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

Answer:

the second homeowner's annual heating cost is $371.42

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 = $\frac{1}{\eta}$  = $\frac{1}{100%}$

COP of pump 1 = 1

so

$\frac{COP 1}{COP 2} = \frac{annual cost 2 }{annual cost 1}$

put here value

$\frac{1}{7} = \frac{annual cost 2 }{2600}$

annual cost = $371.42

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