A refrigerator has a coefficient of performance of 2.25, runs on an input of 135 W of electrical power, and keeps its inside compartment at

Question

A refrigerator has a coefficient of performance of 2.25, runs on an input of 135 W of electrical power, and keeps its inside compartment at 5°C. If you put a dozen 1.0 L plastic bottles of water at 31°C into this refrigerator, how long will it take for them to be cooled down to 5°C? (Ignore any heat that leaves the plastic.). 1 calorie= 4.186J/(g⋅K)

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King 4 years 2021-08-10T21:12:58+00:00 1 Answers 148 views 0

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  1. Amity
    0
    2021-08-10T21:14:06+00:00
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    Answer:

    t = 4299.7 s = 1.19 h

    Explanation:

    First we find the cooling rate of the refrigerator:

    COP = Cooling Rate/Electric Input

    Cooling Rate = (COP)(Electric Input)

    Cooling Rate = (2.25)(135 W)

    Cooling Rate = 303.75 W

    Now, we find the energy required to be removed to cool the water in bottles:

    E = m C ΔT

    where,

    E = Energy required to be removed = ?

    m = mass of water = Vρ = (12 x 1 L)(1 kg/L) = 12 kg

    C = Specific heat of water = 4186 J/kg °C

    ΔT = Change in Temperature = 31°C – 5°C = 26°C

    Therefore,

    E = (12 kg)(4186 J/kg °C)(26 °C)

    E = 1306032 J

    Now, the time required to cool the water is given as:

    Cooling Rate = E/t

    t = E/Cooling Rate

    t = 1306032 J/303.75 W

    t = 4299.7 s = 1.19 h

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