A water heater is operated by solar power. If the solar collector has an area of 6.39 m2, and the intensity delivered by sunlight is 550 W/m

Question

A water heater is operated by solar power. If the solar collector has an area of 6.39 m2, and the intensity delivered by sunlight is 550 W/m2, how long does it take to increase the temperature of 1.00 m3 of water from 19.4∘C to 72.1 ∘C?

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Dâu 4 years 2021-07-29T06:12:36+00:00 1 Answers 22 views 0

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  1. Nho
    0
    2021-07-29T06:14:05+00:00
    Reply

    Answer:

    62979.09 s or 17.49 h

    Explanation:

    From the question,

    The power from the solar needed to increase the temperature of water is given as,

    P = P’A…………. Equation 1

    Where P = power, P’ = intensity of sunlight, A = Area of the solar collector.

    Given: P’ = 550 W/m², A = 6.39 m².

    Substitute into equation 1

    P = 550(6.39)

    P = 3514.5 W.

    The amount heat required to change the temperature  of water is given as,

    Q = cm(t₂-t₁)……………………… Equation 2

    Where Q = amount of heat, c = specific heat capacity of water, m = mass of water, t₂ = Final temperature of water, t₁ = initial temperature of water

    Given: c = 4200 J/kg.°C, m = Density×volume = 1000×1 = 1000 kg, t₂ = 72.1 °C, t₁ = 19.4 °C

    Substitute into equation 2

    Q = 4200(1000)(72.1-19.4)

    Q = 4200(1000)(52.7)

    Q = 221340000 J.

    But,

    P = Q/t

    Where t = time.

    Make t the subject of the equation,

    t = Q/p…………… Equation 3

    t = 221340000/3514.5

    t = 62979.09 s

    t = (62979.09/3600) hrs

    t = 17.49 h

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