A swimming pool, 10.0 m by 4.0 m, is filled with water to a depth of 3.0 m at a temperature of 20.2°C. How much energy is required to raise

Question

A swimming pool, 10.0 m by 4.0 m, is filled with water to a depth of 3.0 m at a temperature of 20.2°C. How much energy is required to raise the temperature of the water to 25.3°C?

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Gia Bảo 3 years 2021-09-05T13:06:59+00:00 1 Answers 11 views 0

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  1. thuthao
    0
    2021-09-05T13:08:08+00:00
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    Energy required to raise the temperature of water is 2.56×10⁹ J

    Explanation:

    We first need to find the volume of water in the pool.

    10.0 m x 4.0 m x 3.0 m = 120 m³

    Next, convert this to ml

    120 m³ x 1×10⁶ = 120×10⁶ ml = 1.2×10⁸ ml

    Now, if we assume that the density of the water is 1g/ml, we can estimate the mass of the water.

    1.2×10⁸ ml x 1 g/ml = 1.2×10⁸ g

    We can now use Q = mC∆T for find the energy needed to raise the temperature of this mass of water from 20.2ºC to 28.1ºC.

    Q = heat = ?

    m = mass = 1.2×10⁸ g

    C = specific heat of water = 4.184 J/g/deg

    ∆T = change in temperature = 5.1ºC

    Solving for Q: Q = (1.2×10⁸ g)(4.184 J/g/deg)(5.1 deg) = 2.56×10⁹ J  

    Therefore, energy required to raise the temperature of water is 2.56×10⁹ J

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