Question

Assume that you heat your home with a heat pump whose heat exchanger is at Tc=2∘C, and which maintains the baseboard radiators at Th=47∘C. If it would cost $1000 to heat the house for one winter with ideal electric heaters (which have a coefficient of performance of 1), how much would it cost if the actual coefficient of performance of the heat pump were 75% of that allowed by thermodynamics?

Answer 1

$187.61

Explanation:

Data provided:

Temperature of the heat exchanger, Tc = 2° C = 273 + 2 = 275 K

Temperature of the base board radiators , Th=47° C = 273 + 47 = 320 K

Cost of heating the house = $1000

Coefficient of performance of the heat pump = 75% = 0.75

Now,

Actual performance = 75% of performance of heat pump

or

Actual performance = 0.75 ×
`\frac{\textup{Th}}{\textup{Th-Tc}}`

or

Actual performance = 0.75 ×
`(320 K)/(320-275)`

or

Actual performance = 0.75 ×
`(320)/(45)`

or

Actual performance = 5.33

Therefore, the cost =
`\frac{\textup{1000}}{\textup{5.33}}`

or

cost = $187.61