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9 July, 14:45

A heat pump operates on a Carnot heat pump cycle with a COP of 8.7. It keeps a space at 24°C by consuming 2.15 kW of power. Determine the temperature of the reservoir from which the heat is absorbed and the heating load provided by the heat pump.

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  1. 9 July, 17:13
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    Heat Absorbed = 263 K, Heating Load = 18.7 KW

    Explanation:

    Since the heat is being absorbed from a reservoir the COP (Coefficient of Performance) is COP is COPhp, max which is given by

    COP (hp, max) = Th / (Th - Tl) = (24 + 273) / { (24 + 273) - Tl}

    8.7 = 297/297 - Tl

    Tl = 263 K

    263 K of heat is absorbed from the reservoir.

    For Heating Load we may use the equation relating COP, Heating Load and the input Power, which is

    COP (hp, max) = Qh/Win, where Qh is the Heating Load and Win is the Input Power

    8.7 = Qh/2.15

    Qh = 8.7 x 2.15 = 18.7 KW

    The heating load provided by the heat pump is 18.7 KW.
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