Answer to Question #305222 in Physics for brooklyn

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. $0.07\degree C$.