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?

Question

Scoobie

Physics

9 June, 13:15

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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Answers (1)

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Nyla Chang · Answer 1

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