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9 August, 08:18

Ice has a specific heat of 2090 J / (kg C) and water has a specific heat of 4186 J / (kg C). Water has a latent heat of fusion of 3.3x10^5 J/K and a latent heat of vaporization of 2.26x10^6 J/K. A 10 kg block of ice begins at - 60 degrees C and is slowly heated until the entire mass is boiled to steam. How much energy is required to bring the ice to steam with a temperature of 100 degrees C?

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  1. 9 August, 09:35
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    3.1 * 10⁷ J

    Explanation:

    The total heat required is the sum of the heats required in each stage.

    1) Solid: from - 60°C to 0°C.

    Q₁ = c (s) * m * ΔT = (2090 J/kg.°C) * 10 kg * (0°C - (-60°C)) = 1.3 * 10⁶ J

    where,

    c (s) : specific heat of the solid

    m: mass

    ΔT: change in the temperature

    2) Solid to liquid at 0°C

    Q₂ = Qf * m = (3.3 * 10⁵ J/kg) * 10 kg = 3.3 * 10⁶ J

    where,

    Qf: latent heat of fusion

    3) Liquid: from 0°C to 100°C

    Q₃ = c (l) * m * ΔT = (4186J/kg.°C) * 10 kg * (100°C - 0°C) = 4.2 * 10⁶ J

    where,

    c (l) : specific heat of the liquid

    4) Liquid to gas at 100 °C

    Q₄ = Qv * m = (2.26 * 10⁶ J/kg) * 10 kg = 2.26 * 10⁷ J

    where,

    Qv: latent heat of vaporization

    Total heat

    Q₁ + Q₂ + Q₃ + Q₄

    1.3 * 10⁶ J + 3.3 * 10⁶ J + 4.2 * 10⁶ J + 2.26 * 10⁷ J = 3.1 * 10⁷ J
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