Question

Water flowing over the Wraith Falls in Yellowstone National Park drops 30 m.

 If all of the water's energy goes to heat it, what is its temperature increase?

Answer 1

Let all potential energy be converted to heat energy:

$$mgh=mc\Delta T$$

where $m$ is the mass of water, $g = 9.8m/s^2$ is the gravitational acceleration, $h=30m$ is the height, $c = 4200J/kg/\degree C$ is the specific heat capacity of water, $\Delta T$ increase in temperature. Thus, obtain:

$$\Delta T = \dfrac{gh}{c} = \dfrac{9.8m/s^2\cdot 30m}{4200J/kg/\degree C} = 0.07\degree C$$

Answer. $0.07\degree C$.