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9 October, 15:42

A windmill produces 1400 watts of electric power that is used to heat water. The efficiency is 100%. How long will it take to raise the temperature of 40 gallons of water by 50∘F?

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  1. 9 October, 17:18
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    3.5 h.

    Explanation:

    The heat required is given by;

    Q = m * Cp * dt

    where,

    m = mass

    Cp = specific heat

    dt = temperature change

    Remember,

    Given,

    Cp = 1 Btu / (°F. lb)

    1 gallon of water = 8.35 lb

    m = 40 * 8.35

    = 334 lb

    dt = 50 °F

    Q = 334 * 1 * 50

    = 16700 Btu.

    Converting Btu to kWh

    1 kWh = 3412 Btu

    1 Btu = 1/3412 kWh

    16700 Btu = 16700 * 1/3412 kWh

    = 4.89 kWh

    Power = 1400 watts

    = 1.4 kWh/h

    Therefore, time required to add 4.89 kWh at a rate of 1.4kW

    = 4.89/1.4

    = 3.5 h.
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