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28 March, 15:23

While painting the top of an antenna 225 m in height, a worker accidentally lets a 1.00-L water bottle fall from his lunchbox. The bottle lands in some bushes at ground level and does not break. If a quantity of heat equal to the magnitude of the change in mechanical energy of the water goes into the water, what is its increase in temperature?

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  1. 28 March, 16:30
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    Increase in temperature of water = 0.53 °C

    Explanation:

    Change in mechanical energy = Potential energy

    Potential energy = mgh

    Mass, m = Mass of 1 L water = 1 kg

    Acceleration due to gravity, g = 9.81 m/s²

    Height, h = 225 m

    Potential energy = 1 x 9.81 x 225 = 2207.25 J

    Because of this 2207.25 J water gets heated.

    Heat energy, E = mcΔT

    Mass, m = Mass of 1 L water = 1 kg

    Specific heat of water, c = 4200 J/kg/C

    Energy, E = 2207.25 J

    Change in temperature, ΔT = ?

    Substituting

    2207.25 = 1 x 4200 x ΔT

    ΔT = 0.53 °C

    Increase in temperature of water = 0.53 °C
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