A heat pump with a COP of 3.15 is used to heat an air-tight house. When running, the heat pump consumes 5 kW of power. If the temperature in

Question

A heat pump with a COP of 3.15 is used to heat an air-tight house. When running, the heat pump consumes 5 kW of power. If the temperature in the house is 7°C when the heat pump is turned on, how long will it take for the heat pump to raise the temperature of the house to 22°C? Assume the entire mass within the house (air, furniture, etc.) is equivalent to 1500 kg of air. The constant volume specific heat of air at room temperature is cv = 0.718 kJ/kg·°C.

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Helga 5 years 2021-08-09T07:39:23+00:00 1 Answers 329 views 1

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  1. Euphemia
    0
    2021-08-09T07:40:51+00:00
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    Answer: 1026s, 17.1m

    Explanation:

    Given

    COP of heat pump = 3.15

    Mass of air, m = 1500kg

    Initial temperature, T1 = 7°C

    Final temperature, T2 = 22°C

    Power of the heat pump, W = 5kW

    The amount of heat needed to increase temperature in the house,

    Q = mcΔT

    Q = 1500 * 0.718 * (22 – 7)

    Q = 1077 * 15

    Q = 16155

    Rate at which heat is supplied to the house is

    Q’ = COP * W

    Q’ = 3.15 * 5

    Q’ = 15.75

    Time required to raise the temperature is

    Δt = Q/Q’

    Δt = 16155 / 15.75

    Δt = 1025.7 s

    Δt ~ 1026 s

    Δt ~ 17.1 min

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