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7 October, 09:24

5.46 By supplying energy at an average rate of 24,000 kJ/h, a heat pump maintains the temperature of a dwelling at 20°C. If electricity costs 8.5 cents per kW · h, determine the minimum theoretical operating cost for each day of operation if the heat pump receives energy by heat transfer from (a) the outdoor air at - 7°C. (b) the ground at 5°C.

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  1. 7 October, 11:26
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    A) $18.36

    B) $10.24

    Explanation:

    Heat supplied Q = 24000 kJ/h

    J/s = watt

    I hour = 3600 sec, therefore 24000 kJ/hr becomes 24000/3600 = 6.67 kW

    Coefficient of performance of heating for heat pump is

    COP = T2 / (T2 - T1)

    T2 (hot temperature) = 20 °C

    T1 (cold temperature) = - 7 °C

    COP = 20 / (20 - (-7)) = 20/27 = 0.741

    Also COP = Q/W

    where W is the power input to the heat pump

    0.741 = 6.67/W

    W = 9 kW

    Operating for one day is 24 hr

    Therefore heat pump uses 9 x 24 = 216 kWh

    Cost per day = ¢8.5 x 216 = ¢1836 = $18.36

    For ground at 5°C

    COP = 20 / (20-5) = 20/15 = 1.33

    1.33 = 6.67/W

    W = 5.02 kW

    For 24 hr it becomes 24 x 5.02 = 120.48 kWh

    Cost = 8.5 x 120.48 = ¢1024.08 = $10.24
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