Water falls from a height of 60 m by how many degrees the temperature of the water at the bottom

Water falls from a height of 60 m by how many degrees the temperature of the water at the bottom of the waterfall is higher than at the top, if 60% of the work done when the water falls is used to heat the water.

h = 60 m.

g = 9.8 m / s2.

k = 60%.

С = 4200 J / kg * ° C.

Δt -?

The amount of heat Q, which is necessary for heating water, is expressed by the formula: Q = C * m * Δt, where C is the specific heat capacity of water, m is the mass of water, Δt is the change in water temperature.

We express the work of gravity A when water falls by the formula: A = m * g * h, where m is the mass of water, g is the acceleration of gravity, h is the height of the fall of water.

Q = k * A / 100%.

C * m * Δt = k * m * g * h / 100%.

Δt = k * m * g * h / C * m * 100% = k * g * h / C * 100%.

Δt = 60% * 9.8 m / s2 * 60 m / 4200 J / kg * ° C * 100% = 0.084 ° C.

Answer: the water temperature will increase by Δt = 0.084 ° C.