www.bls.gov/ro1/cpibosap.pdf A window-mounted air conditioner operates reversibl

Question

www.bls.gov/ro1/cpibosap.pdf

A window-mounted air conditioner operates reversibly to maintain a house at 68 degree F during summer. With the proper working fluid inside the unit, it is possible to transfer 3.15 kW of heat to the outside air at 90 degree F. What is COP of the air conditioner, beta max? How much on a rate basis in kW is the air conditioner capable of transferring heat from the house? What is the weekly electrical bill in Massachusetts if the air conditioner runs an average of 15 hours per day? Use the average price for the Boston-Brockton area: www.bls.gov/rol/cpibosap.pdf What is the real bill if the actual COP is only 25% of the ideal COP in order to account for irreversibilities?

Explanation / Answer

Thot = 90oF = 32.22oC = 305.37 K

Tcool = 68oF = 20oC = 293.15 K

COP = Tcool/(Thot-Tcool) = 23.99 24

also

COP = Qcool/(Qhot-Qcool)

put values of COP and Qhot = 3.15 kW

Qcool = 3.024 kW

it is capable of transferring 3.024 kW from house

work input to AC = 3.15-3.024 - 0.126 kW

usage time per week = 15*7 = 105 hours

energy consumed = 105*0.126 = 13.23 kWh

price = $0.151/kWh

electricity bill per week = 0.151*13.23 = $1.99773 $2

new COP = 0.25*24 = 6

Qhot = 3.15 kW

so,

Qcool = 2.7 kW

new work input = 3.15-2.7 = 0.45 kW

energy consumed per week = 105*0.45 = 47.25 kWh

new bill = 0.151*47.25 = $7.135

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