Question

The difference between the temperature of water at the bottom and the top of a waterfall is 0.2 °C. Calculate the height of the waterfall.

[g = 10 N kg⁻¹, Specific heat capacity of water = 4200 J kg⁻¹ °C⁻¹]

Answer 1

When water falls from the top of the waterfall to the bottom, its potential energy is converted into heat energy. This heat energy raises the temperature of the water.

Let the mass of water be m kg and the height of the waterfall be h.

Rise in temperature (ΔT) = 0.2°C

Potential energy lost = mgh

Heat energy gained by water = mcΔT

Assuming all the potential energy is converted into heat energy:

mgh = mcΔT

Canceling m from both sides:

gh = cΔT

h = \[\frac{cΔT}{g}\]

h = \[\frac{4200 J kg^{-1} °C^{-1} × 0.2°C}{10 N kg^{-1}}\]

h = \[\frac{840}{10}\]

h = 84 m

Therefore, the height of the waterfall is 84 m.