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16 September, 14:14

A vertical piston-cylinder device contains water and is being heated. During the heating process, 70 kJ of heat is transferred to the water, and heat losses from the side walls amount to 8 kJ. The piston rises as a result of evaporation, changing the volume by 0.5 m3. When the atmospheric pressure is 1 atm and the mass of the piston is 50 kg and its cross-sectional area is 0.05 m2, determine the change in the energy of the water for this process.

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  1. 16 September, 16:10
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    Energy change = 59. 5 kJ

    Explanation:

    First, we collect the dа ta:

    Let:

    Q (supplied) be the energy supplied to the water

    Q (lost) be energy lost to surroundings

    Q (piston) be the energy possessed by the piston as it moves up

    v = volume flow (m³/s) ]

    V = velocity of the gas (m/s)

    mass = 50 kg

    Second, calculate the work done by the piston:

    to find velocity, we use this formula:

    v = A * V

    Therefore, V = 0.5 (m³/s) / 0.005 m²

    = 10 m/s

    it means the water is evaporating at a rate of 10 m/s

    the evaporating water transfers energy to the piston, kinetic energy Ek

    Ek = 1/2 mV²

    = 0.5 (50) (10) ²

    = 2 500 J

    = 2.5 kJ

    The net energy, ΔQ is given by:

    ΔQ (net) = Q (supplied) - Q (piston) - Q (lost)

    = 70 - 2.5 - 8

    = 59.5 kJ Ans
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