Question

When water flows through river rapids or over a waterfall, it experiences a decrease in height and thus a decrease in gravitational potential energy. Some of this energy goes into producing noise and eroding rock, but much of the energy goes into heating the water. A river flows over a waterfall of height h = 49 m. Assume all the available gravitational energy is converted into internal energy of the water. There is no change in the kinetic energy, because the flow speed of the river is the same above and below the waterfall.
Enter an expression for the change in temperature of the water, in terms of the height of the waterfall. I the specific heat of water, c, and the acceleration due to gravity.

Answer 1

Answer:

$\Delta t = \frac{gh}{c}$

Explanation:

So if all the potential energy is converted to internal heat energy then we would have the following energy conservation equation between potential and thermal energy:

$E_p = E_h$

$mgh = mc\Delta t$

$\Delta t = \frac{gh}{c}$