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2 January, 10:57

What is the mass of wood required to raise the temperature of 1000 kg of water from 25.0 to 100.0 °C (in kg with at least 3 sig figs.) ? The specific heat of water is 4.184 J/g°C, and the lower heating value of dry wood is 16.72 MJ/kg.

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  1. 2 January, 11:44
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    1.877 x 10⁷ kg

    Explanation:

    To solve this problem we first use the equation:

    Q = m * c * ΔT

    Where Q is the heat needed to increase the temperature of a substance, m is the mass, c is the specific heat and ΔT is the difference in temperature.

    For this problem:

    m = 1000 kg = 1000000 g J = 4.184 J/g°C ΔT = 100°C - 25°C = 75°C

    We put the data in the equation and solve for Q:

    Q = 1000000 g * 4.184 J/g°C * 75°C Q = 313.80 MJ

    So that's the energy required to heat 1000 kg of water, now we calculate the mass of wood using the equation:

    Q = m * b

    Where b is the heating value of wood and m its mass:

    313.80 MJ = m * 16.72 MJ/kg m = 1.877 x 10⁷ kg wood
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