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?

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