. What is the second homeowner's annual heating cost?

Answer 1

the second homeowner's annual heating cost is $371.42

Step-by-step explanation:

given data

efficiency = 100 %

annual cost = $2600

coefficient of performance = 7

to find out

the second homeowner's annual heating cost

solution

we know that COP ( coefficient of performance ) is inversely proportional to electricity bill or annual heating cost

so

we can say COP for heat pump 1 is =
`(1)/(\eta)` =

COP of pump 1 = 1

so

`(COP 1)/(COP 2) = (annual cost 2 )/(annual cost 1)`

put here value

`(1)/(7) = (annual cost 2 )/(2600)`

annual cost = $371.42

so the second homeowner's annual heating cost is $371.42